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8 Papers

Address-bit Differential Power Analysis on Boolean Split Exponent Counter-measure

Topic: Applied Cryptography

Author: Christophe Negre

Affiliation: DALI, Université de Perpignan, France, LIRMM, Université de Montpellier et CNRS, France

Digital Object Identifier: 10.5220/0009891306320637

Proceedings of SECRYPT 2020, ISBN: 978-989-758-446-6

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Current public key cryptographic algorithms (RSA, DSA, ECDSA) can be threaten by side channel analyses. The main approach to counter-act such attacks consists in randomizing sensitive data and address bits used in loads and stores of an exponentiation algorithm. In this paper we study a recent counter-measure ”Boolean split exponent” (Tunstall et al. 2018) preventing differential power analysis on address bits. We show that one of their proposed protections has a flaw. We derive an attack exploiting this flaw and we successfully apply it on a simulated power consumption of an RSA modular exponentiation.

Efficient Randomized Regular Modular Exponentiation using Combined Montgomery and Barrett Multiplications

Topic: Applied Cryptography

Authors: Andrea Lesavourey 1 , Christophe Negre 1 and Thomas Plantard 2

Affiliations: 1 DALI (UPVD) and LIRMM (Univ. of Montpellier and CNRS), France , 2 University of Wollongong, Australia

Digital Object Identifier: 10.5220/0005998503680375

Proceedings of SECRYPT 2016/ICETE, ISBN: 978-989-758-196-0

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Cryptographic operations performed on an embedded device are vulnerable to side channel analysis and particularly to differential and correlation power analysis. The basic protection against such attacks is to randomize the data all along the cryptographic computations. In this paper we present a modular multiplication algorithm which can be used for randomization. We show that we can use it to randomize the modular exponentiation of the RSA cryptosystem. The proposed randomization is free of computation and induces a level of randomization from 210 to 215 for practical RSA modulus size.
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Applied Cryptography

Data Engineering

Information and Systems Security
Cryptographic Techniques and Key Management

Databases and Data Security

Parallel Approaches for Efficient Scalar Multiplication over Elliptic Curve

Topic: Applied Cryptography

Authors: Christophe Negre and Jean-Marc Robert

Affiliation: Equipe DALI, Université de Perpignan, LIRMM, Univ. de Montpellier and CNRS, France

Digital Object Identifier: 10.5220/0005512502020209

Proceedings of SECRYPT 2015/ICETE, ISBN: 978-989-758-117-5

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This paper deals with parallel implementation of scalar multiplication over an elliptic curve. We present parallel approaches which split the scalar into two parts for E(Fp) or three parts for E(F2m ) and perform in parallel the scalar multiplication with each part of the scalar. We present timing results of these approaches implemented over an Intel Core i7 for NIST binary curves B233, B409 and for the twisted Edwards curve Curve25519 (Bernstein, 2006). For the curves B409 and Curve25519 the proposed approaches improve by at least 10% the computation time of the scalar multiplication.
Collapse Button Related Ontology Subjects/Areas/Topics (5)
Applied Cryptography

Data Engineering

Information and Systems Security
Cryptographic Techniques and Key Management

Databases and Data Security

AN EFFICIENT MULTIPLICATION ALGORITHM USING BINOMIAL RESIDUE REPRESENTATION

Topic: Public Key Crypto Applications

Authors: Yin Li 1 and Christophe Negre 2

Affiliations: 1 Institute of Information Security, Shanghai jiaotong University, China , 2 Team DALI/ELIAUS, University of Perpignan, France

Digital Object Identifier: 10.5220/0001924503190324

Proceedings of SECRYPT 2008/ICETE, ISBN: 978-989-8111-59-3

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In this paper, we propose an extension of the algorithm proposed by Bajard, Imbert and Negre in (Bajar et al., 2006), refered as BIN algorithm. We use binomial residue representation of field elements instead of the Lagrange representation of (Bajar et al., 2006). Specifically, every elements in Fpk is represented by a set of residue modulo fixed binomials. We propose two versions of our algorithm, one in general form with a sub-quadratic complexity equal to O(k1.5 ) operations in Fp . The second one is optimized with the use of FFT. In this case the cost is O(k log(k)) operations in Fp . For fields GF ( pk ) suitable for elliptic curve cryptography our algorithm roughly improves the time delay of (Bajar et al., 2006) by 45%.
Collapse Button Related Ontology Subjects/Areas/Topics (3)
Cryptographic Techniques and Key Management

Information and Systems Security

Public Key Crypto Applications

POINT MULTIPLICATION ON SUPERSINGULAR ELLIPTIC CURVES DEFINED OVER FIELDS OF CHARACTERISTIC 2 AND 3

Topic: Public Key Crypto Applications

Authors: Kwang Ho Kim 1 and Christophe Negre 2

Affiliations: 1 Institute of Mathematics, The State Academy of Sciences, Korea, Republic of , 2 Team DALI/ELIAUS, University of Perpignan, France

Digital Object Identifier: 10.5220/0001926103730376

Proceedings of SECRYPT 2008/ICETE, ISBN: 978-989-8111-59-3

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Elliptic curve cryptosystem protocols use two main operations, the scalar multiplication and the pairing computation. Both of them are done through a chain of basic operation on the curve. In this paper we present new formulas for supersingular elliptic curve in characteristic 2 and 3. We improve best known formulas by at least one multiplication in the field.
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Cryptographic Techniques and Key Management

Information and Systems Security

Public Key Crypto Applications

SUBQUADRATIC BINARY FIELD MULTIPLIER IN DOUBLE POLYNOMIAL SYSTEM

Topic: Public Key Crypto Applications

Authors: Pascal Giorgi 1 , Christophe Nègre 1 and Thomas Plantard 2

Affiliations: 1 Équipe DALI, LP2A, Unversité de Perpignan, France , 2 Centre for Computer and Information Security Research, School of Computer Science & Software Engineering, University of Wollongong, Australia

Digital Object Identifier: 10.5220/0002126102290236

Proceedings of SECRYPT 2007/ICETE, ISBN: 978-989-8111-12-8

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We propose a new space efficient operator to multiply elements lying in a binary field F2k . Our approach is based on a novel system of representation called Double Polynomial System which set elements as a bivariate polynomials over F2 . Thanks to this system of representation, we are able to use a Lagrange representation of the polynomials and then get a logarithmic time multiplier with a space complexity of O(k1.31 ) improving previous best known method.
Collapse Button Related Ontology Subjects/Areas/Topics (3)
Cryptographic Techniques and Key Management

Information and Systems Security

Public Key Crypto Applications

FINITE FIELD MULTIPLICATION IN LAGRANGE REPRESENTATION USING FAST FOURRIER TRANSFORM

Topic: Public Key Crypto Applications

Author: Christophe Negre

Affiliation: Équipe DALI, LP2A, Université de Perpignan, France

Digital Object Identifier: 10.5220/0002096503200324

Proceedings of SECRYPT 2006/ICETE, ISBN: 978-972-8865-63-4

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The multiplication in Fpn can be performed using a polynomial version of Montgomery multiplication (Montgomery, 1985). In (Bajard et al., 2003) Bajard et al. improved this method by using a Lagrange representation: the elements of Fpn are represented by their values at a fixed set of points. The costly operations in this new algorithm are the two changes of Lagrange representation which require 2r2 operations in Fp with n ≤ r ≤ 2⌈log2 (n)⌉ . In this paper we present a new method to perform the change of Lagrange representation. This method uses Fast Fourier Transform and has a cost equal to 3rlog2 (r) operations in Fp with r = 2⌈log2 (n)⌉ .
Collapse Button Related Ontology Subjects/Areas/Topics (3)
Cryptographic Techniques and Key Management

Information and Systems Security

Public Key Crypto Applications

PARALLEL MULTIPLICATION IN F2n USING CONDENSED MATRIX REPRESENTATION

Topics: Public Key Crypto Applications; Coding Theory and Practice

Author: Christophe Negre

Affiliation: Équipe DALI, LP2A, Université de Perpignan, France

Digital Object Identifier: 10.5220/0002096402540259

Proceedings of SECRYPT 2006/ICETE, ISBN: 978-972-8865-63-4

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In this paper we explore a matrix representation of binary fields F2n defined by an irreducible trinomial P = X n + X k + 1. We obtain a multiplier with time complexity of TA + (⌈log 2(n)⌉)TX and space 2 complexity of (2n − 1)n AND and (2n − 1)(n − 1) XOR . This multiplier reaches the lower bound on time complexity. Until now this was possible only for binary field defined by AOP (Silverman, 1999), which are quite few. The interest of this multiplier remains theoretical since the size of the architecture is roughly two times bigger than usual polynomial basis multiplier (Mastrovito, 1991; Koc and Sunar, 1999).
Collapse Button Related Ontology Subjects/Areas/Topics (4)
Coding Theory and Practice

Information and Systems Security

Public Key Crypto Applications
Cryptographic Techniques and Key Management

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