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NTRU-Like Random Congruential Public-Key Cryptosystem for Wireless Sensor Networks

SENSORS 2020年第16期20卷 4632页

作者： Ibrahim, Anas Chefranov, Alexander Hamad, Nagham Daraghmi, Yousef-Awwad Al-Khasawneh, Ahmad Rodrigues, Joel J. P. C. Palestine Tech Univ Kadoorie Dept Comp Syst Engn Tulkarm 7 Palestine Eastern Mediterranean Univ Dept Comp Engn Via Mersin 10 TR-99628 Famagusta North Cyprus Turkey Palestine Tech Univ Kadoorie Dept Informat Technol Tulkarm 7 Palestine Irbid Natl Univ POB 2600 Irbid 21110 Jordan Hashemite Univ Dept Comp Informat Syst POB 150459 Zarqa 13115 Jordan Univ Fed Piaui BR-64049550 Teresina PI Brazil Inst Telecomunicacoes P-6201001 Covilha Portugal

Wireless sensor networks (WSNs) are the core of the Internet of Things and require cryptographic protection. Cryptographic methods for WSN should be fast and consume low power as these networks rely on battery-powered devices and microcontrollers. NTRU, the fastest and secure public key cryptosystem, uses high degree,N, polynomials and is susceptible to the lattice basis reduction attack (LBRA). Congruential public key cryptosystem (CPKC), proposed by the NTRU authors, works on integers moduloqand is easily attackable by LBRA since it uses small numbers for the sake of the correct decryption. Herein, RCPKC, a random congruential public key cryptosystem working on degreeN=0polynomials moduloq, is proposed, such that the norm of a two-dimensional vector formed by its private key is greater thanq. RCPKC works as NTRU, and it is a secure version of insecure CPKC. RCPKC specifies a range from which the random numbers shall be selected, and it provides correct decryption for valid users and incorrect decryption for an attacker using LBRA by Gaussian lattice reduction. RCPKC asymmetric encryption padding (RAEP), similar to its NTRU analog, NAEP, is IND-CCA2 secure. Due to the use of big numbers instead of high degree polynomials, RCPKC is about 27 times faster in encryption and decryption than NTRU. Furthermore, RCPKC is more than three times faster than the most effective known NTRU variant, BQTRU. Compared to NTRU, RCPKC reduces energy consumption at least thirty times, which allows increasing the life-time of unattended WSNs more than thirty times.

关键词： wireless sensor network random congruential public-key cryptosystem lattice NTRU polynomial lattice basis reduction attack lll algorithm Gaussian lattice reduction IND-CCA2 security

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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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Secure Outsourcing of Lattice Basis Reduction 26th

Secure Outsourcing of Lattice Basis Reduction

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26th International Conference on Neural Information Processing (ICONIP) of the Asia-Pacific-Neural-Network-Society (APNNS)

作者： Liu, Jiayang Bi, Jingguo Tsinghua Univ Beijing 100084 Peoples R China Beijing Res Inst Telemetry Beijing 100094 Peoples R China

ISBN: (纸本)9783030367114;9783030367107

In the recent twenty years, lattice basis reduction algorithm, such as the celebrated lll (A.K. Lenstra-H.W. Lenstra Jr.-L. Lovasz) algorithm plays an important role in the public-key schemes design and cryptanalysis. To assess the security of the public-key cryptosystems by lattice reduction algorithms, the most time-consuming part is running the lattice reduction algorithm on the corresponding lattice with high dimension or big coefficients. In this paper, we investigate secure out-sourcing for lattice basis reduction for the first time. We propose a lattice basis reduction scheme such that the clients can outsource their main computation workloads to the untrusted cloud servers. We employ rounding technique and unimodular transformation matrix for privacy protection before sending the target lattice basis to the cloud. The results returned from the cloud need to be decrypted and verified to satisfy reduction conditions. The experimental results indicate that our scheme is correct, efficient and feasible.

关键词： Cloud computing Outsource-secure Lattice basis reduction lll algorithm QR-factorization

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New Results on Modular Inversion Hidden Number Problem and Inversive Congruential Generator 1

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39th Annual International Cryptology Conference (CRYPTO)

作者： Xu, Jun Sarkar, Santanu Hu, Lei Wang, Huaxiong Pan, Yanbin 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 Indian Inst Technol Madras Dept Math Sardar Patel Rd Chennai 600036 Tamil Nadu India Nanyang Technol Univ Singapore Sch Phys & Math Sci Div Math Sci Singapore Singapore Chinese Acad Sci Key Lab Math Mech NCMIS Acad Math & Syst Sci Beijing 100190 Peoples R China Univ Chinese Acad Sci Sch Cyber Secur Beijing 100049 Peoples R China

ISBN: (数字)9783030269487

ISBN: (纸本)9783030269487;9783030269470

The Modular Inversion Hidden Number Problem (MIHNP), introduced by Boneh, Halevi and Howgrave-Graham in Asiacrypt 2001, is briefly described as follows: Let MSB delta(z) refer to the delta most significant bits of z. Given many samples (t(i), MSB delta((alpha + t(i))(-1) mod p)) for random t(i) is an element of Z(p), the goal is to recover the hidden number alpha is an element of Z(p). MIHNP is an important class of Hidden Number Problem. In this paper, we revisit the Coppersmith technique for solving a class of modular polynomial equations, which is respectively derived from the recovering problem of the hidden number alpha in MIHNP. For any positive integer constant d, let integer n = d(3+o(1)). Given a sufficiently large modulus p, n + 1 samples of MIHNP, we present a heuristic algorithm to recover the hidden number a with a probability close to 1 when delta/log(2) p > 1/d + 1 + o(1/d). The overall time complexity of attack is polynomial in log(2) p, where the complexity of the lll algorithm grows as d(O(d)) and the complexity of the Grobner basis computation grows as (2d)(O(n2)()). When d > 2, this asymptotic bound outperforms delta/log(2) p > 1/3 which is the asymptotic bound proposed by Boneh, Halevi and Howgrave-Graham in Asiacrypt 2001. It is the first time that a better bound for solving MIHNP is given, which implies that the conjecture that MIHNP is hard whenever delta/log(2)p < 1/3 is broken. Moreover, we also get the best result for attacking the Inversive Congruential Generator (ICG) up to now.

关键词： Modular Inversion Hidden Number Problem Inversive Congruential Generator Lattice lll algorithm The Coppersmith technique

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lll algorithm and the Optimal Finite Wordlength FIR Design

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2012年第3期60卷 1493-1498页

作者： Kodek, Dusan M. Univ Ljubljana Fac Comp & Informat Sci Ljubljana 1000 Slovenia

In practical finite-impulse-response (FIR) digital filter applications, it is often necessary to represent the filter coefficients with a finite number of bits. The finite wordlength restriction increases the filter deviation. This increase can be reduced substantially if the optimal finite wordlength coefficients are used. The time needed to compute these coefficients is greatly reduced with the help of a lower bound on the deviation increase. Derivation of an improved lower bound that uses the well-known lll algorithm is presented in this correspondence.

关键词： Finite wordlength FIR digital filters lll algorithm minimax approximation

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A Lattice Basis Reduction Approach for the Design of Finite Wordlength FIR Filters

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2018年第10期66卷 2673-2684页

作者： Brisebarre, Nicolas Filip, Silviu-Ioan Hanrot, Guillaume Univ Claude Bernard Lyon 1 INRIA ENS Lyon CNRSLab LIPUMR 5668 F-69007 Lyon France Univ Oxford Math Inst Oxford OX1 2JD England

Many applications of finite impulse response (FIR) digital filters impose strict format constraints on the filter coefficients. Such requirements increase the complexity of determining optimal designs for the problem at hand. We introduce a fast and efficient method, based on the computation of good nodes for polynomial interpolation and Euclidean lattice basis reduction. Experiments show that it returns quasi-optimal finite wordlength FIR filters;compared to previous approaches it also scales remarkably well (length 125 filters are treated in < 9 s). It also proves useful for accelerating the determination of optimal finite wordlength FIR filters.

关键词： BKZ algorithm Euclidean Lattice finite wordlength FIR coefficient quantization FIR digital filters HKZ algorithm lattice basis reduction lll algorithm minimax approximation

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Solving a class of modular polynomial equations and its relation to modular inversion hidden number problem and inversive congruential generator

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DESIGNS CODES AND CRYPTOGRAPHY 2018年第9期86卷 1997-2033页

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

In this paper we revisit the modular inversion hidden number problem (MIHNP) and the inversive congruential generator (ICG) and consider how to attack them more efficiently. We consider systems of modular polynomial equations of the form and show the relation between solving such equations and attacking MIHNP and ICG. We present three heuristic strategies using Coppersmith's lattice-based root-finding technique for solving the above modular equations. In the first strategy, we use the polynomial number of samples and get the same asymptotic bound on attacking ICG proposed in PKC 2012, which is the best result so far. However, exponential number of samples is required in the work of PKC 2012. In the second strategy, a part of polynomials chosen for the involved lattice are linear combinations of some polynomials and this enables us to achieve a larger upper bound for the desired root. Corresponding to the analysis of MIHNP we give an explicit lattice construction of the second attack method proposed by Boneh, Halevi and Howgrave-Graham in Asiacrypt 2001. We provide better bound than that in the work of PKC 2012 for attacking ICG. Moreover, we propose the third strategy in order to give a further improvement in the involved lattice construction in the sense of requiring fewer samples.

关键词： Modular inversion hidden number problem Inversive congruential generator Lattice lll algorithm Coppersmith's technique

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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...

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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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Bounding basis reduction properties

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DESIGNS CODES AND CRYPTOGRAPHY 2017年第1-2期84卷 237-259页

作者： Neumaier, Arnold Univ Vienna Fak Math Oskar Morgenstern Pl 1 A-1090 Vienna Austria

The paper describes improved analysis techniques for basis reduction that allow one to prove strong complexity bounds and reduced basis guarantees for traditional reduction algorithms and some of their variants. This is achieved by a careful exploitation of the linear equations and inequalities relating various bit sizes before and after one or more reduction steps.

关键词： Basis reduction Lattices BKZ algorithm lll algorithm

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Generalized Framework to Attack RSA with Special Exposed Bits of the Private Key

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2017年第10期E100A卷 2113-2122页

作者： Wang, Shixiong Qu, Longjiang Li, Chao Fu, Shaojing Natl Univ Def Technol Coll Comp Changsha Hunan Peoples R China Natl Univ Def Technol Coll Sci Changsha Hunan Peoples R China State Key Lab Cryptol Beijing Peoples R China

In this paper, we study partial key exposure attacks on RSA where the number of unexposed blocks of the private key is greater than or equal to one. This situation, called generalized framework of partial key exposure attack, was first shown by Sarkar [22] in 2011. Under a certain condition for the values of exposed bits, we present a new attack which needs fewer exposed bits and thus improves the result in [22]. Our work is a generalization of [28], and the approach is based on Coppersmith's method and the technique of unravelled linearization.

关键词： RSA partial key exposure attack lattice lll algorithm Coppersmith's method unravelled linearization

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