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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.
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 Simple Modules Over Simple Rings
 IN PROCEEDINGS OF MTNS 2002
, 2002
"... The Diffie 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 t ..."
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The Diffie 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 DiffieHellman and ElGamal protocol. This leads naturally to a cryptographic protocol whose difficulty 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.
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
Matrix Power SBox Construction ∗
"... The new symmetric cipher Sbox construction based on matrix power function is presented. 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. The left ..."
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The new symmetric cipher Sbox construction based on matrix power function is presented. 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. The left and right side matrix powers are introduced. 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. It is shown that generic Sbox equations are not transferable to the multivariate polynomial equations in respect of input and key variables and hence the algebraic attack to determine the key variables cannot be applied in this case. 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. Some comparative simulation results are presented. Keywords: symmetric cipher, Sbox, matrix power, oneway function (OWF), resistance to algebraic attack 1
A Novel Public Key Crypto system Based on Semimodules over Quotient Semirings
"... Abstract: In A generalization of the original DiffieHellman key exchange in (ℤ/pℤ) * found a new depth when Miller and Koblitz suggested that such a protocol could be used with the group over an elliptic curve. Maze, Monico and Rosenthal extend such a generalization to the setting of a Semigroup ..."
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Abstract: In A generalization of the original DiffieHellman key exchange in (ℤ/pℤ) * found a new depth when Miller and Koblitz suggested that such a protocol could be used with the group over an elliptic curve. Maze, Monico and Rosenthal extend such a generalization to the setting of a Semigroup action on a finite set, more precisely, linear actions of abelian semirings on semimodules. In this paper, we extend such a generalization to the linear actions of quotient semirings on semimodules. In fact, we show how the action of quotient semirings on a semimodule gives rise to a generalized DiffieHellman and ElGamal protocol. This leads naturally to a cryptographic protocol whose difficulty 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. Keywords: Public key cryptography, DiffieHelman protocol, Oneway trapdoor functions, Semi group actions, Quotient semirings
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.