Toom-Cook Multiplication: Some Theoretical and Practical Aspects

2016/02/08 by M. J. Kronenburg, Kronenburg, M. J. · 1 citation
Computer Science · #Cryptography and Residue Arithmetic #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical Methods and Algorithms #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1602.02740

openalex publication_date 2016/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Toom-Cook multiprecision multiplication is a well-known multiprecision multiplication method, which can make use of multiprocessor systems. In this paper the Toom-Cook complexity is derived, some explicit proofs of the Toom-Cook interpolation method are given, the even-odd method for interpolation is explained, and certain aspects of a 32-bit C++ and assembler implementation, which is in development, are discussed. A performance graph of this implementation is provided. The Toom-Cook method can also be used to multithread other types of multiplication, which is demonstrated for 32-bit GMP FFT multiplication.

Cited by

• Communication-Optimal Parallel Standard and Karatsuba Integer\n Multiplication in the Distributed Memory Model

Related

• Faster Integer Multiplication Using Preprocessing
• Multipliers: comparison of Fourier transformation based method and Synopsys design technique for up to 32 bits inputs in regular and saturation arithmetics
• Multiprecision Arithmetic for Cryptology in C++ - Compile-Time Computations and Beating the Performance of Hand-Optimized Assembly at Run-Time
• Operand Folding Hardware Multipliers
• Multiplication by integer constants