The class TFNP is the search analog of NP with the additional guarantee that any instance has a solution. TFNP has attracted extensive attention due to its natural syntactic subclasses that capture the computational complexity of important search problems from algorithmic game theory, combinatorial optimization and computational topology. Thus, one of the main research objectives in the context of TFNP is to search for efficient algorithms for its subclasses, and at the same time proving hardness results where efficient algorithms cannot exist. Currently, no problem in TFNP is known to be hard under assumptions such as NP hardness, the existence of one-way functions, or even public-key cryptography. The only known hardness results are based on less general assumptions such as the existence of collision-resistant hash functions, one-way permutations less established cryptographic primitives (e.g. program obfuscation or functional encryption). Several works explained this status by showing various barriers to proving hardness of TFNP. In particular, it has been shown that hardness of TFNP hardness cannot be based on worst-case NP hardness, unless NP=coNP. Therefore, we ask the following question: What is the weakest assumption sufficient for showing hardness in TFNP? In this work, we answer this question and show that hard-on-average TFNP problems can be based on the weak assumption that there exists a hard-on-average language in NP. In particular, this includes the assumption of the existence of one-way functions. In terms of techniques, we show an interesting interplay between problems in TFNP, derandomization techniques, and zero-knowledge proofs.
With the rise of Bitcoin, cryptographic currencies have attracted more and more attention. Subsequently, other cryptographic currencies were gradually created, such as Zcash, Moreno, Dash and so on. In cryptographic currency, privacy preserving and expansion are two key technical points. In terms of privacy preserving, more effective solutions were proposed in Zcach, Moreno, Dash and other cryptographic currencies systems, in which ring signature, zero knowledge proof and other cryptographic techniques played important roles. But these schemes mainly considered protecting the addresses of both sides of the transaction. In terms of expansion, lightning network and other projects also give solutions. But most of these projects will bring other problems. In this paper, a signature scheme based on the aggregate signature and the elliptic curve algorithm is proposed to hide the transaction value of a single sender and receiver in the transactions which contain multiple inputs and outputs. This signature scheme achieves the purpose of privacy preserving from the transaction value. Further, the correctness proof and security analysis are given in this paper. In addition to that, another signature scheme that combines aggregation signature with bilinear ring signature is proposed. This aggregate ring signature scheme gives another attempt to solve the problem of expansion in the cryptographic currency system only using cryptographic technologies. At the same time, the sender's addresses can be hidden. Similarly, we also confirmed the correctness of this signature scheme.
Gorjan Alagic, Yfke Dulek, Christian Schaffner, Florian Speelman
Fully-homomorphic encryption (FHE) enables computation on encrypted data while maintaining secrecy. Recent research has shown that such schemes exist even for quantum computation. Given the numerous applications of classical FHE (zero-knowledge proofs, secure two-party computation, obfuscation, etc.) it is reasonable to hope that quantum FHE (or QFHE) will lead to many new results in the quantum setting. However, a crucial ingredient in almost all applications of FHE is circuit verification. Classically, verification is performed by checking a transcript of the homomorphic computation. Quantumly, this strategy is impossible due to no-cloning. This leads to an important open question: can quantum computations be delegated and verified in a non-interactive manner? In this work, we answer this question in the affirmative, by constructing a scheme for QFHE with verification (vQFHE). Our scheme provides authenticated encryption, and enables arbitrary polynomial-time quantum computations without the need of interaction between client and server. Verification is almost entirely classical; for computations that start and end with classical states, it is completely classical. As a first application, we show how to construct quantum one-time programs from classical one-time programs and vQFHE.
Blockchain technology has the potential to disrupt how cryptography is done. In this work, we propose to view blockchains as an âenablerâ, much like indistinguishability obfuscation [5, 23, 46] or one-way functions, for building a variety of cryptographic systems. Our contributions in this work are as follows:
1.
A Framework for Proof-of-Stake based Blockchains: We provide an abstract framework for formally analyzing and defining useful security properties for Proof-of-Stake (POS) based blockchain protocols. Interestingly, for some of our applications, POS based protocols are more suitable. We believe our framework and assumptions would be useful in building applications on top of POS based blockchain protocols even in the future.
2.
Blockchains as an Alternative to Trusted Setup Assumptions in Cryptography: A trusted setup, such as a common reference string (CRS) has been used to realize numerous systems in cryptography. The paragon example of a primitive requiring trusted setup is a non-interactive zero-knowledge (NIZK) system. We show that already existing blockchains systems including Bitcoin, Ethereum etc. can be used as a foundation (instead of a CRS) to realize NIZK systems. The novel aspect of our work is that it allows for utilizing an already existing (and widely trusted) setup rather than proposing a new one. Our construction does not require any additional functionality from the miners over the already existing ones, nor do we need to modify the underlying blockchain protocol. If an adversary can violate the security of our NIZK, it could potentially also take over billions of dollars worth of coins in the Bitcoin, Ethereum or any such cryptocurrency!
We believe that such a âtrusted setupâ represents significant progress over using CRS published by a central trusted party. Indeed, NIZKs could further serve as a foundation for a variety of other cryptographic applications such as round efficient secure computation [33, 36].
3.
One-time programs and pay-per use programs: Goldwasser et al. [29] introduced the notion of one time program and presented a construction using tamper-proof hardware. As noted by Goldwasser et al. [29], clearly a one-time program cannot be solely software based, as software can always be copied and run again. While there have been a number of follow up works [4, 6, 30], there are indeed no known constructions of one-time programs which do not rely on self destructing tamper-proof hardware (even if one uses trusted setup or random oracles). Somewhat surprisingly, we show that it is possible to base one-time programs on POS based blockchain systems without relying on trusted hardware. Our ideas do not seem to translate over to Proof-of-Work (POW) based blockchains.
We also introduce the notion of pay-per-use programs which is simply a contract between two parties â service provider and customer. A service provider supplies a program such that if the customer transfers a specific amount of coins to the provider, it can evaluate the program on any input of its choice once, even if the provider is offline. This is naturally useful in a subscription based model where your payment is based on your usage.
Aiming for strong security assurance, recently there has been an increasing interest in formal verification of cryptographic constructions. This paper presents a mechanised formal verification of the popular Pedersen commitment protocol, proving its security properties of correctness, perfect hiding, and computational binding. To formally verify the protocol, we extended the theory of EasyCrypt, a framework which allows for reasoning in the computational model, to support the discrete logarithm and an abstraction of commitment protocols. Commitments are building blocks of many cryptographic constructions, for example, verifiable secret sharing, zero-knowledge proofs, and e-voting. Our work paves the way for the verification of those more complex constructions.
The law speaks clearly on the standards of proof, but listeners often misunderstand its words. This article tries, with some common sense, to explain how the law expects its standards to be applied, and then to show how the law thereby avoids such complications as the conjunction paradox. First, in accordance with belief function theory, the factfinder should start at zero belief. Given imperfect evidence, the factfinder will end up retaining a fair amount of uncommitted belief. As evidence comes in, though, the factfinder will form a belief in the truth of the disputed fact but also form a disbelief, or a belief in the factâs falsity. At the close of evidence, the standard of proof requires only comparing belief and disbelief. For example, the civil standard, rather than asking whether a fact more likely than not happened according to traditional probability theory, asks whether the factfinder believes the fact more than the factfinder believes that the fact did not happen. The burdened party need not push proof above 50% by dispelling the phantoms of every possibility, while the opponent need not generate a competing version of truth but can instead rely on denial to demand that the burdened party generate a belief.Second, belief and disbelief being nonadditive partial truths, the mathematical result is that one cannot combine beliefs by traditional probability theory, as by using the product rule designed for conjunction of betting odds. Instead, one must use multivalent logic, including its rule that conjoined likelihood equals the likelihood of the least likely element. Linking the elements in a chain tells a story that is as likely as its weakest link. Consequently, if each element of a claim or defense passes the standard of proof, the conjunction of elements will pass the standard of proof. The conjunction paradox thus vaporizes for factfinding, just as the law has always maintained. The law has found the way to decide in accord with our best knowledge of the facts.
Innovative idea using ring theory is raised to build a new algorithm for zero knowledge (ZK) cryptosystem. In this paper we introduce an algorithm for zero knowledge protocol based on a specific kind of rings named weak Armendariz. On the other hand, the aim of this paper focuses on the category of noncommutative algebraic structures to describe a new algebraic scheme of zero knowledge proof using weak Armendariz rings. As a result, we employ for the first time weak Armendariz rings in the science of cryptographic which regards as a new application of this class of rings. Finally, we present a novel idea combining between abstract algebra and cryptography.
Jorge Bernal BernabĂŠ, JosĂŠ L. HernĂĄndez-Ramos, Antonio SkĂĄrmeta
Security and privacy concerns are becoming an important barrier for large scale adoption and deployment of the Internet of Things. To address this issue, the identity management system defined herein provides a novel holistic and privacy-preserving solution aiming to cope with heterogeneous scenarios that requires both traditional online access control and authentication, along with claim-based approach for M2M (machine to machine) interactions required in IoT. It combines a cryptographic approach for claim-based authentication using the Idemix anonymous credential system, together with classic IdM mechanisms by relying on the FIWARE IdM (Keyrock). This symbiosis endows the IdM system with advanced features such as privacy-preserving, minimal disclosure, zero-knowledge proofs, unlikability, confidentiality, pseudonymity, strong authentication, user consent, and offline M2M transactions. The IdM system has been specially tailored for the Internet of Things bearing in mind the management of both usersâ and smart objectsâ identity. Moreover, the IdM system has been successfully implemented, deployed, and tested in the scope of SocIoTal European research project.
Itay Berman, Ron D. Rothblum, Vinod Vaikuntanathan
Š Itay Berman, Ron D. Rothblum and Vinod Vaikuntanathan. Interactive proofs of proximity (IPPs) are interactive proofs in which the verifier runs in time sub-linear in the input length. Since the verifier cannot even read the entire input, following the property testing literature, we only require that the verifier reject inputs that are far from the language (and, as usual, accept inputs that are in the language). In this work, we initiate the study of zero-knowledge proofs of proximity (ZKPP). A ZKPP convinces a sub-linear time verifier that the input is close to the language (similarly to an IPP) while simultaneously guaranteeing a natural zero-knowledge property. Specifically, the verifier learns nothing beyond (1) the fact that the input is in the language, and (2) what it could additionally infer by reading a few bits of the input. Our main focus is the setting of statistical zero-knowledge where we show that the following hold unconditionally (where N denotes the input length): Statistical ZKPPs can be sub-exponentially more efficient than property testers (or even non-interactive IPPs): We show a natural property which has a statistical ZKPP with a polylog(N) time verifier, but requires (N) queries (and hence also runtime) for every property tester. Statistical ZKPPs can be sub-exponentially less efficient than IPPs: We show a property which has an IPP with a polylog(N) time verifier, but cannot have a statistical ZKPP with even an No(1) time verifier. Statistical ZKPPs for some graph-based properties such as promise versions of expansion and bipartiteness, in the bounded degree graph model, with polylog(N) time verifiers exist. Lastly, we also consider the computational setting where we show that: Assuming the existence of one-way functions, every language computable either in (logspace uniform) NC or in SC, has a computational ZKPP with a (roughly) N time verifier. Assuming the existence of collision-resistant hash functions, every language in NP has a statistical zero-knowledge argument of proximity with a polylog(N) time verifier.
Benedikt Bßnz, Jonathan Bootle, Dan Boneh, Andrew Poelstra ¡ 6 authors
We propose Bulletproofs, a new non-interactive zero-knowledge proof protocol with very short proofs and without a trusted setup; the proof size is only logarithmic in the witness size. Bulletproofs are especially well suited for efficient range proofs on committed values: they enable proving that a committed value is in a range using only 2 log_2(n)+9 group and field elements, where n is the bit length of the range. Proof generation and verification times are linear in n. Bulletproofs greatly improve on the linear (in n) sized range proofs in existing proposals for confidential transactions in Bitcoin and other cryptocurrencies. Moreover, Bulletproofs supports aggregation of range proofs, so that a party can prove that m commitments lie in a given range by providing only an additive O(log(m)) group elements over the length of a single proof. To aggregate proofs from multiple parties, we enable the parties to generate a single proof without revealing their inputs to each other via a simple multi-party computation (MPC) protocol for constructing Bulletproofs. This MPC protocol uses either a constant number of rounds and linear communication, or a logarithmic number of rounds and logarithmic communication. We show that verification time, while asymptotically linear, is very efficient in practice. The marginal cost of batch verifying 32 aggregated range proofs is less than the cost of verifying 32 ECDSA signatures. Bulletproofs build on the techniques of Bootle et al. (EUROCRYPT 2016). Beyond range proofs, Bulletproofs provide short zero-knowledge proofs for general arithmetic circuits while only relying on the discrete logarithm assumption and without requiring a trusted setup. We discuss many applications that would benefit from Bulletproofs, primarily in the area of cryptocurrencies. The efficiency of Bulletproofs is particularly well suited for the distributed and trustless nature of blockchains. The full version of this article is available on ePrint.
Pablo Lamela Seijas, Simon Thompson, Darryl McAdams
We give an overview of the scripting languages used in existing cryptocurrencies, and in particular we review in some detail the scripting languages of Bitcoin, Nxt and Ethereum, in the context of a high-level overview of Distributed Ledger Technology and cryptocurrencies. We survey different approaches, and give an overview of critiques of existing languages. We also cover technologies that might be used to underpin extensions and innovations in scripting and contracts, including technologies for verification, such as zero knowledge proofs, proof-carrying code and static analysis, as well as approaches to making systems more efficient, e.g. Merkelized Abstract Syntax Trees.
How is God in the world? Is He, according to Christian theology, both transcendent and immanent? In other words, is He distant and separate from the world and humanity while at the same time working within both? Or, did He create the universe and then remove Himself from it? Are we able to comprehend certain aspects of God through our understanding of the order and beauty of the universe? Or, do humans seek a God who is no longer interested? Many science fiction writers have asked and responded to such questions including Ted Chiang in his collection, Stories of Your Life and Others. Several of his stories deal directly with these questions and we can read them as a critique of faith, religion, belief, and the nature of God. Chiang questions whether God has a role in our lives, what that role may look like, and the ability of religion to provide meaning. Furthermore, these stories are apocalyptic in nature, especially if we think of apocalypse as revelation, the Greek definition. Frederick Krueziger further defines apocalypse as âan unfolding; hence a revelation through unfoldingâ (5). Such unfolding always takes place within a story; thus, we must consider the inherent connection between apocalypse and story. As Krueziger says, âApocalypse as story first of all reveals story as that which shapes our search for meaningâ (5). The revelation, the unfolding, therefore is the story itself as well as what the story means. We can read Chiang's stories as apocalyptic because they reveal our disillusionment with our world and our inability to find meaning in religion alone. For Krueziger, science fiction as apocalypse illustrates our disillusionment with âthe failure of the promise of technology and science to deliver the world from poverty, ignorance, disease, war, famine, plague, and death. &â(6). Although I agree that many science fiction works address these particular disillusionments, Chiang's stories, I would argue, have a certain similarity to the apocalyptic writings of John. People disappointed at the failure of the Second Coming to occur during their lifetime lost faith in the promise of God. John's writings deal with crises of both history and faith. Thus, Chiang's stories are similar to John's writings in that they deal with the disillusionment and failure of faith and religion. Before discussing the stories, it may behoove us to consider the definitions of faith, religion, and belief. Although we may feel we know what these words mean, and may even think they are synonymous, the distinctions among them are of importance to this essay. As John Bishop states, â& at its most general, âfaithâ means the same as âtrustâ.â Greg Popcak defines faith more narrowly, asserting that faith âis merely the innate drive to search for meaning, purpose and significance.â Religion, at its most basic, can be defined as a specific form of human activity as a means of achieving spiritual or material improvement. However, this form of human activity is often cultural because it is a system of behaviors and praxes uniting a community. Belief, according to Eric Schwitzgebel, refers âto the attitude we have, roughly, whenever we take something to be the case or regard it as true.â Interestingly, many define faith as belief without proof. Although many use these three terms interchangeably, Chiang employs them in specific ways in his stories. In the âTower of Babylon,â Chiang uses the biblical story of the tower of Babel as his premise. His focus is not on God's creation of various languages as punishment for defying Him, but on humanity's desire âto see what lay beyond [the earth's] borders, all the rest of Yahweh's creationâ (5-6). This story juxtaposes science with faith and religion as the Babylonians are building the tower so they can break into the vault of heaven. They desire knowledge about their world, but also desire knowledge about God, believing that the tower will enable them âto ascend to see the works of Yahwehâ while allowing Yahweh to âdescend to see the works of manâ (6). In this story, Ted Chiang combines the above definitions of religion as a âsearch for meaning, purpose and significanceâ as well as the desire for material and spiritual improvement (Popcak). The envisaged structure is simple: Earth was seen as being situated in the middle of a great volume of water, with water both above and below Earth. A great dome was thought to be set above Earth (like an inverted glass bowl), maintaining the water above Earth in its place. Earth was pictured as resting on foundations that go down into the deep. These foundations secured the stability of the land as something that is not floating on the water and so could not be tossed about by wind and wave. The waters surrounding Earth were thought to have been gathered together in their place. The stars, sun, moon, and planets moved in their allotted paths across the great dome above Earth, with their movements defining the months, seasons, and year. (60) Chiang brilliantly describes the geocentric worldview through the protagonist of the story, Hillalum, who is an Elamite miner contracted to dig into the vault of heaven. He, along with other Elamite miners, spends four months climbing to the top of the tower. Along the way, he discovers how his world and his universe functions. He comes to know that night is âthe shadow of the earth itself, cast against the skyâ (âTowerâ 11). He and the others reach a point on the tower where they see âstorms from above and from belowâ and where people â[harvest] crops from the airâ (14). After climbing a number of weeks, the miners find themselves âat precisely the same level as the moon when it passed; they had reached the height of the first of the celestial bodiesâ (14). When they reach the level of the sun, the intense heat forces them to travel at night. Passing this level, Hillalum finds that the sun shines âupward, which [seems] unnatural to the utmostâ (15, emphasis in original). When they are level with the stars, the miners discover that a star has hit the tower, leaving âa knotted mass of black heaven-metal, as large as a man could wrap his arms aroundâ (16). Finally, they reach the vault of heaven itself, âa solid carapace enclosing all the sky (16) that â[seems] to be made of fine-grained white granite, unmarred and utterly featurelessâ (18-19). Hillalum's travels to the top of the tower allows him to discover both the meaning and significance of the physical world, not through religion or faith, but through his own observation. Since, in the geocentric view, the Earth is âsituated in the middle of a great volume of water,â the Babylonians and the Elamite miners fear that breaking into the vault of heaven will release another Great Flood (Robishaw 60). They believe Yahweh caused the Great Flood, or the âDeluge,â by releasing âthe waters of the Abyss & from the springs of the earth, and & [from] the sluice gates in the vaultâ (19). Concerned that they may hit one of these reservoirs, the Babylonians enlist Egyptian masons who design a system using large blocks of granite that will âslide down until [they] rest in the recess of the floorâ and will completely block any opening (22). Using this design, they are able to safeguard the world from another flood when their worst fear is realized and the miners accidently dig into a reservoir. Hillalum and two others are trapped within the vault, but only Hillalum survives. The rising water forces him upward and the current of water carries him until âthe walls [open] out away from himâ (25). He awakens in a tunnel, but is able to see light ahead. He comes out of what he discovers is a cave and finds himself in the land of Shinnar, which is south of Babylon. Hillalum's return to earth from the vault of heaven forces him to realize that the world is shaped like a seal cylinder, âwrapped around in some fantastic way so that heaven and earth [touch]â (28). Thus, Hillalum's journey is in itself apocalypticâas his story unfolds, the world reveals itself through his experience. The scientific worldview Chiang incorporates is fascinating; yet, what is even more fascinating is the way the inhabitants view God and their attempts to connect with Him. The people fear God's displeasure and Hillalum feels uneasy at the thought of breaking open the vault of heaven (4). Standing at the base of the tower even Hillalum's senses rebel, âinsisting that nothing should stand so highâ (6). He and the others continually wait for a sign from God âto let men know that their venture was approved,â yet God is silent (14). When the star mentioned above first hit the tower, âeveryone descended &, waiting for retribution from Yahweh for disturbing the workings of Creation. They waited for months, but no sign cameâ (16). God never acknowledges their efforts, either blessing or damning them for their attempts. Their overwhelming desire for knowledge of God's workings cause them to give âthanks that they [are] permitted to see so muchâ while at the same time they âbeg forgiveness for their desire to see moreâ (18). Their reactions show lack of surety regarding their purpose as Yahweh fails to respond. The inhabitants debate how God may perceive their attempts to reach Him. Qurdusa, one of the tower's bricklayers argues that âif the tower were sacrilege, Yahweh would have destroyed it earlierâ causing one of the Elamites to counter: âIf Yahweh looked upon this venture with such favor there would already be a stairway ready-made for us to use in the vaultâ (19). Hillalum, however, takes a more Deistic viewpoint, saying, âYahweh may not punish us, but Yahweh may allow us to bring our judgment upon ourselvesâ (19). The God in this story creates the world but does not actively intervene. When Hillalum and the others hit a reservoir, he believes âhis fate had come at last. Yahweh had not asked men to build the tower or to pierce the vault; the decision to build it belonged to men alone, and they would die in this endeavor just as they did in any of their earthbound tasks. Their righteousness could not save them from the consequences of their actionsâ (24). In this world, the focus is on the choices one makes and the consequences one must pay for those choices. Yes, God exists, but He does not intervene in human lives, nor does He care if they are virtuous or sinful, or if they worship or ignore Him. It was clear now why Yahweh had not struck down the tower, had not punished men for wishing to reach beyond the bounds set for them: for the longest journey would merely return them to the place whence they'd come. Centuries of their labor would not reveal to them any more of Creation than they already knew. Yet through their endeavor, men would glimpse the unimaginable artistry of Yahweh's work, in seeing how ingeniously the world had been constructed. By this construction, Yahweh's work was indicated, and Yahweh's work was concealed. Thus men would know their place. (28). Hillalum comes to understand that faith does not provide meaning or significance to his life. He glimpses âthe unimaginable artistryâ of the world through human endeavor, not through worship or religious ritual. As Alan Gregory states, while all âapocalyptic texts reveal human life in its precarious contingency,â apocalyptic âscience fiction finds the contingency of life before immanent powersâ (161). The inhabitants of this world find âa sense of wonder at the complexity of creationâ that comes from their own exploration of the world (Smith). Yahweh does not open their minds or increase their understanding of their world and their place in it, only an individual's desire for knowledge does so. Chiang's story is apocalyptic in that it is the story itself that reveals our search for meaning. We do not need religion to achieve spiritual or material improvement; what we need is our continuing desire to discover and understand the physical world. The âTower of Babylonâ is a story illustrating the existence of God through the reasoning and observation of its characters, but not by supernatural manifestations. Such is not the case in âHell Is the Absence of God.â In the world of the story, the idea of faith as belief without proof is not an issue. Angels make frequent appearances and inhabitants witness the dead ascending into Heaven or descending into Hell. Hell itself becomes visible on occasion, allowing the living to see a place very similar to their world as going to Hell means âpermanent exile from God, no more and no lessâ (âHellâ 208). Angelic manifestations can lead to miracles but can also lead to indiscriminate death and birth defects because of the destructive power of their visitations. Furthermore, anyone caught in âHeaven's light,â which appears âonly when an angel [enters] or [leaves] the mortal plain,â go to Heaven, even if they are wicked or evil (226). The protagonist of the story, Neil Fisk, believes in God (as do all in this world since there is no question of God's existence), but he does not love God. Neil in the believing that were of unfolding, or without from Neil is of either or about God, he to go to Hell people like Hell was where when exile from God no fear for Neil as it means without His however, is a that Neil since many of such as he in âthe for God that he had love of God had to the then it did make The together even view of God and Neil would have reached the point where he was to However, he is not that is one of during a from the angel is by glass when the of the of the in which was see to Heaven, and while Neil have seen death as a he becomes of He to be with and the only way to achieve this is for Neil to to love God. However, he finds himself in a had been the blessing of his and God had he was to love for it? For it was like a love as a for his he have but was a he He a of those who the but is by the that he should his role as one of God's those who have a to Neil is to his and make with God to find a way to love God, Neil finds a when a and while of the of his an and his was seen ascending to Heaven, to the of his Neil to a one of those who go to where either or the mortal When the angel Neil attempts to him but his into a However, a of light that âthe light to Neil all the he should love As he now God an beyond what humans can for one he that he will go to Heaven since of him to Hell In is and he has a he than was when he was but his only is to love God. & He his being to Hell was not a of he he there was no for it, no His love for God, the us, âis the nature of In âHell Is the Absence of Chiang brilliantly a of those who a religious that God those who love Him. Chiang forces the to with a why would a God on the Chiang believes this âis one of the of and with the that in the this story as of an world in which the is a directly the of the religious that miracles are always I do not agree that it is just the religious who believe miracles are always I do agree that many who would define themselves as religious have such In the world of the story, supernatural can have both and on However, we see on these have no at a witness to the angel believes God has a purpose for him and for âan with the to provide him However, does not either or He Neil death and to which to a of God's people that they can no more in the than in the mortal while them to worship God, just not a one God or not to have no on whether one in heaven or the is to question the of religious faith. In many âHell Is the Absence of is a on In the world of the story, the inhabitants know God there is no or in to believe or not to The or is situated in the love one has or does not have for God. one God and to then one However, if one God and to as does Neil Fisk, then one is no in this world as one God to the argues that is us to take a religious belief and make it a and by so he forces us to think about ways religion can be so and in our Many of us feel certain as either a blessing or a from God, yet of us would feel a birth for as one or the Chiang us into a world where the inhabitants do not have such a world where is not God is not God is not (âHellâ This God is the God for those who do not see religion as a means of achieving any of spiritual improvement. Chiang the and the of God's We never know why God Neil to Hell and to âHell Is the Absence of is an apocalyptic story that reveals a of faith, the disillusionment of those who no longer believe in the promise of God to the The disillusionment of faith those who do not see God as a way of their belief as Eric defines it, something we regard as what when one that something return to what if one can that God does not what when the one to it is the one for religious belief In by and what when the seek and find to the questions surrounding religious belief. understanding of and the universe on of the of For âis the of the the and the As a & is and of being & think and the of is to think and the has always with a of discovers this when is a and the understanding of the universe However, to a that is and discovers âa that any number with any other that any two are which of in the same sense of that has world to this but this sense of to that the of is nor with apocalypse reveals that can no longer provide meaning or structure to life and attempts understanding of himself and the universe on his that a of his allows him to a who âthe between and and he finds his in his ability to in similar as to world, in the other and the other to world is to discover he has no for was it was something he In he feels more than a sense of to a when faith and religion no longer provide structure and meaning, both and their when they discover that what they have always as the of themselves and their world can no longer be Chiang's structure of by further to the of of faith. The story is out in with the of the which only two and The first is one through and a the other two are on either or a in and we can read one as a for faith and belief. For in the us that two The first one in that that may be but are & His that a of the of is just such a it be by any means using the of In other words, and proof are not the same we can know certain to be while not the ability to they are Such is one of the definitions of belief without proof. Chiang us with an look at what when what we believe meaning the is and the proof not from the but from As the that this is to a that there was no God. just it, but it for a For was something and is âthe one who that it is not the same discovers his ability to his belief that meaning his understanding of the does not to for feel He feels as that has the of something he which is why the of the story is However, this this feels for than and their faith and both do so through their and Ted Chiang's apocalyptic stories are on our own search for meaning. Many science fiction writers often consider religion may however, creates and where religion and faith are while at the same time to the As the stories we our own disillusionment and many of us, the in the âTower of Babylonâ are to themselves whether they in knowledge or and Hillalum's and understanding of the world reveals to him that meaning is in scientific not or faith. Fisk, on the other in a world where proof of God is a yet he comes to know that God and may question why God, like the God in âHell is the Absence of the and the without or In by religion for and âthe to of the universe as yet, they find their universe not only but Chiang's story to those belief structure has intense and search for meaning them not to a and but only them further into As with all science Ted Chiang's stories reveal more of our than our reveals to We are not to God's role in our his stories us to question our own Chiang's apocalyptic is out of our own disillusionment that is on the world, but on the promise of God & which has and for some 11). these stories do not us or lead us and Ted Chiang's apocalypse reveals and that meaning and come out of death of
Yasser Shoukry, Konstantinos Gatsis, Amr Alanwar, George J. Pappas ¡ 7 authors
We consider a problem where multiple agents participate in solving a quadratic optimization problem subject to linear inequality constraints in a privacy-preserving manner. Several variables of the objective function as well as the constraints are privacy-sensitive and are known to different agents. We propose a privacy-preserving protocol based on partially homomorphic encryption where each agent encrypts its own information before sending it to an untrusted cloud computing infrastructure. To find the optimal solution the cloud applies a gradient descent algorithm on the encrypted data without the ability to decrypt it. The privacy of the proposed protocol against coalitions of colluding agents is analyzed using the cryptography notion of zero knowledge proofs.
Provable data possession (PDP) is a technique for ensuring the integrity of data in storage outsourcing. In this paper, we address the construction of an efficient PDP scheme for distributed cloud storage to support the scalability of service and data migration, in which we consider the existence of multiple cloud service providers to cooperatively store and maintain the clients' data. We present a cooperative PDP (CPDP) scheme based on homomorphic verifiable response and hash index hierarchy. We prove the security of our scheme based on multi-prover zero-knowledge proof system, which can satisfy completeness, knowledge soundness, and zero-knowledge properties. In addition, we also propose a fuzzy clustering system for analyzing the high dimensional Data bases in cloud Environments. This paper proposes novel effective fuzzy soft clustering systems with the combination of possibilistic c-means.
Roman Matzutt, Oliver Hohlfeld, Martin Henze, Robin Rawiel ¡ 6 authors
As transaction fees skyrocket today, blockchains become increasingly expensive, hurting their adoption in broader applications. This work tackles the saving of transaction fees for economic blockchain applications. The key insight is that other than the existing "default'' mode to execute application logic fully on-chain, i.e., in smart contracts, and in fine granularity, i.e., user request per transaction, there are alternative execution modes with advantages in cost-effectiveness. On Ethereum, we propose a holistic middleware platform supporting flexible and secure transaction executions, including off-chain states and batching of user requests. Furthermore, we propose control-plane schemes to adapt the execution mode to the current workload for optimal runtime cost. We present a case study on the institutional accounts (e.g., coinbase.com) intensively sending Ether on Ethereum blockchains. By collecting real-life transactions, we construct workload benchmarks and show that our work saves 18%\sim 47%18%-47% per invocation than the default baseline while introducing 1.81%\sim 16.59%1.81%-16.59% blocks delay.