A series of algorithms for evaluation of multi-exponentiation are proposed based on the binary greatest common divisor algorithm. The proposed algorithms are inversion free and have the capability to evaluate double o...
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A series of algorithms for evaluation of multi-exponentiation are proposed based on the binary greatest common divisor algorithm. The proposed algorithms are inversion free and have the capability to evaluate double or multi-exponentiation with non-fixed base numbers and exponents. They can also be employed in developing sidechannel countermeasures. For n-bit double and triple exponentiation, they achieve the average complexity of 1.53n and 1.75n multiplications (including squarings), respectively. The proposed algorithms can be very useful for the implementation of many public-key cryptosystems on small devices with limited memory space, e.g., smart cards.
In this article, we prove the existence and uniqueness of a certain distribution function on the unit interval. This distribution appears in Brent's model of the analysis of the binary gcd algorithm. The existence...
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In this article, we prove the existence and uniqueness of a certain distribution function on the unit interval. This distribution appears in Brent's model of the analysis of the binary gcd algorithm. The existence and uniqueness of such a function was conjectured by Richard Brent in his original paper [R.P. Brent, Analysis of the binary Euclidean algorithm, in: J.F. Traub (Ed.), New Directions and Recent Results in algorithms and Complexity, Academic Press, New York, 1976, pp. 321-355]. Donald Knuth also supposes its existence in [D.E. Knuth, The Art of Computer Programming, vol. 2, Seminumerical algorithms, third ed., Addison-Wesley, Reading, MA, 1997] where developments of its properties lead to very good estimates in relation to the algorithm. We settle here the question of existence, giving a basis to these results, and study the relationship between this limiting function and the binary Euclidean operator B-2, proving rigorously that its derivative is a fixed point of B2. (C) 2006 Elsevier B.V. All rights reserved.
The binary gcd algorithm, discovered by Stein, is an alternative to the Euclidean algorithm for computing the greatest common divisor of two integers. In this work, the binary gcd algorithm is applied to Reed-Solomon ...
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The binary gcd algorithm, discovered by Stein, is an alternative to the Euclidean algorithm for computing the greatest common divisor of two integers. In this work, the binary gcd algorithm is applied to Reed-Solomon decoding and a novel iterative algorithm for computing error locator polynomials is proposed. Compared to Euclidean-based algorithms, this algorithm exhibits some speed and area advantages.
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