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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 novel framework for the identification of a multiple-input multiple-output (MIMO) system driven by white, mutually independent unobservable inputs. Samples of the system frequency response are obtained based on parallel factorization (PARAFAC) of three- or four-way tensors constructed based on, respectively, third- or fourth-order cross spectra(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)