Algorithmic number theory
Cryptography and network security (2nd ed.): principles and practice
Cryptography and network security (2nd ed.): principles and practice
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Implementation of fast RSA key generation on smart cards
Proceedings of the 2002 ACM symposium on Applied computing
On Generation of Probable Primes By Incremental Search
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
Speeding up Prime Number Generation
ASIACRYPT '91 Proceedings of the International Conference on the Theory and Applications of Cryptology: Advances in Cryptology
Multiuser cryptographic techniques
AFIPS '76 Proceedings of the June 7-10, 1976, national computer conference and exposition
New directions in cryptography
IEEE Transactions on Information Theory
Fast generation of prime numbers on portable devices: an update
CHES'06 Proceedings of the 8th international conference on Cryptographic Hardware and Embedded Systems
Hi-index | 0.00 |
This paper investigates existing prime generation algorithms on small portable devices, makes optimizations and compares their efficiencies. It shows by comparing the performances that the bit array algorithm is the most efficient among all the existing prime generation algorithms. The paper further optimizes the implementation of the bit array algorithm by using an optimal parameter in the prime generations, namely the small prime set for its sieving procedure. A method for estimating the optimal small prime set for the bit array algorithm is provided. The paper gives generalized bit array algorithms which are able to find primes with special constraints, i.e., DSA primes and strong primes. Finally, the algorithms are implemented in a smart card and a PDA for validation. It shows that there is very little efficiency sacrifice for generating special primes with respect to generating random primes. It also shows that using optimal sets of small primes for prime generations will result in 30-200% efficiency improvement.