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This paper discusses several Montgomery multiplication algorithms, two of which h a ve been proposed before. We describe three additional algorithms, and analyze in detail the space and time requirements of all ve methods. These algorithms have been implemented in C and in assembler. The analyses and actual performance results indicate that the Coarsely(More)
We initiate a provable-security treatment of cryptographic agility. A primitive (for example PRFs, authenticated encryption schemes or digital signatures) is agile when multiple, individually secure schemes can securely share the same key. We provide a surprising connection between two seemingly unrelated but challenging questions. The first, new to this(More)
We show that the multiplication operation c = a br ,1 in the eld GF2 k can be implemented signiicantly faster in software than the standard multiplication, where r is a special xed element of the eld. This operation is the nite eld analogue of the Montgomery multiplication for modular multiplication of integers. We give the bit-level and word-level(More)
We present a new algorithm for computing a e where a 2 GF2 k and e is a positive integer. The proposed algorithm is more suitable for implementation in software , and relies on the Montgomery multiplication in GF2 k. The speed of the exponentiation algorithm largely depends on the availability of a fast method for multiplying two polynomials of length w(More)
approved: C etin K. Ko c Computer and network security systems rely on the privacy and authenticity of information, which requires implementation of cryptographic functions. Software implementations of these functions are often desired because of their exibility and cost eeec-tiveness. In this study, w e concentrate on developing high-speed and area-eecient(More)