离散对数模2/sup k/的数字串行算法

Proceedings. 15th IEEE International Conference on Application-Specific Systems, Architectures and Processors, 2004. Pub Date : 2004-09-27 DOI:10.1109/ASAP.2004.1

A. Fit-Florea, D. Matula

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引用次数: 10

摘要

作为我们的主要结果，我们介绍了一种计算离散对数模2/sup k/ (dlg)的数字-序列剩余算法。“数字继承”是加法、乘法、乘法逆、幂和离散对数等基本运算模2/sup k/共有的基本性质。我们的主要算法使用以3为对数基数的二进制算法来计算dlg，并且在其k次迭代中，每个关键路径包含一个模2/sup k/乘法操作。还描述了将该算法扩展到其他对数基数以及使用更高基数2/sup r/中的数字进行计算。

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A digit-serial algorithm for the discrete logarithm modulo 2/sup k/

We introduce as our main result a digit-serial residue arithmetic algorithm for computing the discrete logarithm modulo 2/sup k/ (dlg). "Digit inheritance" is presented as a fundamental property common to the primitive operations modulo 2/sup k/ of addition, multiplication, multiplicative inverse, exponentiation and discrete logarithm. Our main algorithm computes dlg using binary arithmetic with 3 as the logarithmic base and has a critical path containing one modulo 2/sup k/ multiplication operation for each of its k iterations. Extensions of the algorithm to other logarithmic bases and computations using digits in a higher radix 2/sup r/ are also described.

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Proceedings. 15th IEEE International Conference on Application-Specific Systems, Architectures and Processors, 2004.

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