Methods and apparatus for incomplete modular arithmetic

Details Methods and apparatus for incomplete modular arithmetic Methods and apparatus for incomplete modular arithmetic

2006-07-18

2006-07-18

Mai, Tan V. (Department: 2193)

Electrical computers: arithmetic processing and calculating

Electrical digital calculating computer

Particular function performed

Reexamination Certificate

active

07080109

ABSTRACT:
Methods and apparatus for modular arithmetic operations with respect to a modulus p include representing operands as a series of s w-bit numbers, whereins=⌈kw⌉.Operations are executed word by word and a carry, borrow, or other bit or word is obtained from operations on most significant words of the operands. Depending on the value of this bit or word, an operation-specific correction factor is applied. Cryptographic systems include computer executable instructions for such methods. Bit-level operations are generally avoided and the methods and apparatus are applicable to systems based on, for example, public-key cryptographic algorithms defined over the finite field GF(p).

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Yanik et al, “Incomplete reduction in modular arithmetic”, Computer and Digital Techniques, IEE Proceedings-, vol.: 149, Issue: 2, Mar. pp. 46-52.

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