In mathematics, for positive integers k and s, a vectorial addition chain is a sequence V of k-dimensional vectors of nonnegative integers vi for −k + 1 ≤ i ≤ s together with a sequence w, such that For example, a vectorial addition chain for [22,18,3] is Vectorial addition chains are well suited to perform multi-exponentiation:[1] An addition sequence for the set of integer S ={n0, ..., nr-1} is an addition chain v that contains every element of S. For example, an addition sequence computing is It's possible to find addition sequence from vectorial addition chains and vice versa, so they are in a sense dual.
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