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Fast Inversion in Composite Galois Fields GF((2 n ) m )
 IEEE International Symposium on Information Theory, MIT
, 1998
"... We describe an improvement of Itoh and Tsujii's algorithm for inversion over Galois fields GF ((2 n ) m ). In particular, raising an element to the 2 ln power, l an integer, in polynomial basis representation can be done with a binary, fixed matrix. Finally, we show that the inversion co ..."
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Cited by 2 (0 self)
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We describe an improvement of Itoh and Tsujii's algorithm for inversion over Galois fields GF ((2 n ) m ). In particular, raising an element to the 2 ln power, l an integer, in polynomial basis representation can be done with a binary, fixed matrix. Finally, we show that the inversion
Efficient Multiplier Architectures for Galois Fields GF(2 4n )
 IEEE Transactions on Computers
, 1998
"... This contribution introduces a new class of multipliers for finite fields GF ((2 n ) 4 ). The architecture is based on a modified version of the KaratsubaOfman algorithm (KOA). By determining optimized field polynomials of degree four, the last stage of the KOA and the modulo reduction can b ..."
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Cited by 16 (0 self)
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This contribution introduces a new class of multipliers for finite fields GF ((2 n ) 4 ). The architecture is based on a modified version of the KaratsubaOfman algorithm (KOA). By determining optimized field polynomials of degree four, the last stage of the KOA and the modulo reduction can
Reconfigurable Elliptic Curve CryptoHardware Over the Galois Field GF(2163)
, 1596
"... Abstract: Problem statement: In the last decade, many hardware designs of elliptic curves cryptography have been developed, aiming to accelerate the scalar multiplication process, mainly those based on the Field Programmable Gate Arrays (FPGA), the major issue concerned the ability of embedding this ..."
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of making the scalar multiplication over the GF(2163) in a restricted number of clock cycles, targeting the acceleration of the basic field operations, mainly the multiplication and the inverse process, under the constraint of hardware optimization. Approach: The research was based on using the efficient
An Algorithm to find the Irreducible Polynomials over Galois Field GF(p m
"... Irreducible Polynomials over GF(pm) and the multiplicative inverses under it are important in cryptography. Presently the method of deriving irreducible polynomials of a particular prime modulus is very primitive and time consuming. In this paper, in order to find all irreducible polynomials, be it ..."
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Irreducible Polynomials over GF(pm) and the multiplicative inverses under it are important in cryptography. Presently the method of deriving irreducible polynomials of a particular prime modulus is very primitive and time consuming. In this paper, in order to find all irreducible polynomials
Group rekeying protocol based on modular polynomial arithmetic over galois field GF(2n
 Am. J. Applied Sci
, 2009
"... Abstract: Problem statement: In this study we propose a group rekeying protocol based on modular polynomial arithmetic over Galois Field GF(2n). Common secure group communications requires encryption/decryption for group rekeying process, especially when a group member is leaving the group. Approa ..."
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Cited by 3 (0 self)
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Abstract: Problem statement: In this study we propose a group rekeying protocol based on modular polynomial arithmetic over Galois Field GF(2n). Common secure group communications requires encryption/decryption for group rekeying process, especially when a group member is leaving the group
New Hardware Algorithms and Designs for Montgomery Modular Inverse Computation in Galois Fields GF(p) and GF(2^n)
, 2002
"... The computation of the inverse of a number in finite fields, namely Galois Fields GF(p) or GF(2), is one of the most complex arithmetic operations in cryptographic applications. In this work, we investigate the GF(p) inversion and present several phases in the design of efficient hardware implementa ..."
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Cited by 5 (1 self)
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The computation of the inverse of a number in finite fields, namely Galois Fields GF(p) or GF(2), is one of the most complex arithmetic operations in cryptographic applications. In this work, we investigate the GF(p) inversion and present several phases in the design of efficient hardware
Fast Arithmetic Architectures for PublicKey Algorithms over Galois Fields GF((2 n ) m )
 in Advances in Cryptography  EUROCRYPT '97
, 1997
"... This contribution describes a new class of arithmetic architectures for Galois fields GF (2 k ). The main applications of the architecture are publickey systems which are based on the discrete logarithm problem for elliptic curves. The architectures use a representation of the field GF (2 k ) ..."
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Cited by 11 (3 self)
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This contribution describes a new class of arithmetic architectures for Galois fields GF (2 k ). The main applications of the architecture are publickey systems which are based on the discrete logarithm problem for elliptic curves. The architectures use a representation of the field GF (2 k
Hardware Implementation of the Binary Method for Exponentiation in GF(2 m )
"... Abstract Exponentiation in finite or Galois fields, GF(2 m ), is a basic operation for several algorithms in areas such ..."
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Abstract Exponentiation in finite or Galois fields, GF(2 m ), is a basic operation for several algorithms in areas such
Field Programmable Gate Array Based Realization of SBoxes
"... Abstract: This letter presents the comparative study between Galois Field GF (2) SBox, Gray SBox and ..."
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Abstract: This letter presents the comparative study between Galois Field GF (2) SBox, Gray SBox and
Quantum Arithmetic on Galois Fields
, 2002
"... In this paper we discuss the problem of performing elementary finite field arithmetic on a quantum computer. Of particular interest, is the controlledmultiplication operation, which is the only groupspecific operation in Shor’s algorithms for factoring and solving the Discrete Log Problem. We descr ..."
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describe how to build quantum circuits for performing this operation on the generic Galois fields GF(p k), as well as the boundary cases GF(p) and GF(2 k). We give the detailed size, width and depth complexity of such circuits, which ultimately will allow us to obtain detailed upper bounds on the amount
Results 1  10
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2,662