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1 results

  • Analysis of the Binary Asymmetric Joint Sparse Form

  • CLEMENS HEUBERGER, SARA KROPF
  • Journal:
    Combinatorics, Probability and Computing / Volume 23 / Issue 6 / November 2014
    Published online by Cambridge University Press:
    14 July 2014, pp. 1087-1113

  • We consider redundant binary joint digital expansions of integer vectors. The redundancy is used to minimize the Hamming weight, i.e., the number of non-zero digit vectors. This leads to efficient linear combination algorithms in abelian groups, which are used in elliptic curve cryptography, for instance.

    If the digit set is a set of contiguous integers containing zero, a special syntactical condition is known to minimize the weight. We analyse the optimal weight of all non-negative integer vectors with maximum entry less than N. The expectation and the variance are given with a main term and a periodic fluctuation in the second-order term. Finally, we prove asymptotic normality.