Abstract
Montgomery's algorithm [8], hereafter denoted Mn(·,·), is a process for computing Mn(A,B)=ABN mod n where N is a constant factor depending only on n. Usually, AB mod n is obtained by M n(Mn(A,B),N−2 mod n) but in this article, we introduce an alternative approach consisting in pre-integrating N into cryptographic keys so that a single Mn(·,·) will replace directly each modular multiplication. Except the advantage of halving the number of Montgomery multiplications, our strategy skips the pre-calculation (and the storage) of the constant N −2 mod n and reveals to be particularly efficient when a hardware device implementing Mn(·,·) is the basic computational tool at one's command.
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© 1994 Springer-Verlag Berlin Heidelberg
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Naccache, D., M'Raïhi, D. (1994). Montgomery-suitable cryptosystems. In: Cohen, G., Litsyn, S., Lobstein, A., Zémor, G. (eds) Algebraic Coding. Algebraic Coding 1993. Lecture Notes in Computer Science, vol 781. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57843-9_10
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DOI: https://doi.org/10.1007/3-540-57843-9_10
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