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On finite congruencesimple semirings
 J. Algebra
"... In this paper, we describe finite, additively commutative, congruence simple semirings. The main result is that the only such semirings are those of order 2, zeromultiplication rings of prime order, matrix rings over finite fields, and those that are additively idempotent. ..."
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In this paper, we describe finite, additively commutative, congruence simple semirings. The main result is that the only such semirings are those of order 2, zeromultiplication rings of prime order, matrix rings over finite fields, and those that are additively idempotent.
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.
Public Key Cryptography Based on Simple Modules Over Simple Rings
 in Proceedings of MTNS 2002
, 2002
"... The Di#e Hellman key exchange and the ElGamal oneway trapdoor function are the basic ingredients of public key cryptography. Both these protocols are based on the hardness of the discrete logarithm problem in a finite ring. In this paper we show how the action of a ring on a module gives rise to ..."
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The Di#e Hellman key exchange and the ElGamal oneway trapdoor function are the basic ingredients of public key cryptography. Both these protocols are based on the hardness of the discrete logarithm problem in a finite ring. In this paper we show how the action of a ring on a module gives rise to a generalized Di#eHellman and ElGamal protocol. This leads naturally to a cryptographic protocol whose di#culty is based on the hardness of a particular control problem, namely the problem of steering the state of some dynamical system from an initial vector to some final location.
92 Advanced Studies in Software and Knowledge Engineering KEY AGREEMENT PROTOCOL (KAP) BASED ON MATRIX POWER FUNCTION *
"... Abstract: The key agreement protocol (KAP) is constructed using matrix power functions. These functions are based on matrix ring action on some matrix set. Matrix power functions have some indications as being a oneway function since they are linked with certain generalized satisfiability problems w ..."
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Abstract: The key agreement protocol (KAP) is constructed using matrix power functions. These functions are based on matrix ring action on some matrix set. Matrix power functions have some indications as being a oneway function since they are linked with certain generalized satisfiability problems which are potentially NPComplete. A working example of KAP with guaranteed brute force attack prevention is presented for certain algebraic structures. The main advantage of proposed KAP is considerable fast computations and avoidance of arithmetic operations with long integers.
Outline of Talk: 1. Road Map to Cryptology and Historical Remarks 2. The Data Encryption Standard DES
, 2006
"... 1. Road Map to Cryptology Cryptology is the study of: Cryptography, the design of secret ciphers. Leiria, September 5, 2006 – p.3/82 1. Road Map to Cryptology Cryptology is the study of: Cryptography, the design of secret ciphers. Cryptoanalysis, the analysis of secret ciphers. Leiria, September 5, ..."
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1. Road Map to Cryptology Cryptology is the study of: Cryptography, the design of secret ciphers. Leiria, September 5, 2006 – p.3/82 1. Road Map to Cryptology Cryptology is the study of: Cryptography, the design of secret ciphers. Cryptoanalysis, the analysis of secret ciphers. Leiria, September 5, 2006 – p.4/82 Cryptography Cryptography is the study of mathematical techniques to aspects of (i) Confidentiality during point to point communication. Leiria, September 5, 2006 – p.4/82 Cryptography Cryptography is the study of mathematical techniques to aspects of (i) Confidentiality during point to point communication. (ii) Data integrity (it can be verified that the data is the same as the original); Leiria, September 5, 2006 – p.4/82 Cryptography Cryptography is the study of mathematical techniques to aspects
International Book Series "Information Science and Computing " 97 MATRIX POWER SBOX ANALYSIS 1
"... Abstract: Construction of symmetric cipher Sbox based on matrix power function and dependant on key is analyzed. The matrix consisting of plain data bit strings is combined with three round key matrices using arithmetical addition and exponent operations. The matrix power means the matrix powered b ..."
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Abstract: Construction of symmetric cipher Sbox based on matrix power function and dependant on key is analyzed. The matrix consisting of plain data bit strings is combined with three round key matrices using arithmetical addition and exponent operations. The matrix power means the matrix powered by other matrix. This operation is linked with two sound oneway functions: the discrete logarithm problem and decomposition problem. The latter is used in the infinite noncommutative group based public key cryptosystems. The mathematical description of proposed Sbox in its nature possesses a good “confusion and diffusion ” properties and contains variables “of a complex type ” as was formulated by Shannon. Core properties of matrix power operation are formulated and proven. Some preliminary cryptographic characteristics of constructed Sbox are calculated.