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RSAtype Signatures in the Presence of Transient Faults
, 1997
"... . In this paper, we show that the presence of transient faults can leak some secret information. We prove that only one faulty RSAsignature is needed to recover one bit of the secret key. Thereafter, we extend this result to Lucasbased and elliptic curve systems. Keywords. RSA, Lucas sequences, el ..."
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Cited by 9 (5 self)
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. In this paper, we show that the presence of transient faults can leak some secret information. We prove that only one faulty RSAsignature is needed to recover one bit of the secret key. Thereafter, we extend this result to Lucasbased and elliptic curve systems. Keywords. RSA, Lucas sequences, elliptic curves, transient faults. 1 Introduction At the last Workshop on Security Protocols, Bao, Deng, Han, Jeng, Narasimhalu and Ngair from the Institute of Systems Science (Singapore) exhibited new attacks against several cryptosystems [2]. These attacks exploit the presence of transient faults. By exposing a device to external constraints, one can induce some faults with a nonnegligible probability [1]. In this paper, we show that these attacks are of very general nature and remain valid for cryptosystems based on other algebraic structures. We will illustrate this topic on the Lucasbased and elliptic curve cryptosystems. Moreover, we will focus on the signatures generation, reducing t...
Cryptanalysis of RSAType Cryptosystems: A Visit
 DIMACS Series in Discr. Math. ant Th. Comp. Sci., AMS
, 1998
"... . This paper surveys RSAtype implementations based on Lucas sequences and on elliptic curves. The main focus is the way how some known attacks on RSA were extended to LUC, KMOV and Demytko's system. It also gives some directions for the choice of the most appropriate RSAtype system for a given app ..."
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. This paper surveys RSAtype implementations based on Lucas sequences and on elliptic curves. The main focus is the way how some known attacks on RSA were extended to LUC, KMOV and Demytko's system. It also gives some directions for the choice of the most appropriate RSAtype system for a given application. 1. INTRODUCTION In 1978, Rivest, Shamir and Adleman [63] introduced the socalled RSA cryptosystem. Its security mainly relies on the difficulty of factoring carefully chosen large integers. After this breakthrough, other structures were proposed to produce analogues to RSA. So, Muller and Nobauer [54, 55] presented a cryptosystem using Dickson polynomials. This system was afterwards slightly modified and rephrased in terms of Lucas sequences by Smith and Lennon [70, 72]. More recently, Koyama, Maurer, Okamoto and Vanstone [41] exhibited new oneway trapdoor functions similar to RSA on elliptic curves, the socalled KMOV cryptosystem. Later, Demytko [20] also pointed out a new one...
Topics in PublicKey Cryptography II
, 1999
"... 6> Vn(P; Q) from Dickson polynomials Vn(P; Q) = [ n 2 ] X i=0 n n \Gamma i ` n \Gamma i i ' (\GammaQ) i P n\Gamma2i Fact: Vn(V k (P; Q); Q k ) = V nk (P; Q). In particular, if Q = 1, then Vn(V k (P; 1); 1) = V nk (P; 1) = V k (Vn(P; Q); 1). The above fact forms the bas ..."
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6> Vn(P; Q) from Dickson polynomials Vn(P; Q) = [ n 2 ] X i=0 n n \Gamma i ` n \Gamma i i ' (\GammaQ) i P n\Gamma2i Fact: Vn(V k (P; Q); Q k ) = V nk (P; Q). In particular, if Q = 1, then Vn(V k (P; 1); 1) = V nk (P; 1) = V k (Vn(P; Q); 1). The above fact forms the basis for many RSA and ElGamal type cryptosystems based on Lucas sequences. Observe th
A Survey of Elliptic Curve Cryptosystems, Part I: Introductory
, 2003
"... The theory of elliptic curves is a classical topic in many branches of algebra and number theory, but recently it is receiving more attention in cryptography. An elliptic curve is a twodimensional (planar) curve defined by an equation involving a cubic power of coordinate x and a square power of co ..."
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The theory of elliptic curves is a classical topic in many branches of algebra and number theory, but recently it is receiving more attention in cryptography. An elliptic curve is a twodimensional (planar) curve defined by an equation involving a cubic power of coordinate x and a square power of coordinate y. One class of these curves is
Cryptanalysis of Koyama Scheme
, 2006
"... In this paper we analyze the security of Koyama scheme based on the singular cubic curve for some well known attacks. We provide an efficient algorithm for linearly related plaintext attack and identify isomorphic attack on Koyama scheme. Some other attacks are also discussed in this paper. ..."
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In this paper we analyze the security of Koyama scheme based on the singular cubic curve for some well known attacks. We provide an efficient algorithm for linearly related plaintext attack and identify isomorphic attack on Koyama scheme. Some other attacks are also discussed in this paper.