Fast integer multiplication using modular arithmetic

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn , Issue , 2008, Pages 499-505

  De, Anindya ^a   Kurur, Piyush ^a   Sana, Chandan ^a   Saptharishi, Ramprasad ^a,b  

^a INDIAN INSTITUTE OF TECHNOLOGY KANPUR   (India)

^b CHENNAI MATHEMATICAL INSTITUTE   (India)

Author keywords

Computational algebra; Integer multiplication; Modular arithmetic

Indexed keywords

POLYNOMIALS;

BIT INTEGERS; COMPLEX ARITHMETIC; COMPLEX NUMBER; COMPUTATIONAL ALGEBRA; INTEGER MULTIPLICATIONS; MODULAR ARITHMETIC; MULTIVARIATE POLYNOMIAL;

COMPUTATION THEORY;

EID: 57049170396     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1374376.1374447     Document Type: Conference Paper

References (15)

1. Alan J. Baker. An introduction to p-adic numbers and p-adic analysis. Online Notes, 2007. http://www.maths.gla.ac.uk/~ajb/dvips/padicnotes.pdf.
2. th ACM Symposium on Theory of Computing, pages 57-66, 2007.
3. D. R. Heath-Brown. Zero-free regions for Dirichlet L-functions, and the least prime in an arithmetic progression. In Proceedings of the London Mathematical Society, 64(3), pages 265-338, 1992.
4. I. Martin Isaacs. Character theory of finite groups. Dover publications Inc., New York, 1994.
5. A Karatsuba and Y Ofman. Multipication of multidigit numbers on automata. English Translation in Soviet Physics Doklady, 7:595-596, 1963.
6. Yuri V. Linnik. On the least prime in an arithmetic progression, I. The basic theorem, II. The Deuring-Heilbronn's phenomenon. Rec. Math. (Mat. Sbornik), 15:139-178 and 347-368, 1944.
7. G. L. Miller. Riemann's hypothesis and tests for primarily. Journal of Computer and System Sciences, 13:300-317, 1976.
8. Ivan Niven, Herbert S. Zuckerman, and Hugh L. Montgomery. An Introduction to the Theory of Numbers. John Wiley and Sons, Singapore, 1991.
9. Michael O. Rabin. Probabilistic algorithm for testing primality. Journal of Number Theory, 12:128-138, 1980.
10. A Schönhage and V Strassen. Schnelle Multiplikation grosser Zahlen. Computing, 7:281-292, 1971.
11. Arnold Schönhage. Asymptotically fast algorithms for the numerical multiplication and division of polynomials with complex coefficients. In Computer Algebra, EUROCAM, volume 144 of Lecture Notes in Computer Science, pages 3-15, 1982.
12. Igor R. Shafarevich. Basic Notions of Algebra. Springer Verlag, USA, 1999.
13. Cai Tianxin. Primes representable by polynomials and the lower bound of the least primes in arithmetic progressions. Acta Mathematica Sinica, New Series, 6:289-296, 1990.
14. E. C. Titchmarsh. A divisor problem. Rend. Circ. Mat. Palerme, 54:414-429, 1930.
15. A L. Toom. The complexity of a scheme of functional elements simulating the multiplication of integers. English Translation in Soviet Mathematics, 3:714-716, 1963.