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Low exponent attack against elliptic curve RSA
, 1995
"... Hastad showed that low exponent RSA is not secure if the same message is encrypted to several receivers. This is true even if timestamp is used for each receiver. For example, let e = 3. Then if the number of receivers = 7, the eavesdropper can find the plaintext from the seven ciphertexts of each ..."
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Hastad showed that low exponent RSA is not secure if the same message is encrypted to several receivers. This is true even if timestamp is used for each receiver. For example, let e = 3. Then if the number of receivers = 7, the eavesdropper can find the plaintext from the seven ciphertexts of each receiver. This paper shows that elliptic curve RSA is not secure in the same scinario. It is shown that the KMOV scheme and Demytko's scheme are not secure if e = 5; n 2 1024 and the number of receivers = 428. In Demytko's scheme, e can take the value of 2. In this case, this system is not secure if the number of receiver = 11 for n 2 175 . 1 Introduction Hastad showed that low exponent RSA is not secure if the same message is encrypted to several receivers [1]. This is true even if timestamp is used for each receiver. For example, let e = 3. Then if the number of receivers = 7, the eavesdropper can find the plaintext from the seven ciphertexts of each receiver. On the other hand, el...
Publickey cryptography and invariant theory
, 2002
"... Publickey cryptosystems are suggested based on invariants of groups. We give also an overview of known cryptosystems which involve groups. ..."
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Publickey cryptosystems are suggested based on invariants of groups. We give also an overview of known cryptosystems which involve groups.
A New and Optimal ChosenMessage Attack on RSAType Cryptosystems
 Signatures in the Presence of Transient Faults 7 in the proceedings of the International Conference on Information and Communications Security
, 1997
"... Chosenmessage attack on RSA is usually considered as an inherent property of its homomorphic structure. In this paper, we show that nonhomomorphic RSAtype cryptosystems are also susceptible to a chosenmessage attack. In particular, we prove that only one message is needed to mount a successful c ..."
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Chosenmessage attack on RSA is usually considered as an inherent property of its homomorphic structure. In this paper, we show that nonhomomorphic RSAtype cryptosystems are also susceptible to a chosenmessage attack. In particular, we prove that only one message is needed to mount a successful chosenmessage attack against the Lucasbased systems and Demytko's elliptic curve system.
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.
Reducing the Elliptic Curve Cryptosystem of MeyerMüller to the Cryptosystem of RabinWilliams
, 1996
"... . At Eurocrypt'96, Meyer and Muller presented a new Rabintype cryptosystem based on elliptic curves. In this paper, we will show that this cryptosystem may be reduced to the cryptosystem of WilliamsRabin. 1 Introduction In 1991, Koyama, Maurer, Okamoto and Vanstone [15] pointed out the existe ..."
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. At Eurocrypt'96, Meyer and Muller presented a new Rabintype cryptosystem based on elliptic curves. In this paper, we will show that this cryptosystem may be reduced to the cryptosystem of WilliamsRabin. 1 Introduction In 1991, Koyama, Maurer, Okamoto and Vanstone [15] pointed out the existence of new oneway trapdoor functions similar to the RSA on elliptic curves over a ring. At Eurocrypt'96, Meyer and Muller presented an other elliptic RSAtype cryptosystem with a public encryption exponent equal to 2. We will show that this cryptosystem may be reduced to the cryptosystem of RabinWilliams [20, 22]. The remainder of the paper is organized as follows. Section 2 describes the cryptosystem of Meyer and Muller. In Section 3, we show how it may be reduced to the cryptosystem of RabinWilliams. Finally, we conclude in Section 4. CG1996/4 c fl1996 by UCL Crypto Group For more informations, see http://www.dice.ucl.ac.be/crypto/techreports.html Presented at the rump session of Eurocr...
Elliptic Curve Cryptosystems
, 1997
"... The application of elliptic curves to the field of cryptography has been relatively recent. It has opened up a wealth of possibilities in terms of security, encryption, and realworld applications. In particular, we are interested in publickey cryptosystems that use the elliptic curve discrete loga ..."
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The application of elliptic curves to the field of cryptography has been relatively recent. It has opened up a wealth of possibilities in terms of security, encryption, and realworld applications. In particular, we are interested in publickey cryptosystems that use the elliptic curve discrete logarithm problem to establish security. The objective of this thesis is to assemble the most important facts and findings into a broad, unified overview of this field. To illustrate certain points, we also discuss a sample implementation of the elliptic curve analogue of the El Gamal cryptosystem.
On nonabelian homomorphic publickey cryptosystems
, 2002
"... An important problem of modern cryptography concerns secret publickey computations in algebraic structures. We construct homomorphic cryptosystems being (secret) epimorphisms f: G → H, where G,H are (publically known) groups and H is finite. A letter of a message to be encrypted is an element h ∈ H ..."
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An important problem of modern cryptography concerns secret publickey computations in algebraic structures. We construct homomorphic cryptosystems being (secret) epimorphisms f: G → H, where G,H are (publically known) groups and H is finite. A letter of a message to be encrypted is an element h ∈ H, while its encryption g ∈ G is such that f(g) = h. A homomorphic cryptosystem allows one to perform computations (operating in a group G) with encrypted information (without knowing the original message over H). In this paper certain homomorphic cryptosystems are constructed for the first time for nonabelian groups H (earlier, homomorphic cryptosystems were known only in the Abelian case). In fact, we present such a system for any solvable (fixed) group H. 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.