TY - JOUR
T1 - Can Montgomery parasites be avoided? A design methodology based on key and cryptosystem modifications
AU - Naccache, David
AU - M'raïhi, David
AU - Raphaeli, Dan
PY - 1995/1
Y1 - 1995/1
N2 - 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, A B 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 precalculation (and the storage) of the constant N-2 mod n and turns to be particularly efficient when a hardware device implementing Mn(...,...) is the basic computational tool at one's command.
AB - 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, A B 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 precalculation (and the storage) of the constant N-2 mod n and turns to be particularly efficient when a hardware device implementing Mn(...,...) is the basic computational tool at one's command.
UR - http://www.scopus.com/inward/record.url?scp=3643108759&partnerID=8YFLogxK
U2 - 10.1007/BF01388505
DO - 10.1007/BF01388505
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AN - SCOPUS:3643108759
SN - 0925-1022
VL - 5
SP - 73
EP - 80
JO - Designs, Codes, and Cryptography
JF - Designs, Codes, and Cryptography
IS - 1
ER -