SIAM Journal on Computing
A lower bound for integer greatest common divisor computations
Journal of the ACM (JACM)
Boolean circuits versus arithmetic circuits
Information and Computation
Lower bounds for arithmetic problems
Information Processing Letters
Lower bounds for computations with the floor operation
SIAM Journal on Computing
A binary algorithm for the Jacobi symbol
ACM SIGSAM Bulletin
Algorithmic number theory
Efficient algorithms for computing the Jacobi symbol
Journal of Symbolic Computation
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
Circuit and decision tree complexity of some number theoretic problems
Information and Computation
CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
Hi-index | 0.00 |
We establish lower bounds on the complexity of computing the following number-theoretic functions and relations from piecewise linear primitives: (i) the Legendre and Jacobi symbols, (ii) pseudoprimality, and (iii) modular exponentiation. As a corollary to the lower bound obtained for (i), an algorithm of Shallit and Sorenson is optimal (up to a multiplicative constant).