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Semirings and Semigroup Actions in PublicKey Cryptography
, 2002
"... by Christopher J. Monico In this dissertation, several generalizations of cryptographic protocols based on the Discrete Logarithm Problem (DLP) are examined. ..."
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by Christopher J. Monico In this dissertation, several generalizations of cryptographic protocols based on the Discrete Logarithm Problem (DLP) are examined.
Towards a Uniform Description of Several Group Based Cryptographic Primitives
, 2002
"... The public key cryptosystems MST 1 and MST 2 make use of certain kinds of factorizations of finite groups. We show that generalizing such factorizations to infinite groups allows a uniform description of several proposed cryptographic primitives. In particular, a generalization of MST 2 can be regar ..."
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Cited by 8 (2 self)
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The public key cryptosystems MST 1 and MST 2 make use of certain kinds of factorizations of finite groups. We show that generalizing such factorizations to infinite groups allows a uniform description of several proposed cryptographic primitives. In particular, a generalization of MST 2 can be regarded as a unifying framework for several suggested cryptosystems including the ElGamal public key system, a public key system based on braid groups and the MOR cryptosystem.
Public key cryptography based on semigroup actions, Adv
 in Math. of Communications
"... (Communicated by Andreas Stein) Abstract. A generalization of the original DiffieHellman key exchange in (Z/pZ) ∗ found a new depth when Miller [27] and Koblitz [16] suggested that such a protocol could be used with the group over an elliptic curve. In this paper, we propose a further vast general ..."
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(Communicated by Andreas Stein) Abstract. A generalization of the original DiffieHellman key exchange in (Z/pZ) ∗ found a new depth when Miller [27] and Koblitz [16] suggested that such a protocol could be used with the group over an elliptic curve. In this paper, we propose a further vast generalization where abelian semigroups act on finite sets. We define a DiffieHellman key exchange in this setting and we illustrate how to build interesting semigroup actions using finite (simple) semirings. The practicality of the proposed extensions rely on the orbit sizes of the semigroup actions and at this point it is an open question how to compute the sizes of these orbits in general and also if there exists a square root attack in general. In Section 5 a concrete practical semigroup action built from simple semirings is presented. It will require further research to analyse this system. 1.
Cryptanalysis of a homomorphic publickey cryptosystem
, 2006
"... The aims of this research are to give a precise description of a new homomorphic publickey encryption scheme proposed by Grigoriev and Ponomarenko [7] in 2004 and to break Grigoriev and Ponomarenko homomorphic publickey cryptosystem. Firstly, we prove some properties of linear fractional transform ..."
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The aims of this research are to give a precise description of a new homomorphic publickey encryption scheme proposed by Grigoriev and Ponomarenko [7] in 2004 and to break Grigoriev and Ponomarenko homomorphic publickey cryptosystem. Firstly, we prove some properties of linear fractional transformations. We analyze the Xnrepresentation algorithm which is used in the decryption scheme of Grigoriev and Ponomarenko homomorphic publickey cryptosystem and by these properties of the linear fractional transformations, we correct and modify the Xnrepresentation algorithm. We implement the modified Xnrepresentation algorithm by programming it and we prove the correctness of the modified Xnrepresentation algorithm. Secondly, we find an explicit formula to compute the X(n, S)representations of elements of the group Γn. The X(n, S)representation algorithm is used in the decryption scheme of Grigoriev and Ponomarenko homomorphic publickey cryptosystem and we modify the X(n, S)representation algorithm. We implement the modified X(n, S)representation algorithm by programming it and we justify the modified