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1st International Conference on Number-Theoretic Methods in Cryptology (NuTMiC)

作者： Drylo, Robert Pomykala, Jacek Warsaw Sch Econ Al Niepodleglosci 162 PL-02554 Warsaw Poland Fac Math Informat & Mech Ul Banacha 2 PL-02097 Warsaw Poland

ISBN: (纸本)9783319766201;9783319766195

In this paper we describe the reduction of factorization of a square-free integer n to the problem of determining the number of points in Z(n)(d + 1) on twists of Kummer hypersurfaces y(k) = f (x(1), . . . ,x(d)) mod n, where f (x(1), . . . ,x(d)) epsilon Z(n)[xi,. . . ,x(d)] and k > 1. This reduction is expected to be polynomial time (in log n) for small k and fixed number of prime divisors of n provided that some necessary for this reduction conditions are satisfied. This extends the known reduction of factorization to determining the number of points on elliptic curves y(2) = x(3) + ax + b over Z(n). In particular our reduction implies that factorization of n, can be reduced to determining the number of points on quadrics in Z(n)(d), d > 1, which extends the known reduction of factorization to determining the order of Z(n)(*). We also describe the reduction of factorization to determine the number of points in P-2(Z(n)) on superelliptic curves y(k)= f(x(1)) mod n. To study the complexity of these reductions we introduce some notions and prove useful facts for a more precise analysis. In greater detail we consider the case of the reduction when n = pq is a product of two primes and k = 2.

关键词： Dirichlet characters Least r-th power nonresidue integer factorization Reductions Elliptic and hyperelliptic curve Kummer surface

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A Deterministic Algorithm for Computing Divisors in an Interval 23rd

A Deterministic Algorithm for Computing Divisors in an Inter...

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23rd Australasian Conference on Information Security and Privacy (ACISP)

作者： Peng, Liqiang Lu, Yao Kunihiro, Noboru Zhang, Rui Hu, Lei Chinese Acad Sci Inst Informat Engn State Key Lab Informat Secur Beijing 100093 Peoples R China Chinese Acad Sci Data Assurance & Commun Secur Res Ctr Beijing 100093 Peoples R China Univ Tokyo Tokyo Japan

ISBN: (纸本)9783319936383;9783319936376

We revisit the problem of finding a nontrivial divisor of a composite integer when it has a divisor in an interval [alpha, beta]. We use Strassen's algorithm to solve this problem. Compared with Kim-Cheon's algorithms (Math Comp 84(291): 339-354, 2015), our method is a deterministic algorithm but with the same complexity as Kim-Cheon's probabilistic algorithm, and our algorithm does not need to impose that the divisor is prime. In addition, we can further speed up the theoretical complexity of Kim-Cheon's algorithms and our algorithm by a logarithmic term log(beta - alpha) based on the peculiar property of polynomial arithmetic we consider.

关键词： integer factorization Divisors in an interval Polynomial arithmetic

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Use of SIMD-based data parallelism to speed up sieving in integer-factoring algorithms

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APPLIED MATHEMATICS AND COMPUTATION 2017年第0期293卷 204-217页

作者： Sengupta, Binanda Das, Abhijit Indian Inst Technol Dept Comp Sci & Engn Kharagpur 721302 W Bengal India Indian Stat Inst Appl Stat Unit Kolkata 700108 W Bengal India

Many cryptographic protocols derive their security from the apparent computational intractability of the integer factorization problem. Currently, the best known integer-factoring algorithms run in subexponential time. Efficient parallel implementations of these algorithms constitute an important area of practical research. Most reported implementations use multi-core and/or distributed parallelization. In this paper, we use SIMD-based parallelization to speed up the sieving stage of integer-factoring algorithms. We experiment on the two fastest variants of factoring algorithms: the number-field sieve method and the multiple-polynomial quadratic sieve method. Using Intel's SSE2 and AVX intrinsics, we have been able to speed up index calculations in each core during sieving. This performance enhancement is attributed to a reduction in the packing and unpacking overheads associated with SIMD registers. We handle both line sieving and lattice sieving. We also propose improvements to make our implementations cache-friendly. We obtain speedup figures in the range 5-40%. To the best of our knowledge, no public discussions on SIMD parallelization in the context of integer-factoring algorithms are available in the literature. (C) 2016 Elsevier Inc. All rights reserved.

关键词： integer factorization Multiple-polynomial quadratic sieve method Number-field sieve method Lattice sieve method Single instruction multiple data

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Fast Modular Arithmetic on the Kalray MPPA-256 Processor for an Energy-Efficient Implementation of ECM

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IEEE TRANSACTIONS ON COMPUTERS 2017年第12期66卷 2019-2030页

作者： Ishii, Masahiro Detrey, Jeremie Gaudry, Pierrick Inomata, Atsuo Fujikawa, Kazutoshi Tokyo Inst Technol Tokyo 1528550 Japan CNRS INRIA LORIA F-54000 Nancy France Univ Lorraine F-54000 Nancy France Nara Inst Sci & Technol Informat Initiat Ctr Nara 6300101 Japan

The Kalray MPPA-256 processor is based on a recent low-energy manycore architecture. In this article, we investigate its performance in multiprecision arithmetic for number-theoretic applications. We have developed a library for modular arithmetic that takes full advantage of the particularities of this architecture. This is in turn used in an implementation of the ECM, an algorithm for integer factorization using elliptic curves. For parameters corresponding to a cryptanalytic context, our implementation compares well to state-of-the-art implementations on GPU, while using much less energy.

关键词： Kalray MPPA-256 manycore processor multiprecision modular arithmetic integer factorization elliptic curve method

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Finding special factors of values of polynomials at integer points

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INTERNATIONAL JOURNAL OF NUMBER THEORY 2017年第1期13卷 209-228页

作者： Badziahin, Dmitry Univ Durham Dept Math Sci Stockton Rd Durham DH1 3LE England

We investigate the divisors d of the numbers P(n) for various polynomials P is an element of Z[x] such that d equivalent to 1 (mod n). We obtain the complete classification of such divisors for a class of polynomials, in particular for P(x) = x(4) + 1. We also construct a fast algorithm which provides all such factorizations up to a given limit for another class, for example, for P(x) = 2x(4) vertical bar 1. We use these results to find all the divisors d = 2(m)k vertical bar 1 of numbers 2(4m) + 1 and 2(4m+1) + 1. For the numbers 2(4m) + 1, the complete classification of such divisors is provided while for the numbers 2(4m+1) + 1, the given classification is proved to be exhaustive only for m <= 1000.

关键词： integer factorization Cunningham project Fermat number Diophantine equation

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Efficient and Provably Secure Identity-Based Multi-Signature Schemes for Data Aggregation in Marine Wireless Sensor Networks 14

Efficient and Provably Secure Identity-Based Multi-Signature...

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14th IEEE International Conference on Networking, Sensing and Control (ICNSC)

作者： Wei, Lifei Zhang, Lei Huang, Dongmei Zhang, Kai Shanghai Ocean Univ Coll Informat Technol Shanghai 201306 Peoples R China East China Normal Univ Dept Comp Sci & Technol Shanghai 200241 Peoples R China

ISBN: (纸本)9781509044290

Data aggregation is a significant issue for marine wireless sensor networks. However, marine sensors are always deployed far away from the security monitoring. Thus, the secure data aggregation for marine sensor networks emerges and attracts the researchers and engineers. Multi-signature enables the data aggregation with a single signature to authenticate the message under different signers. However, most of the previous multi-signature schemes rely on the technique of bilinear pairing involving in heavy computational overhead or the management of certificates which can not be afforded by the marine wireless sensors. Combined with the concept of identity-based cryptography, few identity-based multi-signature (IBMS) schemes have been designed based on the integer factorization problem and without the bilinear pairing. In this paper, we propose two efficient IBMS schemes under the cubic residue assumption, which is equal to the integer factorization assumption. We employ two different methods to calculate a cubic root for a cubic residue number during the signer's private key extraction. The algorithms are quite efficient compared to the previous work, especially for the algorithms of the multi-signature generation and its verification.

关键词： Marine Wireless Sensor Networks Identity-Based Multi-Signature Cubic Residues integer factorization Security

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PSDAAP: Provably Secure Data Authenticated Aggregation Protocols Using Identity-Based Multi-Signature in Marine WSNs

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SENSORS 2017年第9期17卷 2117-2117页

作者： Wei, Lifei Zhang, Lei Huang, Dongmei Zhang, Kai Dai, Liang Wu, Guojian Shanghai Ocean Univ Coll Informat Technol Shanghai 201306 Peoples R China East China Normal Univ Dept Comp Sci & Technol Shanghai 200241 Peoples R China

Data authenticated aggregation is always a significant issue for wireless sensor networks (WSNs). The marine sensors are deployed far away from the security monitoring. Secure data aggregation for marine WSNs has emerged and attracted the interest of researchers and engineers. A multi-signature enables the data aggregation through one signature to authenticate various signers on the acknowledgement of a message, which is quite fit for data authenticated aggregation marine WSNs. However, most of the previous multi-signature schemes rely on the technique of bilinear pairing involving heavy computational overhead or the management of certificates, which cannot be afforded by the marine wireless sensors. Combined with the concept of identity-based cryptography, a few pairing-free identity-based multi-signature (IBMS) schemes have been designed on the basis of the integer factorization problem. In this paper, we propose two efficient IBMS schemes that can be used to construct provably secure data authenticated aggregation protocols under the cubic residue assumption, which is equal to integer factorization. We also employ two different methods to calculate a cubic root for the cubic residue number during the signer's private key extraction. The algorithms are quite efficient compared to the previous work, especially for the algorithms of the multi-signature generation and its verification.

关键词： identity-based multi-signature provably secure integer factorization data authenticated aggregation marine WSNs

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A Modification of the Rabin Cryptosystem Based on Cubic Residues

A Modification of the Rabin Cryptosystem Based on Cubic Resi...

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2017 2nd International Conference on Communications, Information Management and Network Security (CIMNS2017)

作者： Xue-dong DONG Shuo HAN Yun-feng BAI College of Information Engineering Dalian University

In the Rabin cryptosystem there are four different decryption results for each ciphertext. Thus, extra complexity is required on decryption to identify which of the four possible decryption results is the true plaintext. We propose a modification of the Rabin cryptosystem based on cubic residues. Let p and q be primes, N pq. The sender Bob computes ciphertext 3 c m（mod N） to Alice, where m is a confidential message. Alice decrypts the ciphertext c by the proposed method in this paper and gets the only one plaintext m. The proposed cryptosystem is provably secure against a chosen plaintext attack if and only if the integer factorization problem is hard.

关键词： Rabin cryptosystem Cubic residue integer factorization Chosen plaintext attack

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Erasing Logic-Memory Boundaries in Superconductor Electronics

Erasing Logic-Memory Boundaries in Superconductor Electronic...

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IEEE International Conference on Rebooting Computing (ICRC)

作者： Semenov, Vasili K. SUNY Stony Brook Dept Phys & Astron Stony Brook NY 11794 USA

ISBN: (纸本)9781509013708

Superconductor electronics holds records for clock frequency and energy efficiency at the chip level, and is also projected to large systems that can absorb the cooling overhead. These advantages have nevertheless only managed to give this technology a back seat to CMOS digital circuits, which offer orders of magnitude more complexity. Furthermore, pursuing the CMOS paradigm with superconductor circuits would bring their clock frequency down to that of CMOS circuits. This makes superconductor technology much more open to risky innovations and even for paradigm changes. In the paper we point out that both (speed and energy efficiency) advantages of superconductor electronics could be preserved due to a unique composition of memory and logic functions of RSFQ cells. We propose to reorganize the original RSFQ cells into a new family of Memory And loGIC (MAGIC) gate/register objects that run arithmetic calculations as well as store results. The new MAGIC objects eliminate the time and energy overheads associated with the conventional transfer of computed data to memory by essentially reducing the transfer distance to zero. The new objects could serve as building blocks for distributed MAGIC-compatible architectures, differing from CMOS-like register files by processing as well as storing data. A simple Logic Unit (LU) would be sufficient to control the MAGIC registers, because the registers would provide most of the arithmetic functions and separate ALUs would not be needed. The reduction of the data exchange between logic and memory units leads to additional energy saving. factorization of large integers is presented as an example illustrating the speed and density advantages of the new approach. The end result will be a superior technology which offers a combination of performance and energy efficiency unattainable by existing technologies or their possible extensions.

关键词： superconductor electronics finite state machines speed of light limitation flip-flops with logic logic in memory integer factorization

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An UF-IBSS-CMA Protected Online/Offline Identity-based Short Signature Technique using PDL

An UF-IBSS-CMA Protected Online/Offline Identity-based Short...

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6th International Conference on Advances in Computing and Communications (ICACC)

作者： Meshram, Chandrashekhar Y. Powar, P. L. Obaidat, Mohammad S. Rani Durgavati Univ Dept Math & Comp Sci Jabalpur MP India Fordham Univ Dept Comp & Informat Sci Bronx NY 10458 USA

In this article, we present an online/offline identity-based short signature scheme using partial discrete logarithm (PDL). It is secure under unforgeability of identity-based short signature (IBSS) under chosen message attack (UF-IBSS-CMA) in random oracle. One of the interesting structures of our techniques is that it gives multi-time usage of the offline storage, which permits the signer to re-utilize the offline pre-processed info in polynomial time, as opposed to one-time usage in all past online/offline signature techniques. Our scheme is practical and feasible to be utilized in the wireless sensor network environment. (C) 2016 The Authors. Published by Elsevier B.V.

关键词： cryptography identity-based short signature(IBSS) PDL random oracle integer factorization

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