The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
A language for computational algebra
SYMSAC '81 Proceedings of the fourth ACM symposium on Symbolic and algebraic computation
A knapsack type public key cryptosystem based on arithmetic in finite fields
Proceedings of CRYPTO 84 on Advances in cryptology
Discrete logarithms in finite fields and their cryptographic significance
Proc. of the EUROCRYPT 84 workshop on Advances in cryptology: theory and application of cryptographic techniques
Constructing normalisers in finite soluble groups
Journal of Symbolic Computation
Intersecting subgroups of finite soluble groups
Journal of Symbolic Computation
Conditionally secure secret sharing schemes with disenrollment capability
CCS '94 Proceedings of the 2nd ACM Conference on Computer and communications security
Software implementation of Tate pairing over GF(2m)
Proceedings of the conference on Design, automation and test in Europe: Designers' forum
Efficient computations of the Tate pairing for the large MOV degrees
ICISC'02 Proceedings of the 5th international conference on Information security and cryptology
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We present a method for determining logarithms in GF(2n). Its asymptotic running time is O( exp (cn1/3log2/3n)) for a small constant c, while, by comparison, Adleman's scheme runs in time O( exp (c'n1/2log1/2n)). The ideas give a dramatic improvement even for moderate-sized fields such as GF(2127), and make (barely) possible computations in fields of size around 2400. The method is not applicable to GF(q) for a large prime q.