16 search results - page 2 / 4 » The Number Field Sieve in the Medium Prime Case |
PKC
2010
Springer
13 years 7 months ago
2010
Springer
Abstract. Pairings on elliptic curves over finite fields are crucial for constructing various cryptographic schemes. The T pairing on supersingular curves over GF(3n ) is particula...
MOC
2002
13 years 5 months ago
2002
In previous work, the author has extended the concept of regular and irregular primes to the setting of arbitrary totally real number fields k0, using the values of the zeta functi...
EUROCRYPT
2007
Springer
13 years 11 months ago
2007
Springer
Significant progress in the design of special purpose hardware for supporting the Number Field Sieve (NFS) has been made. From a practical cryptanalytic point of view, however, no...
INDOCRYPT
2001
Springer
13 years 9 months ago
2001
Springer
We present an algorithm for generating elliptic curves of prime order over Optimal Extension Fields suitable for use in cryptography. The algorithm is based on the theory of Comple...
MOC
2002
13 years 5 months ago
2002
Abstract. In this paper, we are interested in solving the so-called norm equation NL/K(x) = a, where L/K is a given arbitrary extension of number fields and a a given algebraic num...