Exponentiating Faster with Addition Chains

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Exponentiating Faster with Addition Chains

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The similarity between fast computations with huge numbers and data compression is ... number of 1's in the binary representation of n . Erdos [El proved that for.

EXPONENTIATING

FASTER WITH ADDITION

CHAINS

Y. Yacobi Bellcore, 445 South St. Morristown, NJ 07962 [email protected]

The similarity between fast computations with huge numbers and data compression is investigated. For example, in data-compression, frequent messages are assigned short codes, while in fast computations we store and reuse the results of frequent computations. In compression we sometimes send the difference of consecutive messages, if its usually small (A modulation), while in fast computation we compute Xn+&xn .XA, if A? is already known, and A