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RSAbased Undeniable Signatures For General Moduli
 Advances in CTRSA 2002, LNCS 2271
"... Gennaro, Krawczyk and Rabin gave the first undeniable signature scheme based on RSA signatures. However, their solution required the use of RSA moduli which are a product of safe primes. This paper gives techniques which allow RSAbased undeniable signatures for general moduli. ..."
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Cited by 21 (2 self)
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Gennaro, Krawczyk and Rabin gave the first undeniable signature scheme based on RSA signatures. However, their solution required the use of RSA moduli which are a product of safe primes. This paper gives techniques which allow RSAbased undeniable signatures for general moduli.
Implementation of fast RSA key generation on smart cards
 ACM Symposium on Applied Computing
, 2002
"... Although smart cards are becoming used in an increasing number of applications, there is small literature of the implementation issues for smart cards. This paper describes the issues and considerations that need to be taken into account when implementing the key generation step of a cryptographic a ..."
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Cited by 10 (0 self)
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Although smart cards are becoming used in an increasing number of applications, there is small literature of the implementation issues for smart cards. This paper describes the issues and considerations that need to be taken into account when implementing the key generation step of a cryptographic algorithm widely used nowadays, RSA. Smart cards are used in many applications that require a tamper resistant area. Therefore, smart cards that use cryptography have to provide encryption, decryption, as well as key generation inside its security perimeter. RSA key generation is a concern for oncard implementation of RSA cryptosystem, as it usually takes a long time. In this paper, two simple but efficient key generation algorithms are evaluated, in addition to a simple but not very efficient algorithm. The paper discusses in detail how to build fast implementations for the three algorithms presented, using smart cards with cryptocoprocessor.
Fast Generation of Prime Numbers of Portable Devices: An Update
 Proceedings of CHES 2006, LNCS 4249
, 2006
"... Abstract. The generation of prime numbers underlies the use of most publickey cryptosystems, essentially as a primitive needed for the creation of RSA key pairs. Surprisingly enough, despite decades of intense mathematical studies on primality testing and an observed progressive intensification of ..."
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Abstract. The generation of prime numbers underlies the use of most publickey cryptosystems, essentially as a primitive needed for the creation of RSA key pairs. Surprisingly enough, despite decades of intense mathematical studies on primality testing and an observed progressive intensification of cryptography, prime number generation algorithms remain scarcely investigated and most reallife implementations are of dramatically poor performance. We show simple techniques that substantially improve all algorithms previously suggested or extend their capabilities. We derive fast implementations on appropriately equipped portable devices like smartcards embedding a cryptographic coprocessor. This allows onboard generation of RSA keys featuring a very attractive (average) processing time. Our motivation here is to help transferring this task from terminals where this operation usually took place so far, to portable devices themselves in near future for more confidence, security, and compliance with networkscaled distributed protocols such as electronic cash or mobile commerce.
2, where ρq − p  ≤
"... Abstract. In this paper we revisit Wiener’s method (IEEEIT 1990) of continued fraction (CF) to find new weaknesses in RSA. We consider RSA with N = pq, q < p < 2q, public encryption exponent e and private decryption exponent d. Our motivation is to find out when RSA is insecure given d is O(N ..."
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Abstract. In this paper we revisit Wiener’s method (IEEEIT 1990) of continued fraction (CF) to find new weaknesses in RSA. We consider RSA with N = pq, q < p < 2q, public encryption exponent e and private decryption exponent d. Our motivation is to find out when RSA is insecure given d is O(N δ), where we are mostly interested in the range 0.3 ≤ δ ≤ 0.5. Given ρ (1 ≤ ρ ≤ 2) is known to the attacker, we show that the RSA keys are weak when d = N δ and δ < 1 2
RSAbased Undeniable Signatures For General Moduli
, 2001
"... Gennaro, Krawczyk and Rabin gave the first undeniable signature scheme based on RSA signatures. However, their solution required the use of RSA moduli which are a product of safe primes. This paper gives techniques which allow RSAbased undeniable signatures for general moduli. ..."
Abstract
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Gennaro, Krawczyk and Rabin gave the first undeniable signature scheme based on RSA signatures. However, their solution required the use of RSA moduli which are a product of safe primes. This paper gives techniques which allow RSAbased undeniable signatures for general moduli.
Abstract A note on efficient implementation of prime generation algorithms in small portable devices
, 2004
"... This paper investigates existing prime generation algorithms on small portable devices, makes optimizations and compares their efficiencies. It shows by comparing the performances that the bit array algorithm is the most efficient among all the existing prime generation algorithms. The paper further ..."
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This paper investigates existing prime generation algorithms on small portable devices, makes optimizations and compares their efficiencies. It shows by comparing the performances that the bit array algorithm is the most efficient among all the existing prime generation algorithms. The paper further optimizes the implementation of the bit array algorithm by using an optimal parameter in the prime generations, namely the small prime set for its sieving procedure. A method for estimating the optimal small prime set for the bit array algorithm is provided. The paper gives generalized bit array algorithms which are able to find primes with special constraints, i.e., DSA primes and strong primes. Finally, the algorithms are implemented in a smart card and a PDA for validation. It shows that there is very little efficiency sacrifice for generating special primes with respect to generating random primes. It also shows that using optimal sets of small primes for prime generations will result in 30–200 % efficiency improvement. Ó 2005 Elsevier B.V. All rights reserved.
How to Choose Secret Parameters for RSAtype Cryptosystems over Elliptic Curves
, 1997
"... . Recently, and contrary to the common belief, Rivest and Silverman argued that the use of strong primes is unnecessary in the RSA cryptosystem. This paper analyzes how valid this assertion is for RSAtype cryptosystems over elliptic curves. The analysis is more difficult because the underlying grou ..."
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. Recently, and contrary to the common belief, Rivest and Silverman argued that the use of strong primes is unnecessary in the RSA cryptosystem. This paper analyzes how valid this assertion is for RSAtype cryptosystems over elliptic curves. The analysis is more difficult because the underlying groups are not always cyclic. Previous papers suggested the use of strong primes in order to prevent factoring attacks and cycling attacks. In this paper, we only focus on cycling attacks because for both RSA and its elliptic curvebased analogues, the length of the RSAmodulus n is typically the same. Therefore, a factoring attack will succeed with equal probability against all RSAtype cryptosystems. We also prove that cycling attacks reduce to find fixed points, and derive a factorization algorithm which (most probably) completely breaks RSAtype systems over elliptic curves if a fixed point is found. Keywords: RSAtype cryptosystems, Cycling attacks, Elliptic curves, Strong primes. 1. Introd...
How to Choose Secret Parameters for RSA and its Extensions to Elliptic Curves
, 2001
"... Recently, and contrary to the common belief, Rivest and Silverman argued that the use of strong primes is unnecessary in the RSA cryptosystem. This paper analyzes how valid this assertion is for RSA and its extensions to elliptic curves. Over elliptic curves, the analysis is more di#cult because ..."
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Recently, and contrary to the common belief, Rivest and Silverman argued that the use of strong primes is unnecessary in the RSA cryptosystem. This paper analyzes how valid this assertion is for RSA and its extensions to elliptic curves. Over elliptic curves, the analysis is more di#cult because the underlying groups are not always cyclic.