Codes, Cryptology and Information Security by Unknown

Author:Unknown
Language: eng
Format: epub
ISBN: 9783030164584
Publisher: Springer International Publishing

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utilizing a 2-dimensional DAC.

4 Three-Dimensional Differential Addition Chains

A differential addition chain is an addition chain in which each sum is already accompanied by a difference, i.e. whenever a new chain element is formed by adding M and N, the difference was already in the chain. The chain is called n-dimensional, if every element in this chain has the form of n-tuple. For example, the well-known “Montgomery ladder” is a typical one-dimensional DAC.

In this section, we propose two kinds of constructions of 3-dimensional DACs. One is a higher dimensional analogue of the DJB chain. The other comes from observation directly, which is not a higher dimensional analogue of any 2-dimensional DAC.

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