Issue No.08 - August (1992 vol.41)

pp: 949-956

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/12.156537

ABSTRACT

<p>A fast radix-4 modular multiplication hardware algorithm is proposed. It is efficient for modular exponentiation with a large modulus, used in public-key cryptosystems such as the RSA cryptosystem. The operands and the result of multiplication which are intermediate results in modular exponentiation are represented in a redundant representation. The computation proceeds in serial-parallel fashion. Each subtraction for the division for residue calculation is embedded in the repeated multiply-add. Each intermediate result is represented in a more redundant representation than that for the operands and the result, so that the number of the required addition/subtractions is reduced. All addition/subtraction are carried out without carry propagation. A serial-parallel modular multiplier based on the algorithm has a regular cellular array structure with a bit slice feature and is suitable for VLSI implementation.</p>

INDEX TERMS

division subtraction; radix-4 modular multiplication hardware algorithm; modular exponentiation; public-key cryptosystems; RSA cryptosystem; redundant representation; residue calculation; repeated multiply-add; serial-parallel modular multiplier; cellular array structure; bit slice; VLSI; cryptography; digital arithmetic.

CITATION

N. Takagi, "A Radix-4 Modular Multiplication Hardware Algorithm for Modular Exponentiation",

*IEEE Transactions on Computers*, vol.41, no. 8, pp. 949-956, August 1992, doi:10.1109/12.156537