Michel Abdallaâ, Fabrice Benhamouda, Philip MacKenzie
J-PAKE is an efficient password-authenticated key exchange protocol that is included in the Open SSL library and is currently being used in practice. We present the first proof of security for this protocol in a well-known and accepted model for authenticated key-exchange, that incorporates online and offline password guessing, concurrent sessions, forward secrecy, server compromise, and loss of session keys. This proof relies on the Decision Square Diffie-Hellman assumption, as well as a strong security assumption for the non-interactive zero-knowledge (NIZK) proofs in the protocol (specifically, simulation-sound extractability). We show that the Schnorr proof-of-knowledge protocol, which was recommended for the J-PAKE protocol, satisfies this strong security assumption in a model with algebraic adversaries and random oracles, and extend the full J-PAKE proof of security to this model. Finally, we show that by modifying the recommended labels in the Schnorr protocol used in J-PAKE, we can achieve a security proof for J-PAKE with a tighter security reduction.
Ulrich RĂźhrmair, J. L. MartĂnez-Hurtado, Xiaolin Xu, Christian Kraeh ¡ 8 authors
We discuss the question of how physical statements can be proven over digital communication channels between two parties (a "prover" and a "verifier") residing in two separate local systems. Examples include: (i) "a certain object in the prover's system has temperature X°C", (ii) "two certain objects in the prover's system are positioned at distance X", or (iii) "a certain object in the prover's system has been irreversibly altered or destroyed". As illustrated by these examples, our treatment goes beyond classical security sensors in considering more general physical statements. Another distinctive aspect is the underlying security model: We neither assume secret keys in the prover's system, nor do we suppose classical sensor hardware in his system which is tamper-resistant and trusted by the verifier. Without an established name, we call this new type of security protocol a "virtual proof of reality" or simply a "virtual proof" (VP). In order to illustrate our novel concept, we give example VPs based on temperature sensitive integrated circuits, disordered optical scattering media, and quantum systems. The corresponding protocols prove the temperature, relative position, or destruction/modification of certain physical objects in the prover's system to the verifier. These objects (so-called "witness objects") are prepared by the verifier and handed over to the prover prior to the VP. Furthermore, we verify the practical validity of our method for all our optical and circuit-based VPs in detailed proof-of-concept experiments. Our work touches upon, and partly extends, several established concepts in cryptography and security, including physical unclonable functions, quantum cryptography, interactive proof systems, and, most recently, physical zero-knowledge proofs. We also discuss potential advancements of our method, for example "public virtual proofs" that function without exchanging witness objects between the verifier and the prover.
Open access
Physical Unclonable Functions (PUFs) and Hardware Security
Eli BenâSasson, Alessandro Chiesa, Matthew Green, Eran Tromer ¡ 5 authors
Non-interactive zero-knowledge proofs (NIZKs) are a powerful cryptographic tool, with numerous potential applications. However, succinct NIZKs (e.g., zk-SNARK schemes) necessitate a trusted party to generate and publish some public parameters, to be used by all provers and verifiers. This party is trusted to correctly run a probabilistic algorithm (specified by the the proof system) that outputs the public parameters, and publish them, without leaking any other information (such as the internal randomness used by the algorithm), violating either requirement may allow malicious parties to produce convincing "proofs" of false statements. This trust requirement poses a serious impediment to deploying NIZKs in many applications, because a party that is trusted by all users of the envisioned system may simply not exist. In this work, we show how public parameters for a class of NIZKs can be generated by a multi-party protocol, such that if at least one of the parties is honest, then the result is secure (in both aforementioned senses) and can be subsequently used for generating and verifying numerous proofs without any further trust. We design and implement such a protocol, tailored to efficiently support the state-of-the-art NIZK constructions with short and easy-to-verify proofs (Parno et al. IEEE S&P '13, Ben-Sasson et al. USENIX Sec '14, Danezis et al., ASIACRYPT '14). Applications of our system include generating public parameters for systems such as Zero cash (Ben-Sasson et al. IEEE S&P '13) and the scalable zero-knowledge proof system of (Ben-Sasson et al. CRYPTO '14).
Structure-preserving signature, as a special kind of digital signature, provides a way to construct modular cryptographic protocols with reasonable efficiency while retaining conceptual simplicity. This feature makes it suitable to be applied in the construction of non-interactive anonymous credential systems, which allows the user to convince a verifier of the possession of a certificate issued by the trusted authority anonymously and efficiently without interaction. In this paper, we design a secure and efficient structure-preserving signature scheme (SPSIG), and combine the scheme with GrothâSahai non-interactive zero-knowledge (GSNIZK) proof system to construct a non-interactive anonymous credential scheme. The SPSIG is based on q-ADH-SDH assumption and can resist existential forgery in the chosen message attack. The message, signature, and verification keys are group elements, which are fully compatible with the GSNIZK system. The SXDH assumption is employed to instantiate the certificate-proving process, which is considered to be the most efficient instantiation at the moment. We analyze the efficiency and formally prove the security in the standard model. The result shows that our scheme satisfies correctness, zero knowledge, and unforgeability, and achieves identity authentication in the way of anonymity. Besides, our scheme has stronger anonymity, traceability, and non-interaction, and has lower communication cost compared with the conventional schemes.
Jennan A. Phillips, Michael Holland, Debra D. Baldwin, Linda Gifford Meuleveld ¡ 8 authors
Marijuana (cannabis) is the most frequently used illicit drug of abuse in the United States and worldwide. Moreover, it is second only to alcohol as the most prevalent psychoactive substance seen in cases of driving under the influence of drugs.1,2 It is also by a wide margin, the drug most often detected in workplace drug-testing programs. The primary psychoactive substance in marijuana is delta-9-tetrahydrocannabinol, known simply as THC. Present in steadily increasing concentrations in street-purchased, smokeable plant material, the THC content in marijuana averaged 3% in the 1980s, but by 2012 it had increased to 12%.3 The US government classifies marijuana as a Schedule I drug (defined as those drugs with no currently accepted medical use and a high potential for abuse,4 and the use/possession of which is subject to prosecution). Workers covered by federal drug-testing programs are uniformly prohibited from using marijuana at any time. In addition, federal law allows employers in every state to prohibit employees from working while under the influence of marijuana and are permitted to discipline employees who violate this prohibition. Nevertheless, with public attitudes toward marijuana use changing, prohibitions for its consumption outside of federal law now vary from state to state. Although the possession and use of marijuana continue to be prohibited by federal law, numerous states and the District of Columbia currently have enacted laws regarding marijuana use that conflict with federal law and policy,5 with legislation pending in other states.6â8 This changing legal environment and the evolving scientific evidence of its effectiveness for treatment of select health conditions require an assessment of the safety of marijuana use by the American workforce. Although studies have suggested that marijuana may be used with reasonable safety in some controlled environments, there are potential workplace consequences involved in its use that warrant scrutiny and concern. The potential consequences of marijuana use in the workplace include the risk and associated cost of adverse events and the loss of productivity. These safety concerns and the changing legal scene have led the American College of Occupational and Environmental Medicine (ACOEM) and the American Association of Occupational Health Nurses (AAOHN) to develop this guidance document to assist occupational health professionals and employers in identifying and addressing impairment issues related to the use of marijuana and prevention of injuries related to impairment. This guidance summarizes current evidence regarding marijuana consumption, discusses possible side effects including temporary impairment as it relates to the workplace, reviews existing federal and state laws and legal implications for health care professionals and employers, and suggests various strategies available to employers for monitoring workers for marijuana use. It is outside the scope of this article to address any potential medical benefit of marijuana. Studies conducted to evaluate the effects of marijuana drug use by workers have demonstrated variable risk. This variability relates to study design, demographics, work type, and potential confounders (eg, general risk-taking behavior among illicit drug users). This discussion on the effects of marijuana is based on a literature search of the currently available evidence (see the Appendix). Articles were graded using the following criteria: inadequate for evidence due to low-quality research; adequate for evidence (+); or high quality (++). High-quality studies, meta-analyses, or multiple adequate studies with the same conclusion qualified as good evidence for the guidance purposes of this document. Statements referring to evidence without a qualifier reflect the results of an adequate study. Other articles are also cited when appropriate to clarify issues that may not have been addressed by studies qualifying as evidence. LEGAL IMPLICATIONS OF MARIJUANA LEGISLATION In late 2009, the US Department of Justice initiated a change in marijuana enforcement policy by issuing a memorandum encouraging federal prosecutors not to prosecute individuals who distribute marijuana for medical purposes in accordance with state law.9 Nevertheless, after voters in Colorado and Washington approved the recreational use of marijuana, the Department of Justice issued another memorandum in August 2013 that reiterated its right to contest the legality of state marijuana laws, stating that the Department âexpects states like Colorado and Washington to create strong, state-based enforcement efforts... and will defer the right to challenge their legalization laws at this time.â10 This discordance about use, regulation, and legislation places employers in the challenging position of maintaining compliance with divergent and evolving legislation, while continuing to provide a safe workplace. Americans with Disabilities Act The Occupational Health and Safety Act of 1970 contains a general duty clause that requires employers under its jurisdiction to, among other things, maintain conditions or adopt practices reasonably necessary and appropriate to protect workers on the job.11 This duty may necessitate exclusion of those who are impaired or potentially impaired because of marijuana use. As long as marijuana is illegal under federal law, employers who fire or refuse to hire employees for using marijuana are not in violation of the Americans with Disabilities Act (ADA) or any other federal antidiscrimination statute, although there are restrictions on drug testing.12 Nevertheless, some states limit employer action against workers who use marijuana according to state standards. If drug testing is done, the decision to test must be job-related and necessary for business, and conducted when there is evidence of a safety or job performance problem. Currently, the ADA does not require employers to permit marijuana use as a reasonable accommodation for an individual with a disability, even if that person is a registered medical marijuana patient. In some states, court rulings involving the use of marijuana for medical purposes have held that employers are under no obligation to accommodate medical marijuana users, regardless of whether or not its use is permitted by state law.13 The basis of the rulings has been that a person âcurrently engaging in the illegal use of drugsâ is not a âqualified individual with a disability,â and marijuana is still an illegal drug for the purposes of federal law. Nevertheless, the ultimate effects of specific state laws on this issue are yet unknown.14 Drug and Alcohol Testing Regulations The majority of private employers across the United States are not necessarily required to drug test, and many state and local governments have statutes that limit or prohibit workplace testing unless required by state or federal regulations due to the nature of the job. Guidance issued by the US Department of Transportation (DOT) for its Drug and Alcohol Testing Regulations state that marijuana use remains unacceptable for any safety-sensitive employee subject to drug testing under DOT regulations.9 This safety-sensitive category includes pilots, bus and truck drivers, locomotive engineers, subway operators, aircraft maintenance personnel, transit fire-armed security personnel, and ship captains, among others.9 Federal agencies conducting drug testing must follow standardized procedures established by the Substance Abuse and Mental Health Services Administration (SAMHSA).15 Private nonunion employers who require drug testing for applicants employees are not required to follow but to the legality of In the of testing programs must be even when federal regulations require Act The Act enacted in to safety and requires federal to that will provide as a of a federal of or a federal of any and for federal are required to good to with workplace The does not require drug but it does require that employers and distribute a policy that will be against employees who violate the and provide in the workplace about the of drug use and available and employee are not required to fire employees on the basis of the results of a drug The Act requires employees to by the of the policy and the employer if are of a drug violation in the The or must be after that a covered employee has been of a drug violation in the who work for federal may be subject to including if marijuana use is regardless of whether its use is permitted by state Federal and Transportation of Marijuana marijuana are also subject to federal and local of marijuana if state with the even if are states that medical marijuana. As the US Transportation Safety Administration federal on marijuana on an is illegal and to federal drug Federal agencies in some also many states and the District of Columbia enacted medical marijuana laws or its use, an legal right to fire or refuse to hire an for an drug test due to medical marijuana use on whether the state of has a medical marijuana law that includes employee states that have medical marijuana not provide for employee although there are as and an and against action at work for registered when a marijuana on or to work and have an employer from against a registered qualifying employee who has a drug test for marijuana or if the employee or impaired by marijuana at the work or if to an employee who a drug test violate a or benefit under federal States that to have laws recreational marijuana not provide for employee Colorado allows employers to prohibit the use of marijuana at Nevertheless, another state law, the statute, employers in this state from employees for engaging in while and legal have with to employees who have been for testing for marijuana, and as of this issue is under by the Colorado state and federal laws legal and in the workplace will Although state laws laws marijuana require employers to permit drug use in the workplace to employees who to work this employers may to that employees to work in an state and not or while and state laws in to permitted use in the workplace, and drug testing be employer with legal to that with any state or local laws and their testing programs to legal of the legal the medical implications of marijuana use for the must be In to the risk of due to employers must also the that in and may as available to In that of workers were in some of illicit drug use the the legalization of marijuana in states, this that of to work after marijuana majority the drug Although this may not reflect the behavior of the US working as a the the for workplace addressing workers who use and marijuana is THC because of across the THC after due to of the substance to the and as as The and associated impairment as of the of when are and THC is the of the THC is by the the psychoactive which in the after the THC and The or and for or even in This is the in workplace drug-testing programs. vary with the and the of marijuana, impairment after and in about and to after studies that impairment in test studies on the of impairment after use were conducted when marijuana had a THC the of study results to is as the of may be studies have demonstrated impairment to to on specific performance but studies are and the studies this used In addition, no of performance impairment associated with every and accepted in the workplace the the use of As impairment studies were also conducted when had a is available It is that impairment may be and with marijuana. The majority of studies of impairment related to driving and to a state to after marijuana among recreational behavior from use and is good evidence that marijuana impairment from THC users, but the to which impairment is in safety-sensitive is This be to the who has at a alcohol a yet is still or are the to and effects are with concentrations and of among marijuana to the nature of or to is also by not for a because the of the and from the the has been The after after is some evidence that with impairment to a of performance study of demonstrated impairment of driving to after of This impairment not with In addition, although a state may have regulations regarding the of THC to be used in it is not this is may have the in The from marijuana use with THC of and of with the effects are of and increased and a of and effects include of impaired and in and and These effects are by of a in and increased and study that and to were the most related to marijuana of are used by drug law enforcement who of Marijuana Although studies that impairment in the workplace due to marijuana are now to numerous studies using driving and impairment of the necessary for safe of a by use have been of the regarding impairment and risk in the workplace due to alcohol has been from studies of driving impairment and same of studies be used to impairment in the workplace from studies have been to the of driving impairment in to the of THC in or studies of risk associated with use to impairment in because some of studies used the of the as evidence of drug use. In addition, many potentially had for THC after and even from the of the and of THC from the studies and of studies, including driving and that and related to driving performance were impaired in a with increasing THC is good evidence from a and the following and driving studies that marijuana of and and to on from studies of risk have that when marijuana in were to be at and there a with THC concentrations to be for the Studies have that while using individuals impaired performance in driving and In the driving studies, the were in to and maintain and and on for a study of from in an increased for a from for THC to for THC or studies have that with a test were to to be involved in a without In a study of effects of marijuana, that any of the psychoactive associated with the impairment of the to with a of THC and concentrations study that under THC a of to established and of THC to were of study that impaired on THC drivers, and those with of THC were at increased risk of In there is good evidence from a of studies and a that of an of to for and to for marijuana impairment to a of on a of of THC be used as with other medical of impairment from marijuana. The also be and it may provide regarding impairment. Nevertheless, as the of THC and to use as a for impairment is not known at this the the for to impairment and to this impairment to may to use the of THC and to impairment because is to THC. are to impairment by some performance and effects at most of a for allows some for of the in effects to a of or using the seen in the impairment studies the current of alcohol impairment for safety-sensitive workers under federal testing laws this may be used to an of the of this THC and may not impairment in an individual This be only when a medical for impairment has been in with of the which led to the for the basis of the the is a of THC of to impairment. The that there are states using for driving under the influence of drugs (eg, Colorado and Washington use in to in of THC and as a for driving under the influence when by behavior states address marijuana and of have for any of It is the of the that a of be used to a safe workplace Marijuana a is of impaired by marijuana use, and of impairment must be in and of that for testing be This is the same policy as that used for in drug-testing programs. impairment is employees are for alcohol and drug drug testing for marijuana by testing the which be for after use, and has no with impairment. This testing is for programs and in marijuana use is illegal or prohibited by the Nevertheless, a drug test use is not evidence of impairment. Although this use is still prohibited under this not be reasonable or in employer drug testing programs in states with recreational use. to prohibit the use of marijuana in states it is legal with regarding this of THC in the of recreational after legal use of marijuana be to in the of a of results impairment or violation of a law in states marijuana is this in states marijuana use, workplace drug testing of impaired employees be Although alcohol be used to alcohol psychoactive THC be detected in the same and currently requires a It is suggested that the employee of impaired be as the suggests that employers include an of the impaired employee at an occupational in The include a to the or of a alcohol test, and a drug for marijuana, a test for the and evaluate potential impairment from use. The employee be on results established If THC THC for employers who to evaluate psychoactive are a of the employee is impaired by use. THC be in of impairment by a demonstrated on a medical also be Testing of that may in the as a to whether testing is MARIJUANA LEGAL who to be impaired in the workplace be according to employer of THC not with impairment. include an of impairment. The of on impairment includes for the of of and other who to or are required to use of medical recreational marijuana with state law must risk of impairment from marijuana use, for those employees in safety-sensitive The following be medical and other occupational health professionals be with legal in about policy or individual use of marijuana. regarding testing for and possible impairment be and to are for and employees the implications of the results for their based on the policy and for marijuana and other drug use. statutes provide when a is under the influence of alcohol or illegal of use impairment may be necessary in The occupational health for a medical of for duty and on the for which use of medical marijuana be It is for medical to of state for medical the of use to working used (eg, plant material, the for any the job and of use. The occupational health work with to risk based on the safety-sensitive nature of the job. of workplace safety in the of the medical for which marijuana has been may also be who are in federal workplace drug testing programs are prohibited from on state law as a for marijuana or other Schedule I substance Nevertheless, employers be that the and Drug Administration is a Schedule is not a prohibited substance although it may a safety in some Other may be in the are available in other OF Occupational Safety and Health Administration employers have a federal to address impaired workers who to work The for employers is to with a policy regarding use and substance policy includes for and workplace drug assessment workplace drug assessment be based on a the and the employer regarding established by the is a who is by an approved by the US Department of Health and The of the with the and of results test those a test is for the the to about the the used marijuana or a If the use or states that it in the the will about as If that drug has been the this the for of the the the test as for THC whether or not the In the of a test for marijuana in an individual who is a registered medical marijuana the this as a test to the is to the employer to the if under policy and state law. If the test is in the environment (eg, DOT the individual must be from safety-sensitive as driving a In the of an the individual must not be on safety-sensitive in the testing employers in most states may to the registered medical marijuana with a test to that of a recreational legal or The employer and the be in their regulations to for the registered medical marijuana patient. In states this has been the have for the most in of the right to maintain a workplace and medical marijuana with a marijuana test, whether or not use or Although no federal laws prohibit states have laws that limit drug testing for workers in Drug testing is also prohibited in some unless there is reasonable the is impaired and to job workplace that on the of specific individual influence or impairment a specific drug test in may provide a private employer with The of a workplace is a impairment policy that be and by the in with the health and and occupational health also programs to employee including those related to substance without an are also required to follow federal regarding substance The and and DOT regulations drug and alcohol impairment in the workplace at the federal The have a to that and programs are with regulations from Drug and alcohol or impairment programs are not required for every Nevertheless, some state and federal regulations require programs in specific that employee drug testing and in some health care and also require workplace drug regulations drug-testing In the private state laws drug testing for employees or after hire may from nonunion federal regulations require their use, workplace on drug testing must be in and even if of the policy must be laws for medical and recreational marijuana use employers legal when the workplace policy specific to medical marijuana use by employees the work and the job. Although every policy must be to regulations to the specific workplace, employers use the following content as a for workplace for medical marijuana and other of the employees covered by the when the policy prohibited whether employees are required to their of medical marijuana or whether the policy and of the search and of job for work for drug testing with from the consequences for policy whether are after an related to substance to protect employee for policy to policy to occupational health when and and their and is available to substance use or with legal when regarding employee use of medical marijuana. employees in safety-sensitive have been held to regarding use. a reasonable basis for employers to or medical marijuana use by states have the right to employees who were using medical marijuana in accordance with state even if were not using it at the workplace. Nevertheless, currently of simply for the medical use of marijuana. The of legal cases will be in and is is whether the ADA may have implications for medical treatment with marijuana. use of marijuana another issue as some states have laws that protect employees from when in legal outside the workplace the for a policy and medical assessment of employees who to be impaired at the workplace be are often in a position to accommodate state laws that the use of marijuana for medical purposes while federal or based on federal law. workplace safety as as compliance with state and federal legislation, employers state laws on against marijuana and that enacted are with the antidiscrimination Although it that in most states that medical marijuana use, employers continue or the use of marijuana, this may change on the basis of court The that marijuana use be for employees in safety-sensitive whether or not covered by federal drug-testing employers marijuana use at in compliance with state laws, may to simply prohibit their employees from working while using or impaired by marijuana. In some states, employers may to prohibit marijuana use by of their whether on or Nevertheless, in a policy to on when marijuana use is and to evaluate for impairment must be and to policy and is to compliance with and law. and drug-testing regarding impairment and marijuana use outside of work for use by and when referring employees of impairment for an by a qualified occupational health are based on the medical results must also be for and The that employers the following when workplace that address marijuana use in the employees covered by federal drug testing regulations (eg, DOT and other workers under federal marijuana use, on or the is employers may use drug in this in safety-sensitive must not be impaired at work by any whether it be or available may on the job marijuana use for employees in safety-sensitive even when not covered by federal drug testing Nevertheless, legal of the policy in the of state statutes is employers medical marijuana use by with a qualified occupational health is in or states that the use of recreational marijuana must a policy regarding use of marijuana. In many states, the employer may to prohibit employees from simply working while using or under the influence of marijuana or may to prohibit marijuana use on and the job. drug testing or testing at any be reasonable for the employer to and use. a limit of of THC in or as THC the of THC for employers who to evaluate psychoactive the of identifying individuals most to be Nevertheless, employers using the to the of using a to a medical on identifying impairment is is Although it that in most states that the use of medical marijuana, employers may be to continue or the use of marijuana as this may change on the basis of law. the ADA does not in because marijuana is illegal under federal law. is statutes when a is under the influence of alcohol or illegal be as a second test may be of use impairment is required for and a drug test the does not impairment. The of be used for evidence of impairment in is most in of cases because legal may be employers have and procedures for to follow regarding the for identifying potential impairment and the for referring an employee of impairment for an occupational medical include action required by based on the results of the is to compliance with is at hire and at Workers must the substance policy and for The to a workplace and existing policy will influence the a employees their and job and employees also be about to of whether the is medical marijuana, illegal or any In states marijuana use is employers provide regarding the effects of marijuana use, including regarding and effects of This may be from and state The safety of workers and the public must be to workplace and employers must that legalization of marijuana for recreational or medical use does not workplace for safe job The evolving legal on medical and recreational marijuana requires employers to with legal to policy and clarify implications of impaired This changing environment marijuana use requires employers, occupational health and legal to that workplace safety is not The the following for their and
We deal with the general problem of scattering by open arcs in two-dimensional space. We show that this problem can be solved by means of certain second-kind integral equations of the form , where and are first-kind integral operators whose composition gives rise to a generalized CalderĂłn formula of the form in a weighted, periodized Sobolev space. (Here is a continuous and continuously invertible operator and is a compact operator.) The formulation provides, for the first time, a second-kind integral equation for the open-arc scattering problem with Neumann boundary conditions. Numerical experiments show that, for both the Dirichlet and Neumann boundary conditions, our second-kind integral equations have spectra that are bounded away from zero and infinity as k â â; to the authorsâ knowledge these are the first integral equations for these problems that possess this desirable property. This situation is in stark contrast with that arising from the related classical open-surface hypersingular and single-layer operators N and S , whose composition NS maps, for example, the function Ď = 1 into a function that is not even square integrable. Our proofs rely on three main elements: algebraic manipulations enabled by the presence of integral weights; use of the classical result of continuity of the CesĂ ro operator; and explicit characterization of the point spectrum of , which, interestingly, can be decomposed into the union of a countable set and an open set, both of which are tightly clustered around . As shown in a separate contribution, the new approach can be used to construct simple, spectrally accurate numerical solvers and, when used in conjunction with Krylov-subspace iterative solvers such as the generalized minimal residual method, it gives rise to a dramatic reduction in the number of iterations compared with those required by other approaches.
Vehicular communication and networking for intelligent transportation systems are emerging concept which allows forwarding of traffic information. Road traffic crashes are one of the largest problems being faced. VANET's are self-organized networks in which vehicles communicate with each other without the presence of any priori infrastructure. The proposed scheme aims to develop applications related to vehicular safety by providing information related to road and traffic. Vehicles share the surrounding information with each other. In this paper we include the development of self-managed VANET's that does not require the deployment of infrastructure with detection and warning about abnormal traffic condition by the secure routing of vehicles. Initially the vehicle registration is done using the public key generated by RSA algorithm. Then the verification of the vehicles is done using Zero Knowledge Proof algorithm and the attackers are also detected and eliminated from the network.
A secure web browser login system has been implemented with the help of any cryptography techniques for authentication purpose. The Zero-Knowledge Proof and RSA algorithm is a concept which has been used here for providing the more authentication cryptographic systems. The Zero knowledge protocol with RSA cryptography algorithm can applied on the client side and it is working between client and server. In this built an algorithm in authentication system as like firewall or with firewall. It allows a party to prove that he/she knows something (i.e. Credential), without having to send over the value of the credential. In this implementation, it will be used to prove the password of the user without sending over the actual password. The system also allows for no password hashes to be stored on the server. The purpose of the implementation is to make confidential and authentication user login password.
The use of security certificates under the Cloud environment is the foundation to establish mutual trust between the Cloud and the user. In this paper, we propose an authentication method based on zero-knowledge proof and the mind of key escrow. With the method, authentication will not only satisfy the requirement anonymity and security but also can recover the real identity information in special circumstances with the cooperation of multiple parties. We will show that this proposed method is more suitable for promotion through analysis and comparison with an existing scheme.
Zero-knowledge proof protocol is a basic cryptographic technique. And zero-knowledge proof of double discrete logarithm has some particular properties, so it has been widely applied in many security systems. But the efficient problem of zero-knowledge proof of double discrete logarithm has not been solved to this day, since there are some special difficulties in computing this kind of knowledge proof. Hence, the time complexity and the space complexity of existing schemes are all O(k), where k is a security parameter. After redesigning the basic construction of knowledge proof, we provide a new zero-knowledge proof of double discrete logarithm, which is the first scheme with O(1) time complexity and O(1) space complexity. If introducing an off-line TTP (trusted third party), we can provide two additional zeroknowledge proof schemes of double discrete logarithm, one is even more efficient than the first one, the other one solves another open problem, which is how to efficiently prove the equality of double discrete logarithms in zero-knowledge way, and the existing techniques cannot solve this problem. We also provide the detailed security proofs of our designs and efficiency analysis, comparing with the existing schemes. The significant improvement in efficiency of this basic cryptographic technique is also helpful for many security systems.
Ashish Singal, Sheiphali A. Gandhi, Marc Pritzker, Thenappan Thenappan
The human body has two circulation systems: the systemic circulation and the pulmonary circulation. An elevation of blood pressure in either system is referred to as hypertension. PH is elevated blood pressure in the arteries of the lungs. Normal mean PA pressure is about 14 mm Hg at rest. If this pressure is greater than 25 mm Hg at rest, it is classified as PH. According to the World Health Organization, PH is classified in five groups (IâV), with each group characterized by its etiology and pathogenesis. It is important to accurately diagnose the type of PH for treatment planning and disease management. A right heart catheterization (RHC) procedure remains the gold standard that can definitively diagnose PH. Numerous other techniques are being developed that, in conjunction with RHC, can aid in diagnoses of type, severity, cause, treatment options, and functional classification of PH [1].In this study, we developed time-domain digital signal processing methodologies for assessing PA pressure waveforms. We hypothesize that a correlation between PA waveform parameters will allow determination of whether a patient suffers from PH, and potentially the type of PH. This information could prove to be an essential aid for physicians in treatment and management of patients suffering from PH.Minnesota PH repository (measure) is a prospective registry that collects information on all PH patients followed by the PH clinic at the University of Minnesota. All patients gave informed consent before enrolling in this registry. From the measure registry, we identified 66 patients with PH (mean PA pressure âĽ25 mm Hg at rest).Patients underwent RHC using a fluid-filled SwanâGanz catheter at the time of diagnosis of PH. PA tracings from the procedure were digitally acquired at a sampling rate of 240 Hz. Custom matlab programs/routines were developed to postprocess the data and analyze the PA tracings for PH and wave reflections.For every patient, typically ten individual waveforms segments were extracted from the PA waveform tracings (for 66 subjects a total of 842 individual waveforms). These individual waveforms were time sequenced from the initiation of PA pressure systolic upstroke and averaged to create an average waveform (Fig. 1). For every individual waveform and the time averaged waveform, 15 waveform parameters were calculated, which are: (1) pulmonary artery pulse pressure (mm Hg); (2) systolic pulmonary artery pressure (mm Hg); (3) diastolic pulmonary artery pressure (mm Hg); (4) mean pulmonary artery pressure (MPAP, mm Hg); (5) pulmonary artery fractional pulse pressure; (6) augmentation pressure (AP, mm Hg); (7) augmentation index (AI); (8) systolic time (TS, s); (9) diastolic time (TD, s); (10) total time (TT, s); (11) inflection time (TI, s); (12) systolic area under curve (AUCS, mm Hg s); (13) diastolic area under curve (AUCD, mm Hg s); (14) total area under curve (AUCT, mm Hg s); and (15) diastolic decay (mm Hg/s).The characteristics of wave reflections (timing, amplitude, and index) were quantified by performing pressure waveform analysis in time domain as described previously [2]. The human pulmonary pressure waveform may encounter a characteristic impedance change as it flows into the pulmonary vasculature, which manifests itself as wave reflections in the PA waveform. In normal subjects, little wave reflections are expected, however, with underlying pathology (e.g., pulmonary thromboembolism, reduced PA compliance, lung disease, and heart disease), the wave reflections can be significant. The temporal location where the wave reflection occurs is referred to as the inflection point (Fig. 2). The relative change in pressure amplitude above the inflection point is an estimate of the magnitude of the reflected pressure wave and defined as the AP. Measurement of these wave reflections in temporal and spatial domain may allow diagnoses of PH that can further aid in risk stratification and therapy planning.The first derivative of the PA pressure tracing (dP/dt) was calculated for every individual waveform and the time averaged waveform (Fig. 3). If the inflection point occurred before the peak pulse pressure (i.e., in the systolic phase), then the first local-minima or a zero-crossing of dP/dt was defined as the inflection point. If the inflection point occurred after the peak pulse pressure (i.e., in the diastolic phase), then the second local-minima or zero-crossing was defined as the inflection point. Note that one of the local-minima or zero-crossing would signify the peak pulse pressure and another one would signify the dicrotic notch.The correlation between AP, AI, and inflection time is shown in Figs. 4 and 5. AI was defined as the ratio of AP to the pulse pressure, and it could have either a positive or negative value based on the location of the inflection point relative to the peak pulse pressure. In normal subjects, since there are minimal to no wave reflections, both the AP and AI are expected to have a negative value as compared to subjects who have severe form of PH. In PH subjects, wave reflections occurring in the systolic phase make both the AP and AI positive. This correlation is illustrated in Fig. 4. Similarly, inflection times (duration to inflection point) are smaller in PH patients as illustrated in Fig. 5. These markers could be used as a screening tool to stratify patients who require further evaluation.We have developed an automated way of differentiating patients with different types of PH based on time-domain analysis of PA waveform and wave reflections. As a proof of concept, in this study, we identified a subset of patients suffering from PH to understand how PA waveform and wave reflections changes in various states of PH. The fact that we observed correlation between various pulse parameters must be viewed as one of the strengths of this study. These results coupled with further refinement of detection algorithms would allow us to make this process specific, sensitive, and automated.These findings are consistent with results from other studies suggesting that changes in pulmonary tree elasticity and pulse pressure are primarily due to an increase in MPAP in patients with PH. Wave reflections occurring in the systolic phase of the PA pressure tracing are considered abnormal and can be identified using the techniques developed in this investigation. A decrease in pulmonary elasticity or an obstructive pulmonary disease would exhibit greater wave reflections resulting in higher APs, higher AIs, and decreased inflection times as compared to normal subjects.These findings may provide novel insights into the etiology and pathophysiology of PH, which may allow further improvements in risk stratification of patients with PH and development of diagnostic tools for better delivery of care. Knowledge gained from these diagnostic tools may be used as aids in diagnoses, for treatment planning, medication optimization, and disease management. It is clear that a thorough understanding of PH will be important to the future of this evolving era of diagnostic tools.
Kai Chain, KueiâHu Chang, WenâChung Kuo, JarâFerr Yang
Summary Application of authentication protocol and key exchange scheme are major research issues in current internet, and entity identification (users or servers) accuracy and security are thereby safeguarded by various types of verification programs. Therefore, in the last 10 years, it was accompanied with productive discussions, but those discussions mainly focus on single issues, and because of the lack of security, there still existed improvements. The concept of zeroâknowledge proofs is well suited for the identification and signing within network system, which has been widely used since proposed in 1985. However, common identification methods are only fit for individual user. In an increasingly complex network environment of today, information is usually conveyed through many unidentified servers, as a result, we have to encrypt messages by adopting different kinds of session keys. As for the chaotic maps technology, it also serves as a new encryption technology, widely adopted in communication protocols and key agreements over the years. As a consequence, in this study, we are going to propose an authentication protocol with key exchange function by taking advantage of characters of zeroâknowledge proofs and chaotic maps, as well as adopt the BANâlogic to prove the security of this protocol. This study also compares the results of the security analysis of our protocol and related works. As a result, our proposed protocol has more security than others. Copyright Š 2015 John Wiley & Sons, Ltd.
For any pair $(X,Z)$ of correlated random variables we can think of $Z$ as a randomized function of $X$. Provided that $Z$ is short, one can make this function computationally efficient by allowing it to be only approximately correct. In folklore this problem is known as \emph{simulating auxiliary inputs}. This idea of simulating auxiliary information turns out to be a powerful tool in computer science, finding applications in complexity theory, cryptography, pseudorandomness and zero-knowledge. In this paper we revisit this problem, achieving the following results: \begin{enumerate}[(a)] We discuss and compare efficiency of known results, finding the flaw in the best known bound claimed in the TCC'14 paper "How to Fake Auxiliary Inputs". We present a novel boosting algorithm for constructing the simulator. Our technique essentially fixes the flaw. This boosting proof is of independent interest, as it shows how to handle "negative mass" issues when constructing probability measures in descent algorithms. Our bounds are much better than bounds known so far. To make the simulator $(s,Îľ)$-indistinguishable we need the complexity $O\left(s\cdot 2^{5\ell}Îľ^{-2}\right)$ in time/circuit size, which is better by a factor $Îľ^{-2}$ compared to previous bounds. In particular, with our technique we (finally) get meaningful provable security for the EUROCRYPT'09 leakage-resilient stream cipher instantiated with a standard 256-bit block cipher, like $\mathsf{AES256}$.
The practice of orthopaedic surgery has become highly specialized. According to a recent American Academy of Orthopaedic Surgeons (AAOS) census, 77% of members reported a specialty interest [1]. Along those lines, Morrell et al. [12] estimate that at least 90% of graduating orthopaedic surgery residents pursue fellowship training. It would be no surprise, therefore, to discover that the AAOS Board of Specialty Societies boasts 22 member groups. To some, greater specialization is no doubt a step in the wrong direction. Back in the days of the giants, this nostalgic argument goes, a ârealâ surgeon would be happy to fix a femur fracture and straighten a spine on the same day. (In fact, the true giants would fix a fracture and straighten a spine only after removing an appendix and delivering a baby or two.) Today's orthopaedic surgeons, by contrast, are feckless and feeble. A more reasonable view acknowledges the benefits of specialization. For one, surgeons who do only one procedure are apt to become quite efficient [6]. Better still, the high-volume specialist-surgeon will produce superior results [7]. Specialization similarly enhances career prospects: The Top Doctor lists are filled almost exclusively with specialists and academic advancement criteria emphasize depth over breadth. Of course, a reasonable view would also acknowledge the costs of specialization. Specialistsâlike all of usâsee the world through the prism of experience. As such, they can easily overlook or discount important findings. This so-called âavailability biasâ would spur a neurosurgeon to attribute index finger pain to a cervical radiculopathy and a hand surgeon to blame the median nerveâwith both of them relatively blinded to the possibility that a metabolic abnormality, say, is the true cause. Yet even if specialists could break free of their cognitive constraints, patients may still pay as they shuffle from expert to expert in search of total care. This cost comprises not only hassle and dollars, but a potential for poor communication and other forms of uncoordinated care [3]. There is, furthermore, a problem of distribution. Specialists quite rationally tend to congregate in larger urban areas: Places with enough patients to keep them busy in their own narrow practice enclaves. Hence, specialization can lead to a manpower shortage (and impeded access to care) in small towns and a glut (with overtreatment) in big cities. In addition, too much specialization within a surgeon's practice exposes that surgeon to the risk his or her practice might implode if the demand for a particular service disappears. Simply put: The surgeon who knows how to do only knee replacements will be out of work if a medical cure for arthritis is discovered. Of course, it is highly unlikely that a medical cure for arthritis will be discovered so quickly that the surgeon will be unable to adapt, but the risk is not zero. (Those who place the risk at zero have never witnessed a cardiothoracic surgeon crying about the discovery of coronary stents). Maintaining mastery over many surgical procedures is an excellent hedge against the possibility that one of these procedures falls out of favor. But there is an even more pressing reason for surgeons to resist too much specialization: It just might be bad for the soul. In his classic book The Wealth of Nations, Adam Smith noted that the division of labor leads to âuniversal opulence.â Smith clearly recognized the benefits specialization and is rightly considered one of its greatest champions. But Smith went on to assert âThe man whose whole life is spent in performing a few simple operations ⌠generally becomes as stupid and ignorant as it is possible for a human creature to become.â According to Smith, repeatedly doing the same operation (a word we may want to take in its modern medical sense) creates a âtorpor of [the] mind.â This torpor, Smith claims, is a state in which the specialist becomes unable to conceive of any âgenerous, noble, or tender sentiment, and consequently of forming any just judgment concerning many even of the ordinary duties of private life.â In modern parlance: Burnout. So what to do? Because specialization imposes costs on patients, it may be reasonable to insist on professional rules to limit it somewhat. (The broad ABOS recertification examination can be considered such a step, as are normative standards that ask orthopaedic surgeons to provide general emergency room coverage in their community). In addition, our leaders should educate young orthopaedic surgeons about specialization's hidden costs. This knowledge will let enlightened self-interestâwhat Smith called the âinvisible handââmotivate the correct course of action. Pierre J. Hoffmeyer MD Professor of Orthopaedic Surgery University Hospital of Geneva Hyperspecialization in orthopaedic surgery is here to stay. This is especially true in economically favored regions benefitting from high levels of resources [4]. Hyperspecialization has political support because of increasing public pressure stemming from the needs and demands of an aging and active population [2]. In this setting of economic affluence, orthopaedic surgeons have been able to narrow their surgical practice to one joint, to one disease process, or even to one technique. The corollary is that as the number of hyperspecialized experts increases, the quality of the holistic approach towards musculoskeletal care diminishes. How this situation of increasing hyperspecialization will progress will depend on many issues touching on education, legal environment, and economics. Young surgeons training in academic centers are educated by teachers who themselves are highly specialized. These specialists serve not only as mentors but also as role models. It is likely that trainees will follow in the footsteps of their teachers. It is doubtful that this situation is likely to change soon given the structure and organization of most major teaching institutions. The legal environment plays a major role in the molding of surgical practice. In fact, the first question facing a surgeon entangled in a medicolegal issue is how competent he or she is in performing a given procedure. A diploma attesting to the completion of a general orthopaedic education is no longer sufficient to demonstrate competence. Today, proofs of fellowship training as well as the performance of the appropriate numbers of specialized interventions have become mandatory if the surgeon is to convince opposing parties that he or she is competent to safely and effectively perform a given operation. This vision of capability embodied by the high-volume surgeon specialist will undoubtedly persevere [2, 8]. Arguably, regional economics differentiate surgical practice in affluent constituencies from less-prosperous areas. Well-equipped regions with high-quality infrastructures allowing rapid travel to centers of highly specialized expertise will have a large range of hyperspecialized surgeons providing expertise in all the domains of orthopaedics and traumatology. For the individual patient, this could mean better care, fewer complications, and improved efficiency for a given procedure [8, 11]. Conversely, hyperspecialization will entail higher costs because of the increased number of specialists working in a technology-rich environment. For less-favored regions, one surgeon will have to tackle a broad spectrum of diseases, master many techniques, and be knowledgeable in many areas. He or she will have to deal with a variety of situations, but perhaps not as efficiently or complication-free for a given procedure as the hyperspecialized surgeon. Although a generalist approach might appear to be cheaper in the short-term, patients may not always benefit from the latest, safest, and most efficient techniques [2, 11]. Since it appears hyperspecialists are here to stay, solutions must be found. The obvious answer lies in education. All practitioners of orthopaedic surgery, regardless of specialization, must possess a broad base of knowledge in the musculoskeletal field. One should not confound technical and procedural skills with overall expertise and knowledge [13]. The education of surgical trainees and fellows needs to emphasize the necessity of a broad culture in terms of diseases and trauma of the musculoskeletal system regardless of the field of hyperspecialization. This knowledge should be controlled in the recertification process, specializing on the joint, technique, or disease in which the surgeon is focused as well as on his or her general level of knowledge in the broader field of orthopaedics and traumatology. Augusto Sarmiento MD Professor and Chairman Emeritus University of Miami Dr. Bernstein identifies several important issues concerning exaggerated subspecialization in medicine and does not hide his personal concerns regarding its uncontrolled explosion. However, his attempts to propose solutions to the problem do not match his clear exposure of the unhealthy consequences of failure to arrest the progression of the trend. His suggestions along this line are rather timid and sometimes even unrealistic, such as âasking orthopaedic surgeons to provide general emergency room coverage in their community.â This suggestion falls in shallow water even if the fear of litigation could be eliminated. Dr. Bernstein further suggests, âIn addition, our leaders should educate young orthopaedic surgeons about specialization's hidden costs.â In this instance, who will educate the âleadersâ who have been the ones primarily responsible for the creation and perpetuation of the problem? I commend CORRÂŽ for publishing this thoughtful article on a subject that needs a forceful and aggressive debate. However, in his column, Dr. Bernstein underestimates the fact that greed has crept into our profession to the point where many consider it as being primarily a profitable business. Unfortunately, greed is at the very essence of the subspecialization problem. The current situation will not be assuaged with warm compresses and a few aspirins. The entire issue of education of the physician must be brought to the frontline [14-16]. This is a golden opportunity for orthopaedics, as a major and instrumental profession, to provide leadership to a force that requires active input from a variety of disciplines within the medical establishment as well as from other social and political bodies. Harmful, exaggerated fragmentation of our discipline has allowed several traditional medical and paramedical professions to assume the care of musculoskeletal conditions, long a territory exclusively managed by the orthopaedist. For example, podiatrists and chiropractors have expanded the scope of their disciplines into orthopaedic territory, and more recently, nurse practitioners and physician assistants have claimed the right to provide care for conditions they consider themselves qualified to treat. If we cannot appropriately correct the already ridiculous degree of fragmentation in orthopaedics, the overall situation will continue to deteriorate to a degree that could seriously compromise the vitality of our profession. K. Daniel Riew MD Professor, Department of Orthopaedic Surgery Washington University in St. Louis Dr. Bernstein's article is an excellent summary of the benefits and risks of overspecialization. His arguments against specialization are all valid. I would add what Konrad Lorenz said about scientists, (even more appropriate for specialists): They âare people who know more and more about less and less, until they know everything about nothingâ [5]. But as a hyperspecialist who specializes only in cervical spine, I have to respectfully disagree with the final message. In my opinion, not only is specialization inevitable, it is the correct path for science, education, and patient benefit. The history of medicine has demonstrated an inexorable path towards subspecialization. In The Evolution of Orthopaedic Surgery [9], author Leslie Klenerman tells us how orthopaedics became a specialty and seceded from general surgery: âIt is little more than a generation since orthopaedic surgery began its astounding and near exponential ascent from relative obscurity under the dominance of general surgery to itself become a major influence.â But Klenerman notes that the forces are inexorably pushing the subspecialties away from orthopaedics: âHow much longer will the interests of specialization within it, allow it to remain united before it too falls victim to the fragmentation that destroyed the supremacy of its erstwhile master?â The desire to subspecialize is driven by at least three factors. First, we live in a world of information overload. MEDLINE adds more than 5000 articles per weekday. Even if we assume that only 1% of these pertain to orthopaedics, it is nearly impossible for most busy physicians to stay current with all the articles. Would we want the next generation of surgeons to be trained by generalists who cannot keep up, or specialists, current with the literature in their area? Second, legally, general practitioners are held to the same standards as subspecialists. Therefore, if a generalist mismanages a cervical spine fracture, they will be held to the same standards as a cervical spine surgeon. Unless they are current with all aspects of cervical spine care, they are placing themselves at medicolegal risk. Third, in surgery, volume drives success, improves outcomes, shortens operative times, decreases complications, and improves efficiency. We are the cognoscenti when it comes to orthopaedic problems. Who among us would choose to have a delicate tumor removed from our dominant hand by a general orthopaedic surgeon, instead of a hyperspecialized hand surgeon who has great experience with such tumors? Knowing that the results would be highly likely to be better, would we not want the same for all of our family and friends? If we would want these for our loved ones, do our patients deserve any less? A generalist still serves a useful purpose and there are many downsides to everyone becoming a hyperspecialist. However, in my opinion, this is not an adequate reason to recommend that we remain a âjack of all trades and a master of none.â
Paul Lajoie-Mazenc, Emmanuelle Anceaume, Gilles Guette, Thomas Sirvent ¡ 5 authors
âOpen and large-scale systems do not encourage their users to behave trustworthily, which may entail non-negligible risks when interacting with unknown users, for instance when buying an item on an e-commerce platform. Reputation mech-anisms reduce these risks by associating a reputation score to each user, summarizing their past behavior. To be useful to users, reputation mechanisms need to guarantee two main properties: the non-monotonicity of reputation scores, in order to exactly reflect the users' behavior, and the privacy of their users, so that the history of their transactions is not publicly available. We propose a distributed privacy-preserving reputation mechanism handling non-monotonic ratings. Our proposition relies on two distinct distributed third parties and on cryptographic tools, including zero-knowledge proofs of knowledge, anonymous proxy signatures, and verifiable secret sharing. We show that this proposal is computationally efficient, and thus practical. To the best of our knowledge, this solution is the first one that preserves users' privacy and handles both positive and negative ratings without relying on a central authority.
The protocols for member expansion in secret sharing schemes are very useful for key management in dynamic topology networks. In order to reduce the computation complexity of the existed protocols for member expansion in secret sharing schemes, a new protocol is proposed based on the problem of elliptic curve discrete logarithm. This paper examines fifteen most recent patens that were awarded in the area of secret sharing. Unlike traditional detailed patent reviews that are focused on applying the simple secret sharing method, the proposed protocol has the following merits: 1) there is no trust center ; 2) only requesting broadcast 2 1 t + times to generate the sub-secret for the new participant and the new participant can verify the truth of the sub-secret; 3) the old participants can verify the new sub-secret by the noninteractive zero-knowledge proof protocol; 4) In the sub-secret generation stage, not only sub-secrets of old participants but also the sub-secret of new participant is secure. Compared to the existed protocols, the proposed protocol has lower computational complexity and less communications. Therefore, the proposed protocol has higher performance and is suitable for resource-constrained terminals of dynamic networks.
In this paper, we propose a novel zero knowledge grouping proof protocol for RFID Systems. Over the years, several protocols have been proposed in this area but they are either found to be vulnerable to certain attacks or do not comply with the EPC Class 1 Gen 2 (C1G2) standard because they use hash functions or other complex encryption schemes. Also, the unique design requirements of grouping proofs have not been fully addressed by many. Our protocol addresses these important security and design gaps in grouping proofs. We present a novel approach based on pseudo random squares and quadratic residuosity to realize a zero knowledge system. Tag operations are limited to functions such as modulo (MOD), exclusive-or (XOR) and 128 bit Pseudo Random Number Generators (PRNG). These can be easily implemented on passive tags and hence achieves compliance with the EPC Global standard while meeting the security requirements.
This thesis is concerned with certain properties of stochastic growth models. A stochastic growth model is a model of infection spread, through a population of individuals, that incorporates an element of randomness. The models we consider are variations on the contact process, the simplest stochastic growth model with a recurrent infection. Three main examples are considered. The first example is a version of the contact process on the complete graph that incorporates dynamic monogamous partnerships. To our knowledge, this is the first rigorous study of a stochastic spatial model of infection spread that incorporates some form of social dynamics. The second example is a non-monotonic variation on the contact process, taking place on the one-dimensional lattice, in which there is a random incubation time for the infection. Some techniques exist for studying non-monotonic particle systems, specifically models of competing populations [38] [12]. However, ours is the first rigorous study of a non-monotonic stochastic spatial model of infection spread. The third example is an additive two-stage contact process, together with a general duality theory for multi-type additive growth models. The two-stage contact process is first introduced in \cite{krone}, and several open questions are posed, most of which we have answered. There are many examples of additive growth models in the literature [26] [16] [29] [49], and most include a proof of existence of a dual process, although up to this point no general duality theory existed. In each case there are three main goals. The first is to identify a phase transition with a sharp threshold or ``critical value'' of the transmission rate, or a critical surface if there are multiple parameters. The second is to characterize either the invariant measures if the population is infinite, or to characterize the metastable behaviour and the time to extinction of the disease, if the population is finite. The final goal is to determine the asymptotic behaviour of the model, in terms of the invariant measures or the metastable states. In every model considered, we identify the phase transition. In the first and third examples we show the threshold is sharp, and in the first example we calculate the critical value as a rational function of the parameters. In the second example we cannot establish sharpness due to the lack of monotonicity. However, we show there is a phase transition within a range of transmission rates that is uniformly bounded away from zero and infinity, with respect to the incubation time. For the partnership model, we show that below the critical value, the disease dies out within C log N time for some C>0, where N is the population size. Moreover we show that above the critical value, there is a unique metastable proportion of infectious individuals that persists for at least e^{\gamma N}$ time for some $\gamma>0$. For the incubation time model, we use a block construction, with a carefully chosen good event to circumvent the lack of monotonicity, in order to show the existence of a phase transition. This technique also guarantees the existence of a non-trivial invariant measure. Due to the lack of additivity, the identification of all the invariant measures is not feasible. However, we are able to show the following is true. By rescaling time so that the average incubation period is constant, we obtain a limiting process as the incubation time tends to infinity, with a sharp phase transition and a well-defined critical value. We can then show that as the incubation time approaches infinity (or zero), the location of the phase transition in the original model converges to the critical value of the limiting process (respectively, the contact process). For the two-stage contact process, we can show that there are at most two extremal invariant measures: the trivial one, and a non-trivial upper invariant measure that appears above the critical value. This is achieved using known techniques for the contact process. We can show complete convergence, from any initial configuration, to a combination of these measures that is given by the survival probability. This, and some additional results, are in response to the questions posed by Krone in his original paper \cite{krone} on the model. We then generalize these ideas to develop a theory of additive growth models. In particular, we show that any additive growth model, having any number of types and interactions, will always have a dual process that is also an additive growth model. Under the additional technical condition that the model preserves positive correlations, we can then harness existing techniques to conclude existence of at most two extremal invariant measures, as well as complete convergence.
In this issue, we present two very different papers written in two very different styles. The first is a survey of the multiple timescales method for approximating solutions to differential equations. Multiple timescale methods are common in the literature and an integral part of many graduate programs. However, like riding a bicycle, you need some practice, experience, and insight to use it properly and have meaningful results. The second is an exposition on the Mountain Pass Lemma and related mathematical ideas underlying the existence of saddle points. Despite its name, the second article is no ordinary hike through the hills. In âProfits and Pitfalls of Timescales in Asymptotics,â author Ferdinand Verhulst presents a survey of multiple timescale methods. A colleague of mine once sarcastically pointed out that a tremendous amount of insight can be gleaned from the observation that in almost all problems, parameters are either larger than one or smaller than one, leading to an asymptotic approximation in one form or another. However, one does not have to look far to find problems where it is hard to handle the resulting asymptotic series using a simple Taylor series. Multiple timescales can resolve these problems, but the challenge remains of how to know what the multiple timescales should be without having special knowledge of the problem. Verhulst does an admirable job presenting the basic ideas behind determining timescales a priori using two basic concepts: normal forms and bifurcation theory. In the former case, one transforms the problem into a simpler expression to reveal underlying timescales. In the latter case, understanding the dynamics of a system in terms of bifurcations reveals the qualitative structure of the solution and therefore the timescales. Thus, the author puts order to a body of knowledge that can often appear to students as a disjoint collection of tricks for special problems. In âMountain Passes and Saddle Points,â author James Bisgard develops the Mountain Pass Lemma of Ambrosetti and Rabinowitz which specifies sufficient conditions for the existence of saddle points. Beginning with accessible examples of smooth functions $F: R^2 \rightarrow R$, we can think of $F$ as the height of the landscape. The central element of this manuscript is a very clear proof of the Mountain Pass Lemma, which essentially states that if there is a local minimum in a valley surrounded by a mountain range and there is a point somewhere beyond the mountain range that is lower than the local minimum, then with an additional special requirement, it can be shown that there must be a mountain pass (saddle point) somewhere. While it may seem that there should always be a mountain pass without any additional requirements, the authors present some counterexamples early in the paper to show that this is not a trivial issue. (I could not resist the urge to fire up my tablet and explore some of the sample surfaces.) The special requirement is the Palais--Smale condition, which is the seemingly peculiar condition that every sequence $x_n$ having two properties, (1) that the height above these points is bounded and (2) that the $\| \nabla F(x_n) \|$ approaches zero, must have a convergent subsequence. The author goes on to extend the Mountain Pass Lemma to domains of any finite dimension and from there to Hilbert spaces. Finally, the author uses the concepts involved in the proof to develop methods for finding saddle points. In summary, the Education section in this issue has something for everyone. The first offering focuses on methods and techniques and would be ideal for a graduate course on perturbation methods or applied mathematics. The second paper is analytic, anchored to theorems and proofs but having ample discussion. It would find a home in an undergraduate and graduate real analysis course. Both take a fresh look at classic subjects in mathematics and could be used to liven up traditional courses in most undergraduate and graduate programs.
Ecologists warn that the rapid evolution occurring as a result of high-intensity commercial fishing could have significant economic and ecological effects. So far, fishery managers do not take this rapid evolution (called fisheries-induced evolution or FIE) into consideration when determining fishery policy. I model the interactions between the genetics, population structure, and economics of the fishery in order to determine how beneficial altering the fishery managers decision framework to include fisheries induced evolution would be to fishery profit and yield. My model is based on North-East Arctic Cod, which are long lived and for which an abundance of information exists, including proof of FIE. I compare the steady state reached by a `myopic' fishery manager who sets effort and mesh size policy while ignoring evolution, to the steady state reached by a fishery manager who dynamically optimizes his strategy with the knowledge of how evolution will respond. This paper shows that accounting for evolution can increase steady state profits by 29-34%, however this benefit decreases and is eventually eliminated as the discount rate increases from zero. An important auxiliary benefit to accounting for evolution is the effect optimal management has on fishery biomass, maturation rates, and yield.