The parallel complexity of exponentiating polynomials over finite fields

Journal Article · Fri Jul 01 00:00:00 EDT 1988 · J. Assoc. Comput. Mach.; (United States)

DOI:https://doi.org/10.1145/44483.44496· OSTI ID:6508774

Fich, F E; Tompa, M ^[1]

---

1. Dept. of Computer Science, Univ. of Toronto, Toronto, Ontario M5S 1A4 (CA)

Modular integer exponentiation (given a, e, and M, compute a/sup e/ 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))/sup e/ mod m(x)) and polynomial exponentiation (given a(x), e and t compute the coefficient of x/sup t/ in (a(x))/sup e/). It is shown that these latter two problems are in NC/sup 2/ when a(x) and m(x) are polynomials over a finite field whose characteristic is polynomial in the input size.

• OSTI ID: 6508774
• Journal Information: J. Assoc. Comput. Mach.; (United States), Journal Name: J. Assoc. Comput. Mach.; (United States) Vol. 31:9; ISSN JACOA
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990210* -- Supercomputers-- (1987-1989)
COMPUTER CALCULATIONS
FUNCTIONS
PARALLEL PROCESSING
POLYNOMIALS
PROGRAMMING
TECHNOLOGY ASSESSMENT