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32nd IEEE International Conference on Acoustics, Speech and Signal Processing

作者： Seethaler, Dominik Matz, Gerald Hlawatsch, Franz Vienna Univ Technol Inst Commun & Radio Frequency Engn Gusshaustr 25-389 A-1040 Vienna Austria

ISBN: (纸本)1424407281

Lattice reduction (LR) is a powerful technique for improving the performance of suboptimum MIMO data detection methods. For LR-assisted data detection, the lll algorithm has been considered almost exclusively so far. In this paper, we propose and develop the application of Seysen's algorithm (SA) to LR-assisted MIMO detection, and we show that the SA is a promising alternative to, the lll algorithm. Specifically, the SA outperforms the lll algorithm in that it finds better lattice bases for MIMO systems of practical interest, which is reflected by an improved performance of SA-assisted detectors relative to their lll-assisted counterparts. We present an efficient implementation of the SA whose per-iteration complexity is linear in the number of antennas, and we demonstrate that the SA requires significantly fewer iterations than the lll algorithm.

关键词： MIMO data detection spatial multiplexing lattice reduction lll algorithm Seysen's algorithm

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NTRU-Like Secure and Effective Congruential Public-Key Cryptosystem Using Big Numbers 2

NTRU-Like Secure and Effective Congruential Public-Key Crypt...

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2nd International Conference on New Trends in Computing Sciences (ICTCS)

作者： Ibrahim, Anas Chefranov, Alexander Hamad, Nagham Eastern Mediterranean Univ Dept Comp Engn Famagusta North Cyprus Turkey Palestine Tech Univ Tulkarem Palestine

ISBN: (纸本)9781728128825

We propose RCPKC, a random congruential public key cryptosystem working on integers modulo q, such that the norm of a two-dimensional vector formed by its private key, (f;g), is greater than q. RCPKC works similar to NTRU, the fastest and secure PKC. NTRU, uses high order, N, polynomials and is susceptible to the lattice basis reduction attack (LBRA) taking time exponential in N. RCPKC is a secure version of insecure CPKC proposed by NTRU authors and easily attackable by LBRA since CPKC uses small numbers for the sake of the correct decryption. RCPKC specifies a range from which the random numbers shall be selected, it provides correct decryption for valid users and incorrect decryption for an attacker using Gaussian Lattice Reduction (GLR). Because of its resistance to LBRA, RCPKC is more secure, and, due to the use of big numbers instead of high order polynomials, about 24 (7) times faster in encryption (decryption) than NTRU. Also, RCPKC is more than 3 times faster than the most effective known NTRU variant, BQTRU.

关键词： Congruential public-key cryptosystem Integer Lattice Lattice basis reduction attack lll algorithm Minkowski's boundary for a lattice shortest vector norm NTRU Polynomial

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A Gram-Schmidt Based Lattice-Reduction Aided MMSE Detection in MIMO Systems

A Gram-Schmidt Based Lattice-Reduction Aided MMSE Detection ...

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IEEE Global Telecommunications Conference (GLOBECOM 09)

作者： Fujino, Tadashi Wakazono, Shinjiro Sasaki, Yusuke Univ Electrocommun Chofu Tokyo 1828585 Japan

ISBN: (纸本)9781424441471

This paper proposes an improved lattice-reduction aided (IRA) MMSE detection based on the Gram-Schmidt (GS) procedure. The proposed detection reduces the column vectors of the MIMO channel matrix using the lll algorithm and the GS procedure to create mutually purely orthogonal column vectors of the reduced channel matrix. Then the decision boundary becomes the same as that for the ML detection. Compared to the conventional LRA MMSE detector, the proposed detector achieves much closer BER performances to those for the ML detector in both the 4x4 MIMO and the 8x8 MIMO systems.

关键词： Gram-Schmidt orthogonalization lattice-reduction lll algorithm MIMO MMSE signal estimation

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Computing the Shortest Vector in a Lattice Using the Alternating Direction Method of Multipliers

Computing the Shortest Vector in a Lattice Using the Alterna...

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Computing Conference

作者： Al Kendi, Wissam Chretien, Stephane Guyeux, Christophe Univ Franche Comte IUT Belfort Lab DISC FEMTO ST Belfort France

ISBN: (纸本)9783031622830;9783031622816;9783031622809

Computing the shortest vector in a lattice has many applications in computer science and engineering such as in cryptography, coding theory, and quantum computing. One of the best known algorithms for computing such shortest vectors is the Lenstra, Lenstra and Lovasz (lll) algorithm. Unfortunately the lll algorithm has a worst-case exponential running time, and its practical performance depends heavily on the lattice structure. In this paper, we propose an efficient implementation of the Alternating Direction Method of Multipliers for finding the shortest vector in a lattice. Our algorithm is an improved stochastic version of the ADMM algorithm proposed by Takapoui, Moehle, Boyd and Bemporad. The performance of our method is illustrated via extensive numerical experiments on various lattice structures. The numerical results show that our method significantly outperforms the lll algorithm in terms of running time and solution quality.

关键词： Shortest vector Lattice lll algorithm ADMM algorithm

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Partial Key Exposure Attacks on Takagi's Variant of RSA

Partial Key Exposure Attacks on Takagi's Variant of RSA

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12th International Conference on Applied Cryptography and Network Security (ACNS)

作者： Huang, Zhangjie Hu, Lei Xu, Jun Peng, Liqiang Xie, Yonghong Chinese Acad Sci Inst Informat Engn State Key Lab Informat Secur Beijing 100093 Peoples R China

ISBN: (纸本)9783319075365;9783319075358

We present several attacks on a variant of RSA due to Takagi when different parts of the private exponent are known to an attacker. We consider three cases when the exposed bits are the most significant bits, the least significant bits and the middle bits of the private exponent respectively. Our approaches are based on Coppersmith's method for finding small roots of modular polynomial equations. Our results extend the results of partial key exposure attacks on RSA of Ernst, Jochemsz, May and Weger (EUROCRYPT 2005) for moduli from N = pq to N = p(r)q (r >= 2).

关键词： RSA partial key exposure Coppersmith's method lattice reduction lll algorithm

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Cryptanalysis of Multi-Prime Φ-Hiding Assumption 19th

Cryptanalysis of Multi-Prime Φ-Hiding Assumption

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19th Annual International Conference on Information Security (ISC)

作者： Xu, Jun Hu, Lei Sarkar, Santanu Zhang, Xiaona Huang, Zhangjie Peng, Liqiang Chinese Acad Sci State Key Lab Informat Secur Inst Informat Engn Beijing 100093 Peoples R China Chinese Acad Sci Data Assurance & Commun Secur Res Ctr Beijing 100093 Peoples R China Indian Inst Technol Sardar Patel Rd Madras 600036 Tamil Nadu India

ISBN: (纸本)9783319458717;9783319458700

In Crypto 2010, Kiltz, O'Neill and Smith used m-prime RSA modulus N with m >= 3 for constructing lossy RSA. The security of the proposal is based on the Multi-Prime Phi-Hiding Assumption. In this paper, we propose a heuristic algorithm based on the Herrmann-May lattice method (Asiacrypt 2008) to solve the Multi-Prime Phi-Hiding Problem when prime e > N-2/3m. Further, by combining with mixed lattice techniques, we give an improved heuristic algorithm to solve this problem when prime e > N2/3m-1/4m2. These two results are verified by our experiments. Our bounds are better than the existing works.

关键词： Multi-Prime Phi-Hiding Assumption Multi-Prime Phi-Hiding Problem Lattice lll algorithm Coppersmith's technique Gauss algorithm

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Investigating Vulnerabilities in RSA-like Cryptosystems Through Lattice-based Attacks on Small Exponent Keys 11

Investigating Vulnerabilities in RSA-like Cryptosystems Thro...

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11th IEEE International Conference on Consumer Electronics - Taiwan (ICCE-Taiwan) - Empower of Innovative Consumer Technology

作者： Kumagai, Sou Kanzawa, Shota Huda, Samsul Kodera, Yuta Nogami, Yasuyuki Okayama Univ Grad Sch Environm Life Nat Sci & Technol Okayama Japan Japan Res Inst Ltd 2-18-1 HigashigotandaShinagawa Ku Tokyo 1410022 Japan Okayama Univ Green Innovat Ctr Okayama Japan

ISBN: (纸本)9798350386851;9798350386844

RSA-like cryptosystems, based on the original RSA algorithm, are gaining attention as potential alternatives to traditional techniques. They offer better security, efficiency, flexibility, and compatibility in cryptography. However, recent studies have uncovered vulnerabilities in these variants, particularly to Wiener-type attacks, despite initial expectations of security comparable to RSA. In this paper, we further investigate the security vulnerabilities of a variant of this technique, namely the Murru-Saettone (MS) cryptosystem. Our investigation employs lattice-based attacks to exploit weaknesses in systems with small private keys. It demonstrates that if the private exponent is smaller than N-1/4, where N is the product of two distinct balanced primes, the small exponent of the cryptosystem can be recovered.

关键词： RSA-like cryptosystems small exponent attack lattice lll algorithm

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A Combined Forward and Backward Lattice-Reduction Aided MMSE List Detection

A Combined Forward and Backward Lattice-Reduction Aided MMSE...

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International Conference on Advanced Technologies for Communications

作者： Fujino, Tadashi Shimokawa, Tetsuyoshi Tran, Xuan Nam Univ Electrocommun Chofu Tokyo 1828585 Japan Le Qui Don Tech Univ Hanoi Vietnam

ISBN: (纸本)9781424426805

This paper proposes a combined forward and backward lattice-reduction aided detection scheme to improve estimation of transmitted signals in lattice-reduction aided (LRA) MMSE MIMO systems. The cross-cor relation between the forward and the backward reduced channel matrices is also analyzed to make sure that the proposed detector achieves more reliable estimates. The proposed detector achieves much better BER performance than the conventional LRA detector in the 4x4 and the W MIMO systems. It is also shown that the achieved BER curve moves closer to the curve of the ML detector than that of the conventional LRA MMSE detector.

关键词： lattice-reduction lll algorithm MIMO MMSE signal estimation

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Multiplicative dependence between Padovan and Perrin numbers

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BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA 2023年第2期29卷 1-12页

作者： Behera, Mitashree Ray, Prasanta Kumar Sambalpur Univ Sambalpur India

Padovan and Perrin sequences are ternary recurrent sequences that satisfy the same relation w(n) = w(n-2 )+ w(n-3) with different initial conditions (w(0), w(1), w(2)) = (1, 1, 1) and (3, 0, 2), respectively. In this ... 详细信息

关键词： Padovan numbers Perrin numbers Linear forms in logarithms lll algorithm Multiplicative dependent

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Solving Generalized Small Inverse Problems

Solving Generalized Small Inverse Problems

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15th Australasian conference, ACISP 2010

作者： Kunihiro, Noboru Univ Tokyo Tokyo 1138654 Japan

ISBN: (纸本)9783642140808

We introduce a "generalized small inverse problem (GSIP)" and present an algorithm for solving this problem. GSIP is formulated as finding small solutions of f(x(0), x(1), . . , x(n)) = x(0)h(x(1), . . . , x(n)) + C = 0(mod M) for an n-variate polynomial h, non-zero integers C and M. Our algorithm is based on lattice-based Coppersmith technique. We provide a strategy for construction of a lattice basis for solving f = 0, which are systematically transformed from a lattice basis for solving h = 0. Then, we derive an upper bound such that the target problem can be solved in polynomial time in log M in an explicit form. Since GSIPs include some RSA-related problems, our algorithm is applicable to them. For example, the small key attacks by Boneh and Durfee are re-found automatically.

关键词： lll algorithm small inverse problem RSA lattice-based cryptanalysis

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