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Modular Multiplication using Redundant Digit Division

By Ping Tak and Peter Tang


Most implementations of the modular exponentiation, M E mod N, computation in cryptographic algorithms employ Montgomery multiplication, ABR −1 mod N, instead of modular multiplication, AB mod N, even the former requires some transformational overheads. This is so because a state-of-the-art Montgomery multiplication implementation has a performance advantage over direct modular multiplication based on the Barrett algorithm that more than compensates for the overhead. In this paper, we present a direct modular multiplication method that is comparable in speed to Montgomery multiplication. One consequence is that when the exponent in small, direct computation (which does not incur the transformational overhead) using the modular multiplication algorithm presented here results in practical performance gain. For the exponent 17, for instance, which requires five modular multiplication, a saving of up to 40 % can be achieved. 1

Year: 2010
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