The quadratic sieve factoring algorithm
Proc. of the EUROCRYPT 84 workshop on Advances in cryptology: theory and application of cryptographic techniques
Algorithmic number theory
Efficient algorithms for computing the Jacobi symbol
Journal of Symbolic Computation
On the Computation of Square Roots in Finite Fields
Designs, Codes and Cryptography
Improved Computation of Square Roots in Specific Finite Fields
IEEE Transactions on Computers
Improved generalized Atkin algorithm for computing square roots in finite fields
Information Processing Letters
An improved algorithm for computing logarithms over and its cryptographic significance (Corresp.)
IEEE Transactions on Information Theory
Algorithms for Relatively Cyclotomic Primes
Fundamenta Informaticae
| Hi-index | 0.00 |
Atkin's algorithm [2] for computing square roots in $Z^*_p$, where p is a prime such that p ≡ 5 mod 8, has been extended by Müller [15] for the case p ≡ 9 mod 16. In this paper we extend Atkin's algorithm to the general case p ≡ 2s + 1 mod 2s + 1, for any s ≥ 2, thus providing a complete solution for the case p ≡ 1 mod 4. Complexity analysis and comparisons with other methods are also provided.