Journal of Mathematical Cryptology最新文献

{"title":"Preface to the First Annual MathCrypt Proceedings Volume","authors":"J. Cheon, K. Lauter, Donggeon Yhee","doi":"10.1515/jmc-2020-0060","DOIUrl":"https://doi.org/10.1515/jmc-2020-0060","url":null,"abstract":"In 2017, we decided to start the annual series of MathCryptWorkshops in order to encouragemore mathematicians and computational number theorists to propose and work on hard problems in cryptography. This is the first volume of papers from our first annual MathCrypt conference hosted at Crypto 2018, on August 19, 2018 in Santa Barbara. We were motivated to launch this series of workshops to attract more mathematicians to work on hard problems in cryptography. There is a gap in the publishing culture betweenmathematics and computer science which we hope to bridge with this effort. Mathematicians primarily recognize publications in journals, whereas cryptographers almost always publish their results quickly in proceedings volumes of conferenceswhich are themost prestigious venues for the research area. Manymathematicians are not accustomed to the model of submitting a paper by the conference deadline, presenting the work at the conference, and publishing in the proceedings volume.Wewanted to provide a regular annual venue for mathematicians to contribute to the cryptographic research community at this accelerated pace, and the Journal of Mathematical Cryptology was an ideal place and a willing partner to create this opportunity. We are at a point in time where it is increasingly important for mathematicians to be involved in cryptography research, as we set out to determine the next generation of cryptographic systems based on hard math problems which can withstand attacks from a quantum computer once it is built. In 2017, NIST launched a 5-year international competition to determine post-quantum cryptosystems (PQC). MathCrypt can play a complimentary role by encouragingmathematicians to work on and publish attacks on new proposals, including both preliminary results and also even results which represent the failure of a certain approach to effectively attack a new system. This creates the culture of sharing information on approacheswhich have been tried and their measure of success. Currently there is such a high bar for publishing papers with new attacks. Attacking the underlying hard math problems in cryptography is an extremely challenging endeavor, and so the incentives are not aligned to encourage new researchers and young researchers to work and commit themselves to this direction. The opportunity to publish intermediate results in venues like MathCrypt should help to de-risk this endeavor and encourage more mathematician to pursue these research directions. The MathCrypt proceedings volumes are also intended as a place to publish proposals for new cryptographic systems based on new ideas for hard math problems. The post quantum era provides both an opportunity and a challenge tomathematicians to create new systems based on new ideas.When an idea for a hard math problem is first proposed, it can be hard to evaluate the long-term potential in the span of a few weeks during a short review cycle. Thus more established venues may be reluctant to ","PeriodicalId":43866,"journal":{"name":"Journal of Mathematical Cryptology","volume":"14 1","pages":"1 - 4"},"PeriodicalIF":1.2,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/jmc-2020-0060","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43783959","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Privacy-preserving verifiable delegation of polynomial and matrix functions","authors":"L. Zhang, R. Safavi-Naini","doi":"10.1515/jmc-2018-0039","DOIUrl":"https://doi.org/10.1515/jmc-2018-0039","url":null,"abstract":"Abstract Outsourcing computation has gained significant popularity in recent years due to the development of cloud computing and mobile services. In a basic outsourcing model, a client delegates computation of a function f on an input x to a server. There are two main security requirements in this setting: guaranteeing the server performs the computation correctly, and protecting the client’s input (and hence the function value) from the server. The verifiable computation model of Gennaro, Gentry and Parno achieves the above requirements, but the resulting schemes lack efficiency. This is due to the use of computationally expensive primitives such as fully homomorphic encryption (FHE) and garbled circuits, and the need to represent f as a Boolean circuit. Also, the security model does not allow verification queries, which implies the server cannot learn if the client accepts the computation result. This is a weak security model that does not match many real life scenarios. In this paper, we construct efficient (i.e., without using FHE, garbled circuits and Boolean circuit representations) verifiable computation schemes that provide privacy for the client’s input, and prove their security in a strong model that allows verification queries. We first propose a transformation that provides input privacy for a number of existing schemes for verifiable delegation of multivariate polynomial f over a finite field. Our transformation is based on noisy encoding of x and keeps x semantically secure under the noisy curve reconstruction (CR) assumption. We then propose a construction for verifiable delegation of matrix-vector multiplication, where the delegated function f is a matrix and the input to the function is a vector. The scheme uses PRFs with amortized closed-form efficiency and achieves high efficiency. We outline applications of our results to outsourced two-party protocols.","PeriodicalId":43866,"journal":{"name":"Journal of Mathematical Cryptology","volume":"14 1","pages":"153 - 171"},"PeriodicalIF":1.2,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/jmc-2018-0039","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46745146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Recovering Secrets From Prefix-Dependent Leakage","authors":"Houda Ferradi, R. Géraud, S. Guilley, D. Naccache, Mehdi Tibouchi","doi":"10.1515/jmc-2015-0048","DOIUrl":"https://doi.org/10.1515/jmc-2015-0048","url":null,"abstract":"Abstract We discuss how to recover a secret bitstring given partial information obtained during a computation over that string, assuming the computation is a deterministic algorithm processing the secret bits sequentially. That abstract situation models certain types of side-channel attacks against discrete logarithm and RSA-based cryptosystems, where the adversary obtains information not on the secret exponent directly, but instead on the group or ring element that varies at each step of the exponentiation algorithm. Our main result shows that for a leakage of a single bit per iteration, under suitable statistical independence assumptions, one can recover the whole secret bitstring in polynomial time. We also discuss how to cope with imperfect leakage, extend the model to k-bit leaks, and show how our algorithm yields attacks on popular cryptosystems such as (EC)DSA.","PeriodicalId":43866,"journal":{"name":"Journal of Mathematical Cryptology","volume":"14 1","pages":"15 - 24"},"PeriodicalIF":1.2,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/jmc-2015-0048","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47745720","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Short Principal Ideal Problem in multicubic fields","authors":"Andrea Lesavourey, T. Plantard, W. Susilo","doi":"10.1515/jmc-2019-0028","DOIUrl":"https://doi.org/10.1515/jmc-2019-0028","url":null,"abstract":"Abstract One family of candidates to build a post-quantum cryptosystem upon relies on euclidean lattices. In order to make such cryptosystems more efficient, one can consider special lattices with an additional algebraic structure such as ideal lattices. Ideal lattices can be seen as ideals in a number field. However recent progress in both quantum and classical computing showed that such cryptosystems can be cryptanalysed efficiently over some number fields. It is therefore important to study the security of such cryptosystems for other number fields in order to have a better understanding of the complexity of the underlying mathematical problems. We study in this paper the case of multicubic fields.","PeriodicalId":43866,"journal":{"name":"Journal of Mathematical Cryptology","volume":"14 1","pages":"359 - 392"},"PeriodicalIF":1.2,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/jmc-2019-0028","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49239222","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Integer factoring and compositeness witnesses","authors":"J. Pomykala, M. Radziejewski","doi":"10.1515/jmc-2019-0023","DOIUrl":"https://doi.org/10.1515/jmc-2019-0023","url":null,"abstract":"Abstract We describe a reduction of the problem of factorization of integers n ≤ x in polynomial-time (log x)M+O(1) to computing Euler’s totient function, with exceptions of at most xO(1/M) composite integers that cannot be factored at all, and at most x exp −cM(loglog⁡x)3(logloglog⁡x)2 $begin{array}{} displaystyle left(-frac{c_M(loglog x)^3}{(logloglog x)^2}right) end{array}$ integers that cannot be factored completely. The problem of factoring square-free integers n is similarly reduced to that of computing a multiple D of ϕ(n), where D ≪ exp((log x)O(1)), with the exception of at most xO(1/M) integers that cannot be factored at all, in particular O(x1/M) integers of the form n = pq that cannot be factored.","PeriodicalId":43866,"journal":{"name":"Journal of Mathematical Cryptology","volume":"14 1","pages":"346 - 358"},"PeriodicalIF":1.2,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/jmc-2019-0023","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43154657","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"New Techniques for SIDH-based NIKE","authors":"D. Urbanik, David Jao","doi":"10.1515/jmc-2015-0056","DOIUrl":"https://doi.org/10.1515/jmc-2015-0056","url":null,"abstract":"Abstract We consider the problem of producing an efficient, practical, quantum-resistant non-interactive key exchange (NIKE) protocol based on Supersingular Isogeny Diffie-Hellman (SIDH). An attack of Galbraith, Petit, Shani and Ti rules out the use of naïve forms of the SIDH construction for this application, as they showed that an adversary can recover private key information when supplying an honest party with malformed public keys. Subsequently, Azarderakhsh, Jao and Leonardi presented a method for overcoming this attack using multiple instances of the SIDH protocol, but which increases the costs associated with performing a key exchange by factors of up to several thousand at typical security levels. In this paper, we present two new techniques to reduce the cost of SIDH-based NIKE, with various possible tradeoffs between key size and computational cost.","PeriodicalId":43866,"journal":{"name":"Journal of Mathematical Cryptology","volume":"14 1","pages":"120 - 128"},"PeriodicalIF":1.2,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/jmc-2015-0056","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47068904","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quasi-subfield Polynomials and the Elliptic Curve Discrete Logarithm Problem","authors":"Ming-Deh A. Huang, M. Kosters, C. Petit, S. Yeo, Yang Yun","doi":"10.1515/jmc-2015-0049","DOIUrl":"https://doi.org/10.1515/jmc-2015-0049","url":null,"abstract":"Abstract We initiate the study of a new class of polynomials which we call quasi-subfield polynomials. First, we show that this class of polynomials could lead to more efficient attacks for the elliptic curve discrete logarithm problem via the index calculus approach. Specifically, we use these polynomials to construct factor bases for the index calculus approach and we provide explicit complexity bounds. Next, we investigate the existence of quasi-subfield polynomials.","PeriodicalId":43866,"journal":{"name":"Journal of Mathematical Cryptology","volume":"14 1","pages":"25 - 38"},"PeriodicalIF":1.2,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/jmc-2015-0049","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43989020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A signature scheme from the finite field isomorphism problem","authors":"J. Hoffstein, J. Silverman, William Whyte, Zhenfei Zhang","doi":"10.1515/jmc-2015-0050","DOIUrl":"https://doi.org/10.1515/jmc-2015-0050","url":null,"abstract":"Abstract In a recent paper the authors and their collaborators proposed a new hard problem, called the finite field isomorphism problem, and they used it to construct a fully homomorphic encryption scheme. In this paper, we investigate how one might build a digital signature scheme from this new problem. Intuitively, the hidden field isomorphism allows us to convert short vectors in the underlying lattice of one field into generic looking vectors in an isomorphic field.","PeriodicalId":43866,"journal":{"name":"Journal of Mathematical Cryptology","volume":"14 1","pages":"39 - 54"},"PeriodicalIF":1.2,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/jmc-2015-0050","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47527402","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Complexity bounds on Semaev’s naive index calculus method for ECDLP","authors":"K. Yokoyama, Masaya Yasuda, Yasushi Takahashi, Jun Kogure","doi":"10.1515/jmc-2019-0029","DOIUrl":"https://doi.org/10.1515/jmc-2019-0029","url":null,"abstract":"Abstract Since Semaev introduced summation polynomials in 2004, a number of studies have been devoted to improving the index calculus method for solving the elliptic curve discrete logarithm problem (ECDLP) with better complexity than generic methods such as Pollard’s rho method and the baby-step and giant-step method (BSGS). In this paper, we provide a deep analysis of Gröbner basis computation for solving polynomial systems appearing in the point decomposition problem (PDP) in Semaev’s naive index calculus method. Our analysis relies on linear algebra under simple statistical assumptions on summation polynomials. We show that the ideal derived from PDP has a special structure and Gröbner basis computation for the ideal is regarded as an extension of the extended Euclidean algorithm. This enables us to obtain a lower bound on the cost of Gröbner basis computation. With the lower bound, we prove that the naive index calculus method cannot be more efficient than generic methods.","PeriodicalId":43866,"journal":{"name":"Journal of Mathematical Cryptology","volume":"14 1","pages":"460 - 485"},"PeriodicalIF":1.2,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/jmc-2019-0029","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49130029","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An elementary proof of Fermat’s last theorem for all even exponents","authors":"S. B. Karmakar","doi":"10.1515/jmc-2016-0018","DOIUrl":"https://doi.org/10.1515/jmc-2016-0018","url":null,"abstract":"Abstract An elementary proof that the equation x2n + y2n = z2n can not have any non-zero positive integer solutions when n is an integer ≥ 2 is presented. To prove that the equation has no integer solutions it is first hypothesized that the equation has integer solutions. The absence of any integer solutions of the equation is justified by contradicting the hypothesis.","PeriodicalId":43866,"journal":{"name":"Journal of Mathematical Cryptology","volume":"14 1","pages":"139 - 142"},"PeriodicalIF":1.2,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/jmc-2016-0018","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47660715","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}