Method and apparatus for elliptic curve scalar multiplication

Cryptography – Key management – Key distribution

Reexamination Certificate

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C380S282000, C380S285000

Reexamination Certificate

active

10058214

ABSTRACT:
The applicants have recognized an alternate method of performing modular reduction that admits precomputation. The precomputation is enabled by approximating the inverse of the truncator T, which does not depend on the scalar.The applicants have also recognized that the representation of a scalar in a τ-adic representation may be optimized for each scalar that is needed.The applicants have further recognized that a standard rounding algorithm may be used to perform reduction modulo the truncator.In general terms, there is provided a method of reducing a scalar modulo a truncator, by pre-computing an inverse of the truncator. Each scalar multiplication then utilizes the pre-computed inverse to enable computation of the scalar multiplication without requiring a division by the truncator for each scalar multiplication.

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patent: 6212279 (2001-04-01), Reiter et al.
patent: 6243467 (2001-06-01), Reiter et al.
patent: 6430588 (2002-08-01), Kobayashi et al.
Jerome A. Solinas, An Improved Algorithm for Arithmetic on a Family of Elliptic Curves, Advances in Cryptology—CRYPTO '97, 1997, 357-371.
Jerome A. Solinas, Improved Algorithms for Arithmetic on Anormalous Binary Curves, Technical Report, 1999. Available at http://cacr.uwaterloo.ca.

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