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A Public Key Cryptosystem Based on Elliptic Curves over Z/nZ Equivalent to Factoring
"... . Elliptic curves over the ring ZZ=nZZ where n is the product of two large primes have first been proposed for public key cryptosystems in [4]. The security of this system is based on the integer factorization problem, but it is unknown whether breaking the system is equivalent to factoring. In this ..."
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. Elliptic curves over the ring ZZ=nZZ where n is the product of two large primes have first been proposed for public key cryptosystems in [4]. The security of this system is based on the integer factorization problem, but it is unknown whether breaking the system is equivalent to factoring. In this paper, we present a variant of this cryptosystem for which breaking the system is equivalent to factoring the modulus n. Moreover, we extend the ideas to get a signature scheme based on elliptic curves over ZZ=nZZ. 1 Introduction In recent years, elliptic curves over finite fields have gained a lot of attention. The use of elliptic curves over finite fields in public key cryptography was suggested by Koblitz [3] and Miller [7]. The security of these cryptosystems is based on the difficulty of the discrete logarithm problem in the group of points on an elliptic curve. Later Vanstone et. al. proposed to use elliptic curves over the ring ZZ=nZZ, where n is the product of two large prime num...
An efficient semantically secure elliptic curve cryptosystem based on KMOV scheme
, 2002
"... We propose an elliptic curve scheme over the ring Z n 2, which is efficient and semantically secure in the standard model. There appears to be no previous elliptic curve cryptosystem based on factoring that enjoys both of these properties. KMOV scheme has been used as an underlying primitive to obta ..."
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We propose an elliptic curve scheme over the ring Z n 2, which is efficient and semantically secure in the standard model. There appears to be no previous elliptic curve cryptosystem based on factoring that enjoys both of these properties. KMOV scheme has been used as an underlying primitive to obtain efficiency and probabilistic encryption. Semantic security of the scheme is based on a new decisional assumption, namely, the Decisional Smallx eMultiples Assumption. Confidence on this assumption is also discussed.
Cryptanalysis of RSAtype cryptosystem: A visit
 Theoretical Computer Science
, 1998
"... ABSTRACT. 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 g ..."
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ABSTRACT. 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.
Public Key Cryptosystems using Elliptic Curves
, 1997
"... This report is a survey on public key cryptosystems that use the theory of elliptic curves. A considerable part will be about the theory of elliptic curves. Encryption systems, digital signature schemes and key agreement schemes using elliptic curves will be described. Their workload and bandwidth w ..."
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This report is a survey on public key cryptosystems that use the theory of elliptic curves. A considerable part will be about the theory of elliptic curves. Encryption systems, digital signature schemes and key agreement schemes using elliptic curves will be described. Their workload and bandwidth will be addressed and some attacks will be described. For all systems the security is based either on the elliptic curve discrete logarithm problem or on the difficulty of factorization. The differences between conventional and elliptic curve systems shall be addressed. Systems based on the elliptic curve discrete logarithm problem can be used with shorter keys to provide the same security, compared to similar conventional systems. Elliptic curve systems based on factoring are slightly more resistant as conventional systems against some attacks.