A Fast Software Implementation for Arithmetic Operations in GF(2n)
作者： Erik De Win , Antoon Bosselaers , Servaas Vandenberghe , Peter De Gersem , Joos Vandewalle
DOI: 10.1007/BFB0034836
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摘要: We present a software implementation of arithmetic operations in finite field GF(2n), based on an alternative representation the elements. An important application is elliptic curve crypto-systems. Whereas previously reported implementations cryptosystems use standard basis or optimal normal to perform operations, we represent elements as polynomials with coefficients smaller GF(216). Calculations this are carried out using pre-calculated lookup tables. This results rather simple routines matching structure computer memory very well. The irreducible trinomial polynomial, was proposed at Crypto'95 by R. Schroeppel et al., can be extended representation. In our implementation, resulting slightly faster than routines.
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sci-hub.se 参考文章(12)
Richard Schroeppel, Hilarie Orman, Sean O’Malley, Oliver Spatscheck, Fast Key Exchange with Elliptic Curve Systems international cryptology conference. pp. 43- 56 ,(1995) , 10.1007/3-540-44750-4_4
Greg Harper, Alfred Menezes, Scott Vanstone, Public-key cryptosystems with very small key lengths theory and application of cryptographic techniques. pp. 163- 173 ,(1992) , 10.1007/3-540-47555-9_14
Reynald Lercier, François Morain, Counting the number of points on elliptic curves over finite fields: strategies and performances theory and application of cryptographic techniques. ,vol. 921, pp. 79- 94 ,(1995) , 10.1007/3-540-49264-X_7
S. Pohlig, M. Hellman, An improved algorithm for computing logarithms over GF(p) and its cryptographic significance (Corresp.) IEEE Transactions on Information Theory. ,vol. 24, pp. 106- 110 ,(1978) , 10.1109/TIT.1978.1055817
Victor S. Miller, Use of Elliptic Curves in Cryptography international cryptology conference. pp. 417- 426 ,(1985) , 10.1007/3-540-39799-X_31
Neal Koblitz, Elliptic curve cryptosystems Mathematics of Computation. ,vol. 48, pp. 203- 209 ,(1987) , 10.1090/S0025-5718-1987-0866109-5
R.C. Mullin, I.M. Onyszchuk, S.A. Vanstone, R.M. Wilson, Optimal normal bases in GF( p n ) Discrete Applied Mathematics. ,vol. 22, pp. 149- 161 ,(1989) , 10.1016/0166-218X(88)90090-X
H. Brunner, A. Curiger, M. Hofstetter, On computing multiplicative inverses in GF(2/sup m/) IEEE Transactions on Computers. ,vol. 42, pp. 1010- 1015 ,(1993) , 10.1109/12.238496
Ren{é Schoof, Elliptic Curves Over Finite Fields and the Computation of Square Roots mod p Mathematics of Computation. ,vol. 44, pp. 483- 494 ,(1985) , 10.1090/S0025-5718-1985-0777280-6
Neal Koblitz, Alfred J. Menezes, Elliptic Curve Public Key Cryptosystems ,(2011)