论文信息 - Computing Logarithms in GF(2n)

Computing Logarithms in GF(2n)

Consider the finite field having q elements and denote it by GF(q). Let α be a generator for the nonzero elements of GF(q). Hence, for any element b≠0 there exists an integer x, 0≤x≤q−2, such that b=αx. We call x the discrete logarithm of b to the base α and we denote it by x=log α b and more simply by log b when the base is fixed for the discussion. The discrete logarithm problem is stated as follows:

[1] T. Elgamal. A public key cryptosystem and a signature scheme based on discrete logarithms , 1984, CRYPTO 1984.

[2] S. Vanstone,et al. Computing Logarithms in Finite Fields of Characteristic Two , 1984 .

[3] Avi Wigderson,et al. How discreet is the discrete log? , 1983, STOC.

[4] Don Coppersmith,et al. Fast evaluation of logarithms in fields of characteristic two , 1984, IEEE Trans. Inf. Theory.

[5] Rolf Johannesson,et al. On computing logarithms overGF(2p) , 1981 .

[6] Andrew M. Odlyzko,et al. Discrete Logarithms in Finite Fields and Their Cryptographic Significance , 1985, EUROCRYPT.

[7] A. E. Western,et al. Tables of indices and primitive roots , 1968 .

[8] Martin E. Hellman,et al. An improved algorithm for computing logarithms over GF(p) and its cryptographic significance (Corresp.) , 1978, IEEE Trans. Inf. Theory.

[9] Whitfield Diffie,et al. New Directions in Cryptography , 1976, IEEE Trans. Inf. Theory.

[10] Leonard M. Adleman,et al. A subexponential algorithm for the discrete logarithm problem with applications to cryptography , 1979, 20th Annual Symposium on Foundations of Computer Science (sfcs 1979).