Asymmetric Squaring Formulae

Abstract. We present efficient squaring formulae based on the Toom-Cook multiplication algorithm. The latter always requires at least one non-trivial constant division in the interpolation step. We show such non-trivial divisions are not needed in the case two operands are equal for 3, 4, 5-way squarings. Our analysis shows that our 3-way squaring algorithms have much less overhead than the best known 3-way Toom-Cook algorithm. Our experimental results show that one of our new 3-term squaring methods performs faster than mpz_mul() in GNU multiple precision library (GMP) for squaring integers of 2880-6912 bits on Pentium 4 Prescott. For squaring in Z[x], our algorithms are much superior to other known squaring algorithms for certain range of input size. In addition, we present 4-way and 5-way squaring formulae which do not require any constant divisions by integers other than a power of 2. Under some reasonable assumptions, our 5-way squaring formula is faster than the recently propose...

• Type: Conference
• Year: 2007
• Where: ARITH
• Authors: Jaewook Chung, M. Anwar Hasan
• Keywords: Applied Computing, ARITH 2007, Squaring, Squaring Algorithms, Squaring Formulae