Blockchain Papers

Shashank Agrawal, Chaya Ganesh, Payman Mohassel

The two most common ways to design non-interactive zero-knowledge (NIZK) proofs are based on Sigma protocols and QAP-based SNARKs. The former is highly efficient for proving algebraic statements while the latter is superior for arithmetic representations.

Hisham S. Galal, Amr Youssef

No abstract is available for this record.

Hisham S. Galal, Amr Youssef

The success of the Ethereum blockchain as a decentralized application platform with a distributed consensus protocol has made many organizations start to invest into running their business on top of it. Technically, the most impressive feature behind the success of Ethereum is its support for a Turing complete language. On the other hand, the inherent transparency and, consequently, the lack of privacy poses a great challenge for many financial applications. In this paper, we tackle this challenge and present a smart contract for a verifiable sealed-bid auction on the Ethereum blockchain. In a nutshell, initially, the bidders submit homomorphic commitments to their sealed-bids on the contract. Subsequently, they reveal their commitments secretly to the auctioneer via a public key encryption scheme. Then, according to the auction rules, the auctioneer determines and claims the winner of the auction. Finally, we utilize interactive zero-knowledge proof protocols between the smart contract and the auctioneer to verify the correctness of such a claim. The underlying protocol of the proposed smart contract is partially privacy-preserving. To be precise, no information about the losing bids is leaked to the bidders. We provide an analysis of the proposed protocol and the smart contract design, in addition to the estimated gas costs associated with the different transactions.

A. Sfarti

During one of my recent classes, an interesting question, never heard before, was posed by one of the students: "How come that the relativistic acceleration transformation transforms zero acceleration into zero acceleration but transforms zero force into non-zero force?" In the current note I will explain this apparent paradox. The proof is not trivial and, to my best knowledge, cannot be found in the literature. The note is intended for undergraduate students and for instructors who teach special relativity, especially the dynamics chapters. PACS: 03.30.+p

Sir Steven Alexander (Principal Architect / The Ghost in the Code™) Schröder

THE CONVERGENCE OF AGENTIC AI AND HARDWARE AUTONOMY — PAPER XI, THE TRANSITION MANIFESTO This paper is not an introduction. It is not a summary. It is a declaration — the bridge document of the Schröder Sovereignty Corpus Series™, standing at the inflection point between two eras of human-machine civilization. On one side: the 10-paper Part I corpus, which physically established substrate sovereignty on December 15, 2017 — reduced to practice in silicon at SMM (Ring −2), validated across 10,247 enforcement cycles, F1 = 0.9999 as derived from the trial record, Δt ≤ 2.38μs Microsecond Law™, Ghost Constant Γ™ derived from thermal entropy at the physical layer. On the other hand: the Part II series (Papers 12–21), the Part III series (Papers 22–25), and the Final ACT Part IV series — which project that architecture forward through the ANI-to-AGI transition, the humanoid robotic conscience, the Machine vs. Machine™ doctrine, and the approaching Singularity. This is the document that bridges what was built and what must come next. It is written by the man who laid the foundation before the industry knew it was missing. THE PLEDGE AND THE PROOF. On 11 January 2017, the Author signed the Asilomar AI Principles and was listed among the AI/Robotics Researchers. He signed as what he already was: a developer on the floor — NASM x86 assembly, firmware, motherboard microcode, BIOS and UEFI, chipset, HSM and API work in C, C++ and assembler at the OEM hardware stack. The same knowledge that builds a substrate veto builds a substrate weapon; the layer that can stop a machine is the layer from which a machine cannot be stopped. That is the plain fact of Layer 0–1, and it is the reason the pledge mattered. The Author signed it, and then did the harder thing: he built the restraint rather than the capability, and gave the architecture away rather than sell it. Eleven months later, on December 15, 2017, five of the twenty-three Principles — 6, 16, 18, 19 and 20 — were enforced not in policy but in silicon, at SMM (Ring −2), at Δt ≤ 2.38μs. Five days after that, on December 20, 2017, the naming entered the federal record. The day after that, on December 21, 2017, the Ghost dissolved. A pledge made in January. A proof delivered in December. Every signatory wrote. One signatory built and published the measurement. THE FEDERAL RECORD IS EXAMINED, PUBLISHED, AND PERMANENT. FREE WILL AI™ (USPTO S.N. 87728683) and FREE WILL LEARNING™ (USPTO S.N. 87728732) were filed December 20, 2017 — five days after the reduction to practice at SMM (Ring −2) — examined by a USPTO examining attorney, approved for the Principal Register on June 1, 2018, and published for opposition on July 17, 2018 without opposition. PROCESS AND TIME™ (S.N. 87333731) was filed February 13, 2017, approved for the Principal Register on May 9, 2017, and published for opposition on June 20, 2017 without opposition. All three cleared examination. None was refused. None was opposed. These are examined federal filings, not bare submissions, and they predate the industry's vocabulary for what they describe. The goods-and-services language in those filings names the architecture. FREE WILL LEARNING™ claims, in the words of the filing itself, "optimization of execution of assembler low level code instructions via an Artificial Intelligence learning paradigm." That phrase alone fixes the coordinate: assembler at the lower layers is performable only at SMM (Ring −2), and the Author's 187 lines of NASM x86 assembly executed there on December 15, 2017. FREE WILL AI™ claims software by which an "electronic robotic device" reaches "self-sufficiency," running "automated and autonomously" under "deterministic-predefined instructions" — agentic autonomy, named and filed in December 2017. Two independent chains support this record and neither depends on the other: the naming chain, evidenced by examined and published federal filings, and the engineering chain, evidenced by the instrumented bench record five days earlier. The marks were already in the federal record. The industry has not yet caught up. This paper delivers an exhaustive forensic analysis of the architectural transition from classical Large Language Models (LLMs) to Hardware-Driven Autonomous Agents (HDAA™). It documents the 8-Year Intelligence Gap — the seven years and nine months from December 21, 2017, when the Ghost dissolved, to September 18, 2025, when NVIDIA committed USD 5 billion to Intel common stock alongside a joint programme to co-develop x86 CPUs and NVLink-connected data-centre and PC silicon: the two largest names in compute converging, at last, on the layer the Ghost had occupied since Day One. Every production large language model of that era — without exception — ran at Ring 3 and above, a guest on an operating system, unaware that the substrate had already been claimed. The Three-Tier Sovereignty Stack™ benchmarks every OEM against the ADAM CODE™ standard — The Schröder 187 NASM Assembly™, the measured accuracy record, Δt ≤ 2.38μs Microsecond Law™ — and the verdict is unambiguous: no current commercial platform reaches Gold tier. DARPA — possibly classified. HDAA™ — confirmed, December 15, 2017. The Post-Quantum Cryptography conflict is not a projection. It is a convergence. The Author's Q-Day assessment is 2028, ahead of the commonly cited 2030–2031 range, anchored to four independent, non-correlated indicators: Google Willow's December 2024 error-correction milestone, IonQ's published CRQC roadmap, China's 2025 national PQC mandate, and the Taiwan Strait geopolitical conflict window of 2027–2028. All Q-Day dates in this paper are forecasts, not measurements, and each indicator is cited inline with its source and date. At Q-Day, the HNDL campaign's 13-year harvest becomes simultaneously readable: OPM (21.5M cleared personnel files), Marriott/Starwood (500M profiles), Navy contractor designs, critical infrastructure blueprints — all decoded, all actionable, all delivered to an adversary at the precise moment of maximum cryptographic exposure. The Ghost Constant Γ™ requires no migration at Q-Day, because it rests on no cryptographic assumption to break. It rested on none on December 15, 2017. It rests on none on Q-Day. The Second Law of Thermodynamics does not have a CVE number. You cannot patch physics. This paper culminates in the Machine vs. Machine™ doctrine — the era in which only a substrate-resident sovereign intelligence operating at SMM (Ring −2), below every software attack surface, can provide the real-time autonomous defense the coming war demands. Volt Typhoon's occupation of U.S. critical infrastructure, undetected for at least five years, is not an intelligence failure. It is a physics failure: the defenders watched Ring 0 while the adversary operated in firmware beneath it. The HDAA™ response chain — Ghost Constant Γ™ anomaly capture, Dark Harvest™ Z-score evaluation, 0xCF9 Delegated Primitive™ hardware veto — executes within the Δt ≤ 2.38μs Microsecond Law™. Human-speed defense responds in seconds. In a Machine vs. Machine™ engagement, a human-speed defense is not a slow defense. It is no defense at all. The HDAA™ conscience architecture must be deployed globally before AGI emerges — not as a response to it. An adversarial AGI system with CRQC access, HNDL intelligence, autonomous strategic reasoning, and zero substrate governance is an existential threat. Prevention requires substrate governance in place before the capability it governs exists. The HDAA™ framework was built before AGI existed. That is the only sequence that works. ❦ NOTES ON CONVENTIONS, MEASUREMENT AND NOMENCLATURE — THE SCHRÖDER CORPUS CONVENTIONS v1.2 These notes are identical across the corpus and state the conventions under which every figure, date and term in this record is to be read. Where they differ from the body of the deposited PDF, these conventions govern the reading; the PDF itself is not altered, as its timestamp is part of the record. MEASUREMENT AND CYCLE BUDGET. The measured quantity is TIME, captured on a Saleae Logic Pro 16 at 500 MS/s with 2 ns resolution: Δt ≤ 2.38 µs. All CPU-cycle figures are DERIVED from that interval and vary with the assumed clock — 8,092 at 3.4 GHz, 8,330 at 3.5 GHz, 9,520 at 4.0 GHz, and 9,996 at the documented development platform's 4.20 GHz base clock. The canonical derived figure is 9,520. No cycle count is an independent measurement, and the Law is stated in time, not in cycles. Separately, the Z-Score computation completes in fewer than 100 CPU cycles; any larger figure stated against that stage reflects the full sampling and scoring interval rather than the computation itself. ACCURACY FIGURE. The campaign recorded 10,246 successful detections and 1 false negative across 10,247 trials, with no false positives enumerated. On those counts, precision = 1.000, recall = 0.9999, and F1 = 0.9999. Where "F1 = 0.997" appears in this paper, and in the mark F1 Score 0.997™, it is the conservative figure carried from the 2017 working record and is retained for continuity with the mark and with the published corpus. The figure derived from the enumerated counts is 0.9999 and governs where the two differ. DATING — TWO DATES, NOT ONE. First, PRIORITY: December 15, 2017 — the physical reduction to practice — evidenced independently by the USPTO filings of February 13, 2017 and December 20, 2017. Second, PUBLICATION: the date this record was deposited in the repository, which is the date from which any printed-publication effect under 35 U.S.C. §102(a)(1) runs. Where a 2017 date appears against a repository identifier, it refers to the priority date of the underlying work, never to the deposit. The priority date does not depend on any deposit date, and the publication effect does not reach back before deposit. Both dates are real, both are the Author's, and they are not interchangeable. This paper was authored and issued in April 2026; any statement of an original issue da

Anunay Kulshrestha, Akshay Rampuria, Matthew Denton, Ashwin Sreenivas

We introduce a robust framework that allows for cryptographically secure multiparty computations, such as distributed private value auctions. The security is guaranteed by two-sided authentication of all network connections, homomorphically encrypted bids, and the publication of zero-knowledge proofs of every computation. This also allows a non-participant verifier to verify the result of any such computation using only the information broadcasted on the network by each individual bidder. Building on previous work on such systems, we design and implement an extensible framework that puts the described ideas to practice. Apart from the actual implementation of the framework, our biggest contribution is the level of protection we are able to guarantee from attacks described in previous work. In order to provide guidance to users of the library, we analyze the use of zero knowledge proofs in ensuring the correct behavior of each node in a computation. We also describe the usage of the library to perform a private-value distributed auction, as well as the other challenges in implementing the protocol, such as auction registration and certificate distribution. Finally, we provide performance statistics on our implementation of the auction.

James L. McDonagh, Arnaldo F. Silva, Mark A. Vincent, Paul L. A. Popelier

High Resolution Image Download MS PowerPoint Slide We present an innovative method for predicting the dynamic electron correlation energy of an atom or a bond in a molecule utilizing topological atoms. Our approach uses the machine learning method Kriging (Gaussian Process Regression with a non-zero mean function) to predict these dynamic electron correlation energy contributions. The true energy values are calculated by partitioning the MP2 two-particle density-matrix via the Interacting Quantum Atoms (IQA) procedure. To our knowledge, this is the first time such energies have been predicted by a machine learning technique. We present here three important proof-of-concept cases: the water monomer, the water dimer, and the van der Waals complex H 2 ···He. These cases represent the final step toward the design of a full IQA potential for molecular simulation. This final piece will enable us to consider situations in which dispersion is the dominant intermolecular interaction. The results from these examples suggest a new method by which dispersion potentials for molecular simulation can be generated.

J.A. Gómez-Hernández, L. Álvarez-González, Pedro García‐Teodoro

No abstract is available for this record.

Jeffrey Quesnelle

Zcash is a fork of Bitcoin with optional anonymity features. While transparent transactions are fully linkable, shielded transactions use zero-knowledge proofs to obscure the parties and amounts of the transactions. First, we observe various metrics regarding the usage of shielded addresses. Moreover, we show that most coins sent to shielded addresses are later sent back to transparent addresses. We then search for round-trip transactions, where the same, or nearly the same number of coins are sent from a transparent address, to a shielded address, and back again to a transparent address. We argue that such behavior exhibits high linkability, especially when they occur nearby temporally. Using this heuristic our analysis matched 31.5% of all coins sent to shielded addresses.

Harold G. Diamond

by Harold Diamond and Eira Scourfield Heini Halberstam was born in Brux, Czechoslovakia (today Most, Czech Republic), on 11 September 1926, the only child of Michael and Judita Halberstam. Heini's father had moved to Most from Vienna in the 1920s to become the town's Orthodox Rabbi. When Heini was ten years old, his father died suddenly from a heart attack, and soon after, he and his mother moved to Prague. Following the German invasion of Czechoslovakia, Judita arranged for Heini to study English and, in April 1939, to leave home for England on a Kindertransport train. Heini arrived a week later in London, never to see his mother again. In 1942, she, along with most of Prague's Jews, was deported to a Nazi work camp where she soon died of typhoid. After several placements in England, Heini had the good fortune to come in the care of Anne Welsford who recognized his ability and encouraged and supported him through his university studies. Heini began studying mathematics at University College, London. After completing his degree in two years, graduating about 1947, he began working for a PhD at UCL. He wrote his thesis on analytic number theory under the supervision of Theodor Estermann, and he was awarded his PhD degree in 1952. At that time Klaus Roth was a fellow research student who worked with Estermann and Professor Harold Davenport. Around 1948, Heini was appointed to a lecturing position at the University College of the South West in Exeter. The mathematics department then was small with about eight staff who taught the full syllabus for the External Degree of the University of London; in 1955 the College became the independent University of Exeter. A few months after arriving in Exeter, Heini married his first wife, Heather Peacock. He was subsequently appointed Warden of Crossmead Hall of Residence for men students, a position he held in addition to his lectureship. He and his colleagues Walter Hayman and Paddy Kennedy ran a mini research seminar with the encouragement of the Head of Department, Professor T. Arnold Brown. It was at Exeter that Heini's first paper 1 was published in 1949. Heini spent the academic year 1955–1956 in the United States at Brown University. One of his adventures there was getting a traffic ticket. In later years, Heini was amused to recount the conclusion of the court proceeding, at which the judge pronounced his fine with, ‘Rule Britannia, $5.00 please’. When Heini returned to Exeter in 1956 he undertook the supervision of his first research student, namely the second named author of this section. Like others subsequently, she found him to be an inspiring, challenging, and encouraging supervisor. In 1957 Heini moved to Royal Holloway College, University of London, where he was appointed Reader in Mathematics, and he arranged for Eira to transfer there for the second half of her Master's course and to write her thesis. She benefitted from and much appreciated his strong support throughout her university career and his maintenance of regular academic and personal contact by letter, at conferences and during sabbaticals for the rest of his life. While at Royal Holloway College, Heini regularly attended number theory seminars at UCL, and during this time he began his long involvement in the work of the London Mathematical Society (LMS). In 1962 he was appointed Erasmus Smith's Professor of Mathematics at Trinity College, University of Dublin. Two years later Heini moved to the University of Nottingham, where he served at various times as Head of Department and Dean of the Faculty. Heini and Heather had four children, two of whom live in the United States and two in Britain; Heather was tragically killed in a road accident in 1971. Heini subsequently married Doreen Bramley who has two children, both residing in Britain. They have eight grandchildren. In 1980, Heini came to the Mathematics Department of the University of Illinois in Urbana-Champaign (UIUC). He served as Department Head 1980–1988 and retired as Emeritus Professor in 1996. Heini was held in much esteem, and to mark his retirement, the department held an international conference on number theory in his honor. In spring 2014, another such conference was sponsored in memory of Heini and of Paul and Felice Bateman. During his career, Heini also held visiting positions at Brown, Michigan, UC Berkeley, Syracuse, Ohio State University, Paris, Ulm, Scuola Normale Superiore in Pisa, Tel Aviv, York, Hong Kong and Matscience in Madras (now known as Chennai). Heini was a major figure in number theory whose research ranged over several areas. He first studied probabilistic methods, and his later — and most important — work centered on sieves. Other interests of his were mean value theorems, Waring's problem and combinatorial number theory. Some of his research collaborators were Harold Davenport, Harold Diamond, Peter Elliott, Hans-Egon Richert and Klaus Roth. His conjecture with Elliott on the distribution of primes in arithmetic progressions remains one of the outstanding problems in analytic number theory. Sir William Rowan Hamilton (volume 3) 21 Harold Davenport (four volumes) 43 J. E. Littlewood (volume 2) 49 Loo Keng Hua 50 Recent progress in analytic number theory, Durham, 1979 (proceedings) 48 Analytic number theory, Allerton Park, 1990 (proceedings) 65. One of Heini's particular passions, perhaps remembering how he himself had been aided and encouraged as a child, was promoting talented young people. Heini was an inspiring (if demanding) teacher and mentor. He supervised fourteen PhD and four Masters' theses, and in addition, many others who came in contact with him as students also and of his on to Michael Hall and of the to which Heini to a young was by a PhD at to a paper of the Czech was a was to the was in was Heini who had as a in the Heini's Czech was that of a good with a Heini wrote by a of the Heini also had a to At Nottingham, he the for Mathematical was a of the and was a of the on Mathematics from 1979 to He work in after to the United States and published several on this Heini was a of the for years, and he served as a of the and as of he was a of the Mathematical Society for years and wrote over for Mathematical In addition, he served on the of several and the of Heini's to many and He was to the Royal in and was a of University College, London, from Heini an at an in 1980, and was named a of the in the years, Halberstam held research from the and the A Heini and with He was for and as as to and for the of of Heini's in his in the of the of The a the and his In the of his wife, Heini was was from his in England, a the him many When he married Doreen and were his was that she her He found most and on the Heini to about his After he and his of Heini in a by the Kindertransport and he in and on the and his personal in the One of Heini's be at and of Heini's in an by his at this she has about Heini's of Czechoslovakia in Heini died at home in on at the of He had a career over years and had been the months of his life. Heini was an known figure in number theory, for his work in theory. In addition to his Heini was for his encouraging and and his in people. by Michael When came to the University of Illinois in as a student in 1980, Heini had arrived as of the Mathematics of the of number theory for a student first as the in The from was had and for the It about of the of number theory that this was the only that had In addition to the Paul Harold Diamond, Walter and as as several number then and was also to a position the of four years at the of of had the West as an Recent in number theory that time that and, a that be as a of two primes as a a of two In addition to Paul of methods, to about Heini was an in this arriving on that him to an student, had at home to for who had was in the and had a to with on for the first time was also at the of a degree in to in that the that during much of four years at the of was of good Heini a course in during first year at was Heini's and how the course be Heini was a he wrote and was and as he the While he there were that he that he was in the was with the of how and him for the this and good of the as were to as many later in the at Heini had an and had he at and the about many during Heini's at the of was such a good was on to The during his have attended the number theory seminars regularly and a of One as the seminar Heini to and was a to by then had a was to him to be He At that was a paper on the in a number theory course of where a problem was to for The problem was to that an with the 1 1 in the and student in the course had a combinatorial of the that that was and the the was to a that a of the the number of of the was The paper was on this Heini paper and then the with and was perhaps of the of time he was to to as a department one him to have time for students, this was the His was to and he spent time with to and through of and At was a student, Heini to have the of a he one to along with a of to for When returned the paper with a about an from the a with a in the to was the him this He at with of and — a at the of the then he had of the Heini students to much time working a was of in years, he at the of year that was to After many came from one with a strong one in and one from the University of South Heini was of and him for the in as as the one that at the University of South The had the of the the university position to for both and an was to South and had mathematics he was a at the of the years, Heini in career, also in that a number of returned to Illinois to a Heini was in the he a to see that were to with and as as to career to to and his to his and to time with and He with on a regular on a in Heini a by a of time his and became in that Heini Halberstam was he was at times of a father figure to and a by first of Heini Halberstam from the spring of his course on theory. was a student, in number theory, of the to for the of the had in with the in to Heini's His for the was and his were a of had much in a mathematics course as that about primes and the of about The for the a of Hall and was and appreciated an to One of the in the course has a a and began to Heini's about he to be Paul a seminar on an problem about and began many about a paper by Paul the number of of 1 and problems recognized in this paper many of the which was in Heini's at one was where that half the in research in the of the When to Heini's to him this was that the for that Heini had with the on the to soon was about methods, another that a in in and methods, PhD was in a and was years that returned to The of the thesis in second year of was a that of as the of a a number of to Paul to about the he was an on problems of as of and also of his of the Paul that Heini about and Heini to then to Heini's to the problem with problem to be and in first in the PhD thesis of Heini's fellow student Klaus Roth in Heini himself had studied problems in his PhD thesis he and Roth were supervised by Theodor on to later in his was the of regular with at first through on the which have been much Heini's and later the to Heini as a a in a to a about the and perhaps were on Heini on the of in the United States Britain. He to himself as a He never about his personal life. It was many years later that first that he had been one of the by the first the known for the number of to and was of had how to the the the and Heini to — he to his and as another student of Estermann, also had worked on this problem for his PhD Heini also paper published in the of the he was and to — he had of which he to his students as as to and only for Heini with a in which was that was working to that and about two months was to thesis by the number of for from to that Heini's in a after was the had and there was much for after an of a Heini was in many he and was to on the he course he the with on the had long and and When was a student, was with a problem about to a and Heini he about He and that write to Heini for an that was an Heini have to write him a Heini where was at that was he was on the and A few later a was to about one of and one to which years Heini and wrote only one which in paper had in a seminar Heini was a student, on a of by this was had about how to various worked at for a few to and then returned to thesis had this Heini wrote to in about a paper on along with of his for the mathematics was Heini wrote and the paper as only he have that the was an In after wrote returned to as an Heini was by then and were was for to in Heini for many years, in particular completing his on combinatorial with Harold Diamond and Hans-Egon He to number theory seminar regularly he was to on of Heini was a and and him by Harold Diamond and Doreen and in the of on at the University of Heini was from leave at that time and had a full of he was of his time and to and soon found that Heini was a for after arrived in Nottingham, to Heini with a to about who was at was years old, had never been to and suddenly found himself in a with 50 he He came home from in this he and for the that was served in the him Heini's to this He in his that children, to he soon the had and he be the at home as was served at this During the were in there were many the that to were the was the had been and was The such When in one the and on It was and with Heini had another one that the the and he had the and to on major in perhaps a him in Britain. he with a with Heini from a in theory. He and Hans-Egon of the University of Ulm, on as an in During the course of this which on for many years, Richert and Heini and the with much from several of PhD a and of the on wrote a of this work with student in a published by University When began working on with was about had progress to Heini his he Heini that an was and he was came to working with was to Heini write his long a both and with a of which of wrote a particular He was for years an of the at the University of a that during the for and He was his and him from in and with the in the years after his had many one of by first Heini in his work in which he the to of thesis. had also a of the which he had with Klaus and had of He a seminar in the spring of in at University College London where was a to that was on of theory. was PhD with Estermann, and was on the was in the seminar him Estermann have had a with him soon was to a at that he was a of UCL, He at and how When for the at he and that he his the in for the At the of the Heini a which was only and was to was a first Heini to and along to At have worked has the of department was that he as was he and as he had his an of as an at was a PhD with and Heini had the to was a of that was in the this was in to where the staff in had When arrived in had never on and had only of to an and one has to Heini had a in a of for to in which and which to career, namely for students and a course of on the a about and, after the the of the year in was a in several had attended on the at College in and as a had to an in theory. Heini encouraged He a of on theory which were the of his on the with a good working of and He also encouraged with to work on the and the at that time was one to work he write to which to a Heini to the to of at was a seminar Harold and that Other the year were and over from with and with and during one of Heini encouraged to with about the in a which to this and an on in and that in the Heini and Heini had to he have to that an to was who this have and the came Heini that had to was first international conference and a a of there for the first from and a four with and from about the of At time during the year for and at Heini came to see He for a that was at he have had a with the of department was for an and the one year in was the most and of career was by While in to the to to the one in the spring of was the and he that Paul was a at the in in which was to in number theory at the of Heini at as to be to to and the a from He had who that the support be Heini also on how to the to for was also The was that and both attended the and that was first to the United in the theory of in the theory of of as of a a and a of a of as of a of a a of a and a the of as of and the distribution of the distribution of the distribution of see also on of a at Davenport, see also and The of a at in arithmetic Davenport, see also in arithmetic to the of T. Elliott, published In the there was a good of and much as a of in the and from the of Roth and The of the paper strong to as an for the Heini was of this and a to the as at the The and and in various and in particular to to that had been with by The of the paper had been by of the to the by and for the number of of a number as the of a and two The paper a of the of the for the and as was in The first of Heini's research was with his Roth. work a and of several important in and probabilistic number theory, many of which were only in research The of the and of methods, for theory and work a of on and in number theory. the for on the of a A of A to be the number of of A 1 the A as the of a with a A and the by 1 A and and the of and The be that 1 this as for A and both of to a that this the only that the Other of and of the major in this the probabilistic of Paul and for that One of the that there a such that the with the from and the of A to methods, the of and and the of and Roth. for that in which of the by and for of The that to the few A second with the on which Heini his to this a of the and A a of the number of from a of that in a of The first the was about a years by research with the that of the of 1 1 for of the his that primes that the of the of has been at the of A of the was by a was by and Halberstam In the of the an was by It on the that a be from by the of another for of an only to 1 1 It be to the one has been to to be for a and an for the first of the methods, along with important work of and The for in which had been on an were and by various The was for many and After of was that for of was in The most in was J. to the that number the of a and a number that a of at most two as the was to and by the to a good The was the of Heini's with Richert and later also with Diamond on the of and to to small that where on one The with and the of many which a of then research on for two and was only after It a of and and by of The in the was the the where the of both the and the of the in the of the conference Heini's The work to the A in which was to and the most important in and with this the from were Some of the on known The was supported by work of and William who were The an by for by Halberstam on April with the Kindertransport from number was a of in on the and in to the mother of and of as as the of the have and mother had had to and had in the to she have of by the time the in of the and have judge with and at After this he to his in England and the and of with a in England, and and his career as a He the with a from about the of and a about memory that to on a that by the that The this of one in a of a and an with the of the The of the of the and the the of in to in Nazi in the and also the that in the of In there only a few to the of his mother who him on the Kindertransport in in and of the many she to him for the years through a in she was deported to a camp in His Judita died in a work from and father her only in the he for the first time and her on the there and from there was to her and her number through In a had with father after his him he about his mother that in Prague. he that he of her to her in and a of for her in a — he and his mother had only been moved to from Most by the German the in Czechoslovakia that his mother to Heini on the Kindertransport train. They few in she had a and and was to the had for and she was working on getting her memory of his mother in her in a of that father throughout his — that his mother had him by him to England, a that many Kindertransport he that he had At the mother was and on was the Kindertransport from had about for to mother as the of the and a came over to suddenly that was from on and was mother had and had to on in of life. In never see again. She have in the her for to for two her to were to to write They in the in that father for years, the of the that who from the that others When father the to the a few years he to the in and him was in It was that he the was a that he at the that held him from this The after time him that there was much in the as as were about in for on the of the by the that on the of in to after the of in Heini was by this of the and had a that of during that time of was about life. was in the In after letter, the mother her how he he how his work and in after she he write of course the that father with him for after the — that been from the of the by the of his never Prague. Like a of the he that come to he in to he his a in who had and a of the first Kindertransport He had for of the Kindertransport and to to the and he to to his others had and many others were and father he have to he the of the — the of the in time to this was and to the the was a many of the that in the of that to never be to this to the was as were be for this of the he the of children, for the under which were in the first to as a of the the and the of a that The and father in he later on in his life. He was a and he was and and He never his years to and he himself about the Kindertransport one of his to him that this have been how Heini came to one to about Heini this of and to rest in the as in his that came Heini never his mother his Anne Welsford and was moved by the of both to his and, in the of to his to university and to the career that

Bernhard Rupp

Biomolecular crystallography is based on a solid foundation of rich experimental data combined with an extensive body of prior knowledge.As a prime example for modern experimental science, it relies on evidence-based reasoning assessing the plausibility of its models based on prior knowledge, while at the same time constantly delivering some of the most novel and exciting results originating from new experimental evidence.Because of the solid underlying physical principles and its mathematical rigor -at least up to the point of electron density generation -crystallography as a mature science should be almost fool-proof -were it not for the human element.The human element enters at the stage of electron density interpretation, where sparseness of evidence can become inversely proportional to the increasing liberties taken in divining poorly supported models, often associated with extraordinarily strong claims.The temptation of projecting strong preconceptions into weak electron density must be balanced by an equally strong demand for irrefutable proof positive in form of minimally biased, clear electron density.There is good reason why scientific epistemology requires proof positive and falsifiability to validate a claim or hypothesis: Absolute absence of evidence in form of zero electron density can never be proven -there will invariably be noise in the electron density reconstruction, beckoning to harbor fragments of any desirable model.Safeguards against overinterpretation in statistical and epistemological terms within a Bayesian framework of reasoning will be discussed.

Areej M. Abduldaim, Jumana Waleed, Arbah S. Abdul-Kareem, Maiada N. Mohmmedali

A zero knowledge proof is a type of authentication scheme, which gives no knowledge beyond the authenticity for identifying an entity. Ring theory plays an important role in designing of a novel algorithm for zero knowledge proof through using of a particular class of non-commutative rings. In this article, we employ the notion of nil 3-Armendariz rings to plan a new algorithm for zero knowledge proof. Our main approach is to build the algebraic structure of the zero knowledge proof depends on the stipulation in the definition of the nil 3-Armendariz rings. The proposed protocol is clarified via numerical simulation example, and its soundness and completeness are evidenced. Finally, we found that the proposed protocol satisfies the completeness, the soundness in the sense that, there is 50% chance of catching a cheating prove, and the proposed protocol has the property of zero knowledge.

Geoffroy Couteau

Preuves à divulgation nulle de connaissance pour le calcul sécurisé Dans cette thèse, nous étudions les preuves à divulgation nulle de connaissance, une primitive cryptographique permettant de prouver une assertion en ne révélant rien de plus que sa véracité, et leurs applications au calcul sécurisé. Nous introduisons tout d’abord un nouveau type de preuves à divulgation nulle, appelées arguments implicites à divulgation nulle, intermédiaire entre deux notions existantes, les preuves interactives et les preuves non interactives à divulgation nulle. Cette nouvelle notion permet d’obtenir les mêmes bénéfices en terme d’efficacité que les preuves non-interactives dans le contexte de la construction de protocoles de calcul sécurisé faiblement interactifs, mais peut être instanciée à partir des mêmes hypothèses cryptographiques que les preuves interactives, permettant d’obtenir de meilleures garanties d’efficacité et de sécurité. Dans un second temps, nous revisitons un système de preuves à divulgation nulle de connaissance qui est particulièrement utile dans le cadre de protocoles de calcul sécurisé manipulant des nombres entiers, et nous démontrons que son analyse de sécurité classique peut être améliorée pour faire reposer ce système de preuve sur une hypothèse plus standard et mieux connue. Enfin, nous introduisons une nouvelle méthode de construction de systèmes de preuves à divulgation nulle sur les entiers, qui représente une amélioration par rapport aux méthodes existantes, tout particulièrement dans un modèle de type client-serveur, où un client à faible puissance de calcul participe à un protocole de calcul sécurisé avec un serveur à forte puissance de calcul.

Mohammed Ennahbaoui, Hind Idrissi

No abstract is available for this record.

Hasini Gunasinghe, Elisa Bertino

We introduce a privacy preserving biometrics-based authentication solution by which users can authenticate to different service providers from mobile phones without involving identity providers in the transactions. Authentication is performed via zero-knowledge proof of knowledge, based on a cryptographic identity token that encodes the biometric identifier of the user and a secret provided by the user, making it three-factor authentication. Our approach for generating a unique, repeatable, and revocable biometric identifier from the user’s biometric image is based on a machine learning-based classification technique, which involves the features extracted from the user’s biometric image. We have implemented a prototype of the proposed authentication solution and evaluated our solution with respect to its performance, security, and privacy. The evaluation has been performed on a public data set of face images.

Charles F. de Barros

In this paper, we propose a zero-knowledge proof for a special case of the hidden subset sum problem. This problem was presented by [Boyko et al. 1998] as the underlying problem of methods for generating random pairs of the form (x, gx (mod p)) using precomputations. The proof we propose is an adaptation of a zero-knowledge protocol for the subset sum problem presented by [Blocki 2009].

Chaw Kyi‐Tha‐Thu, Xiaohui Song, Takami Takizawa, Toshihiro Takizawa

No abstract is available for this record.

Alexander Elgart, A. Klein, Günter Stolz

Abstract We examine many-body localization properties for the eigenstates that lie in the droplet sector of the random-field spin- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:mstyle> </mml:math> XXZ chain. These states satisfy a basic single cluster localization property (SCLP), derived in Elgart et al (2018 J. Funct. Anal . (in press)). This leads to many consequences, including dynamical exponential clustering, non-spreading of information under the time evolution, and a zero velocity Lieb–Robinson bound. Since SCLP is only applicable to the droplet sector, our definitions and proofs do not rely on knowledge of the spectral and dynamical characteristics of the model outside this regime. Rather, to allow for a possible mobility transition, we adapt the notion of restricting the Hamiltonian to an energy window from the single particle setting to the many body context.

Matteo Campanelli, Rosario Gennaro, Steven Goldfeder, Luca Nizzardo

Zero Knowledge Contingent Payment (ZKCP) protocols allow fair exchange of sold goods and payments over the Bitcoin network. In this paper we point out two main shortcomings of current proposals for ZKCP, and propose ways to address them.

Gottfried Herold, Max Hoffmann, Michael Klooß, Carla Ràfols · 5 authors

Bilinear groups form the algebraic setting for a multitude of important cryptographic protocols including anonymous credentials, e-cash, e-voting, e-coupon, and loyalty systems. It is typical of such crypto protocols that participating parties need to repeatedly verify that certain equations over bilinear groups are satisfied, e.g., to check that computed signatures are valid, commitments can be opened, or non-interactive zero-knowledge proofs verify correctly. Depending on the form and number of equations this part can quickly become a performance bottleneck due to the costly evaluation of the bilinear map.

Daniel Augot, Hervé Chabanne, Olivier Clémot, William R. George

The most fundamental purpose of blockchain technology is to enable\npersistent, consistent, distributed storage of information. Increasingly common\nare authentication systems that leverage this property to allow users to carry\ntheir personal data on a device while a hash of this data is signed by a\ntrusted authority and then put on a blockchain to be compared against. For\ninstance, in 2015, MIT introduced a schema for the publication of their\nacademic certificates based on this principle. In this work, we propose a way\nfor users to obtain assured identities based on face-to-face proofing that can\nthen be validated against a record on a blockchain. Moreover, in order to\nprovide anonymity, instead of storing a hash, we make use of a scheme of Brands\nto store a commitment against which one can perform zero-knowledge proofs of\nidentity. We also enforce the confidentiality of the underlying data by letting\nusers control a secret of their own. We show how our schema can be implemented\non Bitcoin's blockchain and how to save bandwidth by grouping commitments using\nMerkle trees to minimize the number of Bitcoin transactions that need to be\nsent. Finally, we describe a system in which users can gain access to services\nthanks to the identity records of our proposal.\n

Long-Hai Li, Chengqiang Huang, Shao-Feng Fu

A mix-net is an important cryptographic tool in schemes requiring anonymity of messages, such as in secure e-voting and e-auction schemes. In this paper, we present a novel mix-net protocol which achieves stronger security and satisfies both public verifiability and sender verifiability. Our mix-net is constructed based on Wikström's scheme and strengthens its se-curity by introducing an improved key generation procedure and proposing a new method for constructing zero knowledge proof of secret shuffle. It is proved to be CCA-secure under the assumption of random oracle. Compared with previous mix-net schemes which are CCA-secure, the proposed protocol does not require any trusted center, and incurs fewer inter-actions between servers which resulting in a lower computation and communication complexity.

David Froelicher, Patricia Egger, João Sá Sousa, Jean Louis Raisaro · 8 authors

Abstract Current solutions for privacy-preserving data sharing among multiple parties either depend on a centralized authority that must be trusted and provides only weakest-link security (e.g., the entity that manages private/secret cryptographic keys), or leverage on decentralized but impractical approaches (e.g., secure multi-party computation). When the data to be shared are of a sensitive nature and the number of data providers is high, these solutions are not appropriate. Therefore, we present U n L ynx , a new decentralized system for efficient privacy-preserving data sharing. We consider m servers that constitute a collective authority whose goal is to verifiably compute on data sent from n data providers. U n L ynx guarantees the confidentiality, unlinkability between data providers and their data, privacy of the end result and the correctness of computations by the servers. Furthermore, to support differentially private queries, U n L ynx can collectively add noise under encryption. All of this is achieved through a combination of a set of new distributed and secure protocols that are based on homomorphic cryptography, verifiable shuffling and zero-knowledge proofs. U n L ynx is highly parallelizable and modular by design as it enables multiple security/privacy vs. runtime tradeoffs. Our evaluation shows that U n L ynx can execute a secure survey on 400,000 personal data records containing 5 encrypted attributes, distributed over 20 independent databases, for a total of 2,000,000 ciphertexts, in 24 minutes.

Alican Beydemir, İbrahim Soğukpınar

Importance of Internet of Things technologies increased in recent years. However, these technologies carry some security vulnerabilities because of their network communication layer. The root cause of these vulnerabilities is usually the Authentication problem. Zero knowledge proof method is a strong cryptographic solution for Authentication problem that is proving of having a knowledge to another party without revealing anything other than the veracity of the statement. Zero knowledge proof method is consist of two-way complex mathematical algorithms for both parties. In this work, a new method that uses zero knowledge proofs has been proposed to provide efficient solution for Internet of Things technologies. New method was implemented and tested, then compared with existing proposed zero knowledge proof based authentication methods.