Parallel algorithms for algebraic problems
SIAM Journal on Computing
A taxonomy of problems with fast parallel algorithms
Information and Control
Log depth circuits for division and related problems
SIAM Journal on Computing
SIAM Journal on Computing
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Structure of Computers and Computations
Structure of Computers and Computations
Ambiguity and Decision Problems Concerning Number Systems
Proceedings of the 10th Colloquium on Automata, Languages and Programming
Comparison of arithmetic functions with respect to boolean circuit depth
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
DIGITALIZED SIGNATURES AND PUBLIC-KEY FUNCTIONS AS INTRACTABLE AS FACTORIZATION
DIGITALIZED SIGNATURES AND PUBLIC-KEY FUNCTIONS AS INTRACTABLE AS FACTORIZATION
Inversion in finite fields using logarithmic depth
Journal of Symbolic Computation
On the complexity of powering in finite fields
Proceedings of the forty-third annual ACM symposium on Theory of computing
Constant-Depth circuits for arithmetic in finite fields of characteristic two
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
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Modular integer exponentiation (given a, e, and m, compute ae mod m) is a fundamental problem in algebraic complexity for which no efficient parallel algorithm is known. Two closely related problems are modular polynomial exponentiation (given a(x), e, and m(x), compute (a(x))e mod m(x)) and polynomial exponentiation (given a(x), e. and t, compute the coefficient of xt in (a(x))e). It is shown that these latter two problems are in NC2 when a(x) and m(x) are polynomials over a finite field whose characteristic is polynomial in the input size.