A course in computational algebraic number theory
A course in computational algebraic number theory
Algorithmic number theory
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
Generating Large Instances of the Gong-Harn Cryptosystem
Proceedings of the 8th IMA International Conference on Cryptography and Coding
Fast Irreducibility and Subgroup Membership Testing in XTR
PKC '01 Proceedings of the 4th International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
Public-key cryptosystems based on cubic finite field extensions
IEEE Transactions on Information Theory
Algorithms for Relatively Cyclotomic Primes
Fundamenta Informaticae
| Hi-index | 0.00 |
In 1999 Gong and Harn proposed a new cryptosystem based on third-order characteristic sequences with period p 2k + p k + 1 for a large prime p and fixed k . In order to find key parameters and therefore to construct a polynomial whose characteristic sequence is equal to p 2k + p k + 1 one should generate a prime p such that the prime factorization of the number p 2k + p k + 1 is known. In this paper we propose new, efficient methods for finding the prime p and the factorization of the aforementioned number. Our algorithms work faster in practice than those proposed before. Moreover, when used for generating of XTR key parameters, they are a significant improvement over the Lenstra-Verheul Algorithm. Our methods have been implemented in C++ using LiDIA and numerical test are presented.