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Random small Hamming weight products with applications to cryptography

✍ Scribed by Jeffrey Hoffstein; Joseph H. Silverman

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 163 KB
Volume: 130
Category: Article
ISSN: 0166-218X
DOI: 10.1016/s0166-218x(02)00588-7

No coin nor oath required. For personal study only.

✦ Synopsis

There are many cryptographic constructions in which one uses a random power or multiple of an element in a group or a ring. We describe a fast method to compute random powers and multiples in certain important situations including powers in the Galois ÿeld F2n , multiples on Koblitz elliptic curves, and multiples in NTRU convolution polynomial rings. The underlying idea is to form a random exponent or multiplier as a product of factors, each of which has low Hamming weight when expanded as a sum of powers of some fast operation.

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