Shamir's shared secret scheme in GF(p/sup m/)

Leong Peng Chor, Tan Peng Chong
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Abstract

A. Shamir's (1979) shared secret scheme is adapted to operate over an extension field GF(p)[x]/x/sup m/-/spl omega/ where p is an odd prime p. Both multiplication and multiplicative inverse in such a field can be efficiently computed on 8-bit microcontrollers with appropriate choice of p and exploiting the built-in byte-multiply instruction. In applications with fixed p, m, and /spl omega/ further acceleration can be achieved via a small set of pre-computed values. Pre-computation also eliminates the necessity for division at the sub-field level. A brief discussion on efficiency and memory trade-off is provided. It is found that reconstruction of a 128-bit secret under a (2,3) threshold scheme on a low-end smart card is not impractical.
Shamir在GF中的共享秘密计划(p/sup /)
a . Shamir(1979)的共享秘密方案适用于在扩展域GF(p)[x]/x/sup m/-/spl omega/上操作,其中p是奇数素数p。在这样的域中,乘法和乘法逆都可以在8位微控制器上有效地计算,适当选择p并利用内置的字节乘法指令。在具有固定p、m和/spl ω /的应用中,可以通过一小组预先计算的值来实现进一步的加速。预计算还消除了在子字段级别划分的必要性。简要讨论了效率和内存的权衡。研究发现,在(2,3)阈值方案下,在低端智能卡上重构128位密钥是可行的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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