Many number-theoretic algorithms rely on a result of Ankeny, which states that if the
Extended Riemann Hypothesis (ERH) is true, any nontrivial multiplicative subgroup of the …

Let GF (p) be the finite field with p'~ elements where p is prime. We consider the problem of
how to deterministically generate in polynomial time a subset of GF (pn) that contains a …

Factoring Polynomials Over Finite Fields: A Survey Page 1 doi:10.1006/jsco.1999.1002
Available online at http://www.idealibrary.com on J. Symbolic Computation (2001) 31, 3–17 …

We present a new deterministic algorithm for factoring polynomials over Z p of degree n. We
show that the worst-case running time of our algorithm is O (p 1 2 (log p) 2 n 2+∈), which is …

This conference (ANTS-I) marks the beginning of what we hope will be a long series of
international conferences on algorithmic number theory. It seems appropropriate, at the …

We survey the modern theory of schemes (coherent configurations). The main attention is
paid to the schurity problem and the separability problem. Several applications of schemes …

This paper is a report on algorithms to solve problems in number theory. I believe the most
interesting such problems to be those from elementary number theory whose complexity is …

In modern as well as ancient ciphers of public key cryptography, substitution boxes find a
permanent seat. Generation and cryptanalysis of 4-bit as well as 8-bit crypto S-boxes is of …

We show assuming the Generalized Riemann Hypothethis that the factorization of a one-
variable polynomial of degree n over an explicitly given finite field of cardinality q can be …

Let F be a finite field or an algebraic number field. In previous work we have shown how to
find the basic building blocks (the radical and the simple components) of a finite dimensional …