Montgomery-Suitable Cryptosystems

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 Mn(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.

• Type: Conference
• Year: 1993
• Where: FIWAC
• Authors: David Naccache, David M'Raïhi
• Keywords: ABN Mod, Constant Factor, Constant N−2 Mod, Cryptology, FIWAC 1993