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检索条件"主题词=LLL Algorithm"

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A Lattice Attack on Homomorphic NTRU with Non-invertible Public Keys 19th

A Lattice Attack on Homomorphic NTRU with Non-invertible Pub...

引用

19th International Conference on Information and Communications Security (ICICS)

作者： Ahn, Soyoung Lee, Hyang-Sook Lim, Seongan Yie, Ikkwon Ewha Womans Univ Dept Math Seoul South Korea Ewha Womans Univ Inst Math Sci Seoul South Korea Inha Univ Dept Math Incheon South Korea

ISBN: (纸本)9783319895000;9783319894997

In 2011, Stehle and Steinfeld modified the original NTRU to get a provably IND-CPA secure NTRU under the hardness assumption of standard worst-case problems over ideal lattices. In 2012, Lopez-Alt et al. proposed the first multikey fully homomorphic encryption scheme based on the IND-CPA secure NTRU. Interestingly, this homomorphic NTRU and subsequent homomorphic variants of NTRU removed the condition 'invertible public key' of the underlying IND-CPA secure NTRU. In this paper, we investigate the security influence of using non-invertible public key in the homomorphic NTRU. As a result, we present how to mount a lattice attack to message recovery for the homomorphic NTRU when the public key is non-invertible. Our result suggests that using invertible public keys in the homomorphic NTRU is necessary for its security.

关键词： NTRU Homomorphic NTRU IND-CPA security Lattices lll algorithm

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Decoding by Embedding: Correct Decoding Radius and DMT Optimality

Decoding by Embedding: Correct Decoding Radius and DMT Optim...

引用

IEEE International Symposium on Information Theory (ISIT)

作者： Ling, Cong Liu, Shuiyin Luzzi, Laura Stehle, Damien Univ London Imperial Coll Sci Technol & Med Dept Elect & Elect Engn London SW7 2AZ England

ISBN: (纸本)9781457705953

In lattice-coded multiple-input multiple-output (MIMO) systems, optimal decoding amounts to solving the closest vector problem (CVP). Embedding is a powerful technique for the approximate CVP, yet its remarkable performance is not well understood. In this paper, we analyze the embedding technique from a bounded distance decoding (BDD) viewpoint. 1/(2 gamma)-BDD is referred to as a decoder that finds the closest vector when the noise norm is smaller than lambda(1)/(2 gamma), where lambda(1) is the minimum distance of the lattice. We prove that the Lenstra, Lenstra and Lovasz (lll) algorithm can achieve 1/(2 gamma)-BDD for gamma approximate to O(2(n/4)). This substantially improves the existing result gamma = O(2(n)) for embedding decoding. We also prove that BDD of the regularized lattice is optimal in terms of the diversity-multiplexing gain tradeoff (DMT).

关键词： BDD viewpoint Boolean functions CVP Complexity theory DMT optimality Data structures lll algorithm Lattices MIMO communication MIMO system Maximum likelihood decoding Signal to noise ratio bounded distance decoding viewpoint closest vector problem decoding diversity reception diversity-multiplexing gain tradeoff embedding decoding radius lattice-coded multiple-input multiple-output systems

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Enhancing an Attack to DSA Schemes 8th

Enhancing an Attack to DSA Schemes

引用

8th International Conference on Algebraic Informatics (CAI)

作者： Adamoudis, Marios Draziotis, Konstantinos A. Poulakis, Dimitrios Aristotle Univ Thessaloniki Dept Math Thessaloniki Greece Aristotle Univ Thessaloniki Dept Informat Thessaloniki Greece

In this paper, we improve the theoretical background of the attacks on the DSA schemes of a previous paper, and we present some new more practical attacks.

ISBN: (纸本)9783030213633;9783030213626

In this paper, we improve the theoretical background of the attacks on the DSA schemes of a previous paper, and we present some new more practical attacks.

关键词： Public key cryptography Digital Signature algorithm Elliptic Curve Digital Signature algorithm Closest Vector Problem lll algorithm BKZ algorithm Babai's Nearest Plane algorithm

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Cryptanalysis of a Privacy Preserving Auditing for Data Integrity Protocol from TrustCom 2013 1

引用

12th International Conference on Information Security Practice and Experience (ISPEC)

作者： Bi, Jingguo Liu, Jiayang Tsinghua Univ Inst Adv Study Beijing 100084 Peoples R China State Key Lab Cryptol Beijing 100878 Peoples R China Tsinghua Univ Dept Comp Sci & Technol Beijing 100084 Peoples R China

ISBN: (数字)9783319491516

ISBN: (纸本)9783319491516;9783319491509

At TrustCom 2013, Govinda Ramaiah and Vijaya Kumari proposed a new protocol for verifying the integrity of the data stored at the remote cloud server, based on a practical version of homomorphic encryption based on integers. This protocol attempted to combine the data integrity and confidentiality in new ways. The authors claimed that the privacy guarantee of this new protocol is totally dependent on the security of the homomorphic encryption scheme. In this paper, we present a chosen-plaintext attack on this homomorphic encryption scheme. Our attack only needs to apply lll algorithm twice on two small dimension lattices, and the experiments data shows that the user data can be recovered in seconds for the security parameters recommended by the authors. Hence, the privacy of the user data in this protocol can not be guaranteed and the security of this protocol is overestimated.

关键词： Cloud computing Homomorphic encryption Auditing protocol lll algorithm Chosen-plaintext attack

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LOW-COMPLEXITY LATTICE REDUCTION ARCHITECTURE USING INTERPOLATION-BASED QR DECOMPOSITION FOR MIMO-OFDM SYSTEMS

LOW-COMPLEXITY LATTICE REDUCTION ARCHITECTURE USING INTERPOL...

引用

IEEE Asia Pacific Conference on Circuits and Systems (APCCAS)

作者： Liu, I-Wen Liao, Chun-Fu Lan, Fang-Chun Huang, Yuan-Hao Natl Tsing Hua Univ Inst Commun Engn Hsinchu Taiwan Natl Tsing Hua Univ Dept Elect Engn Hsinchu Taiwan

ISBN: (纸本)9781457717284;9781457717291

Lattice reduction (LR) technique is well known for its capability of improving MIMO detection performance. Nevertheless, the complexity increases significantly when LR is applied to all sub-carriers in the orthogonal-frequency division-multiplexing (OFDM) system. To address this issue, this research proposes an interpolation-based preprocessing architecture for LR-aided MIMO-OFDM system. The proposed architecture combines the interpolation-based QR decomposition and grouping architecture to decrease the iteration loops of LR by adopting lattice matrix of adjacent sub-carrier. The experiment compares the BER performance of the proposed method with those of other works in the channel of the 3GPP-LTE system. The experimental results show that the proposed LR architecture not only shortens latency but also reduce computational complexity and hardware cost for MIMO-OFDM systems.

关键词： Lattice Reduction QR decomposition lll algorithm MIMO OFDM

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Efficient Quantization Scheme for Lattice-Reduction Aided MIMO Detection

Efficient Quantization Scheme for Lattice-Reduction Aided MI...

引用

International Conference on Advanced Technologies for Communications (ATC)

作者： Hou, Wei Fujino, Tadashi Kojima, Toshiharu Univ Electrocommun Grad Sch Informat & Commun Engn & Informat Tokyo 1828585 Japan

ISBN: (纸本)9781479910861;9781479910885

In this paper, we present an efficient quantization scheme for lattice-reduction (LR) aided (LRA) MIMO detection using Gram-Schmidt orthogonalization. For the LRA detection, the quantization step applies the simple rounding operation, which often leads to the quantization errors. Meanwhile, these errors may result in the detection errors. Hence, the motivation of the proposed detection is to further solve the problem of degrading the performance due to the quantization errors in the signal estimation. In this paper, the proposed quantization scheme decreases the quantization errors using a simple tree search with a threshold function. Through the analysis and the simulation results, the proposed detection can achieve the near-ML performance with only a little additional complexity.

关键词： Gram-Schmidt Orthogonalization lll algorithm Lattice-reduction MIMO Quantization error

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Factoring RSA Moduli with Weak Prime Factors 1st

Factoring RSA Moduli with Weak Prime Factors

引用

1st International Conference on Codes, Cryptology, and Information Security (C2SI) In Honor of Thierry Berger

作者： Nitaj, Abderrahmane Rachidi, Tajjeeddine Univ Caen Basse Normandie Lab Math Nicolas Oresme Caen France Al Akhawayn Univ Sch Sci & Engn Ifrane Morocco

ISBN: (纸本)9783319186818;9783319186801

In this paper, we study the problem of factoring an RSA modulus N = pq in polynomial time, when p is a weak prime, that is, p can be expressed as ap = u(0) + M(1)u(1) + ... + M(k)u(k) for some k integers M-1, ... , M-k and k+2 suitably small parameters a, u(0), ... u(k). We further compute a lower bound for the set of weak moduli, that is, moduli made of at least one weak prime, in the interval [2(2n), 2(2(n+1))] and show that this number is much larger than the set of RSA prime factors satisfying Coppersmith's conditions, effectively extending the likelihood for factoring RSA moduli. We also prolong our findings to moduli composed of two weak primes.

关键词： RSA Cryptanalysis Factorization lll algorithm Weak primes

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Recovering a Sum of Two Squares Decomposition Revisited 11th

Recovering a Sum of Two Squares Decomposition Revisited

引用

11th China International Conference on Information Security and Cryptology (Inscrypt)

作者： Zhang, Xiaona Wang, Li-Ping Xu, Jun Hu, Lei Peng, Liqiang Huang, Zhangjie Liu, Zeyi 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 Univ Chinese Acad Sci Beijing Peoples R China

ISBN: (纸本)9783319388984;9783319388977

Recently, in [6] Gomez et al. presented algorithms to recover a decomposition of an integer N = rA(2) + sB(2), where N, r, s are positive integers, and A, B are the wanted unknowns. Their first algorithm recovers two addends by directly using rigorous Coppersmith's bivariate integer method when the error bounds of given approximations to A and B are less than N-1/6. Then by combining with the linearization technique, they improved this theoretical bound to N-1/4. In this paper, we heuristically reach the bound N-1/4 with experimental supports by transforming the integer polynomial concerned in their first algorithm into a modular one. Then we describe a better heuristic algorithm, the dimension of the lattice involved in this improved method is much smaller under the same error bounds.

关键词： Sum of squares Lattice lll algorithm Coppersmith's method

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New Attacks on the RSA Cryptosystem

New Attacks on the RSA Cryptosystem

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7th International Conference on Cryptology in Africa (AFRICACRYPT)

作者： Nitaj, Abderrahmane Ariffin, Muhammad Rezal Kamel Nassr, Dieaa I. Bahig, Hatem M. Univ Caen Basse Normandie Lab Math Nicolas Oresme Caen France Inst Math Res Al Kindi Cryptog Res Lab Serdang Malaysia Univ Putra Malaysia Fac Sci Dept Math Serdang 43400 Malaysia Ain Shams Univ Fac Sci Dept Math Div Comp Sci Cairo Egypt

ISBN: (纸本)9783319067339;9783319067346

This paper presents three new attacks on the RSA cryptosystem. The first two attacks work when k RSA public keys (N-i, e(i)) are such that there exist k relations of the shape e(i)x-y(i)phi(N-i) = z(i) or of the shape e(i)x(i) - y phi(N-i) = z(i) where N-i = p(i)q(i), phi(N-i) = (p(i) -1)(q(i) -1) and the parameters x, x(i), y, y(i), z(i) are suitably small in terms of the prime factors of the moduli. We show that our attacks enable us to simultaneously factor the k RSA moduli Ni. The third attack works when the prime factors p and q of the modulus N = pq share an amount of their least significant bits (LSBs) in the presence of two decryption exponents d(1) and d(2) sharing an amount of their most significant bits (MSBs). The three attacks improve the bounds of some former attacks that make RSA insecure.

关键词： RSA Cryptanalysis Factorization lll algorithm Simultaneous diophantine approximations Coppersmith's method

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New Results of Breaking the CLS Scheme from ACM-CCS 2014 24th

New Results of Breaking the CLS Scheme from ACM-CCS 2014

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24th International Conference on Information and Communications Security (ICICS)

作者： Gao, Jing Xu, Jun Wang, Tianyu Hu, Lei Chinese Acad Sci Inst Informat Engn State Key Lab Informat Secur Beijing 100093 Peoples R China Univ Chinese Acad Sci Sch Cyber Secur Beijing 100093 Peoples R China

ISBN: (纸本)9783031157776;9783031157769

At ACM-CCS 2014, Cheon, Lee and Seo introduced a particularly fast additively homomorphic encryption scheme (CLS scheme) based on a new number theoretic assumption, the co-Approximate Common Divisor (co-ACD) assumption. However, at Crypto 2015, Fouque et al. presented several lattice-based attacks that effectively devastated this scheme. They proved that a few known plaintexts are sufficient to break both the symmetric-key and the public-key variants, and they gave a heuristic lattice method for solving the search co-ACD problem. In this paper, we mainly improve in terms of the number of samples, and propose a new key-retrieval attack. We first give an effective attack by Coppersmith's method to break the co-ACD problem with N = p(1) center dot center dot center dot p(n) is known. If n is within a certain range, our work is theoretically valid for a wider range of parameters. When n = 2, we can successfully solve it with only two samples, that is the smallest number of needed samples to the best of our knowledge. A known plaintext attack on the CLS scheme can be simply converted to solving the co-ACD problem with a known N, again requiring fewer samples than before to retrieve the private key. Finally, we show a ciphertext-only attack with a hybrid approach of direct lattice and Coppersmith's method that can recover the key with a smaller number of ciphertexts and without any restriction on the plaintext size, but N is needed. All of our attacks are heuristic, but we have experimentally verified that these attacks work efficiently for the parameters proposed in the CLS scheme, which can be broken in seconds by experiments.

关键词： co-ACD problem Lattice lll algorithm Coppersmith's method

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