抄録
Since the invention of the public-key cryptosystem in the 1970's, some number theoretic problems such as the integer factoring and the discrete logarithm problem in finite fields have received a lot of attention. The number field sieve method is currently known as the asymptotically fastest integer factoring algorithm. It is also known that the number field sieve method can be made use of computing discrete logarithms in finite fields due to Gordon and Schirokauer. Besides, Adleman proposed a function field analogue of the number field sieve method, which is known as the function field sieve, to compute discrete logarithms in finite fields. This paper surveys recent results on these two methods, the number field sieve and the function field sieve, of computing discrete logarithms in finite fields.
