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RADIX MODULAR MULTIPLICATION ALGORITHM
Journal of Circuits, Systems and Computers, 1996In this paper, the concept of a new Radix Modular Multiplication Algorithm (MMA) is proposed. The novelty of the new Radix-2n MMA is that the intermediate partial sums (IPSs) are not restricted to be less than the modulus M, but only to be represented by N bits, where N is the number of bits needed to represent the modulus M.
M. C. Mekhallalati +2 more
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Unfolded Modular Multiplication
2003Sedlak’s [Sed] modular multiplication algorithm is one of the first real silicon implementations to speed up the RSA signature generation [RSA] on a smartcard, cf. [DQ]. Although it is nearly unknown in the scientific literature on cryptographic hardware it received in the practical smartcard world a considerable amount of interest, cf. [HP1, HP2, NMR].
Wieland Fischer, Jean-Pierre Seifert
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An RNS Montgomery modular multiplication algorithm
IEEE Transactions on Computers, 1998We present a new RNS modular multiplication for very large operands. The algorithm is based on Montgomery's method adapted to mixed radix, and is performed using a residue number system. By choosing the moduli of the RNS system reasonably large and implementing the system on a ring of fairly simple processors, an effect corresponding to a redundant ...
Jean-Claude Bajard +2 more
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Proportionally modular diophantine inequalities and their multiplicity
Acta Mathematica Sinica, English Series, 2010A proportionally modular Diophantine inequality has the form \(ax \, \text{mod} \, b \leq cx\), where \(a,b,c\) are positive integers. The set of integer solutions is a numerical semigroup: a subset of the natural numbers which contains zero, is closed under addition, and has finite complement. The authors present properties of such semigroups.
Rosales, J.C., Branco, M.B., Vasco, P
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Modular matrix multiplication on a linear array
Proceedings of the 11th annual international symposium on Computer architecture - ISCA '84, 1984A matrix-multiplication algorithm on a linear array using an optimal number of processing elements is proposed. The local storage required by the processing elements and the I/O bandwidth required to drive the array are both constants that are independent of the sizes of the matrices being multiplied.
I. V. Ramakrishnan, Peter J. Varman
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IEE Proceedings - Computers and Digital Techniques, 1998
The Montgomery algorithm has been widely used in modern cryptography because it is effective for modular exponentiation. However, it is not efficient when used for just a few modular multiplications. Inefficiency is due to the large overhead involved in the residue transformation of arguments.
J.–H. Oh, S.–J. Moon
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The Montgomery algorithm has been widely used in modern cryptography because it is effective for modular exponentiation. However, it is not efficient when used for just a few modular multiplications. Inefficiency is due to the large overhead involved in the residue transformation of arguments.
J.–H. Oh, S.–J. Moon
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High-Speed Modular Multiplication
2004Sedlak’s [Sed] modular multiplication algorithm is one of the first real silicon implementations to speed up the RSA signature generation [RSA] on a smartcard, cf. [DQ]. Theoretically, Sedlak’s algorithm needs on average n/3 steps (i.e., additions/subtractions) to compute the modular product of n-bit numbers.
Wieland Fischer, Jean-Pierre Seifert
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A faster modular multiplication algorithm
International Journal of Computer Mathematics, 1991This paper describes a method for quickly computing AB mod N where N is odd. It is shown to have significant advantages over other algorithms which make it suitable for use in hardware for public key encryption. Such hardware could run at approximately twice the speed of the best currently available.
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Design of modular multiplication
2022Constituting many advanced mathematical operations, multiplication has been thoroughly studied from many perspectives including latency, area, and power. The modified Booth encoding is a very important optimization that reduces the number of partial products during multiplication. Since the compression results of partial products could have a potential
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General modular multiplication by block multiplication and table lookup
Proceedings of IEEE International Symposium on Circuits and Systems - ISCAS '94, 2002This paper deals with the problem of general modular multiplication, i.e., A/spl times/B mod M. To solve it in hardware, we suggest a simple lookup-table based approach and use the novel block multiplier which we have developed earlier on. The area (A) and time (T) complexities of this multiplier are both O(n log n) if carry-lookahead adders are used ...
Cheng-Wen Wu, Yung-Fa Chou
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