Electrical computers: arithmetic processing and calculating – Electrical digital calculating computer – Particular function performed
Reexamination Certificate
2006-05-25
2010-11-09
Mai, Tan V (Department: 2193)
Electrical computers: arithmetic processing and calculating
Electrical digital calculating computer
Particular function performed
Reexamination Certificate
active
07831650
ABSTRACT:
In a method for modular multiplication using a multiplication look-ahead process for computing a multiplication shift value and a reduction look-ahead process for computing a reduction shift value, a modulus is first transformed into a transformed modulus that is greater than said modulus. The transformation is carried out such that a predetermined fraction of the transformed modulus has a higher-order digit with a first predetermined value that is followed by at least one low-order digit having a second predetermined value. During the iterative working off of the modular multiplication using the multiplication look-ahead process and the reduction look-ahead process, the transformed modulus is utilized so as to obtain at the end of the iteration a transformed result for the modular multiplication. Finally, the transformed result is re-transformed by modular reduction using the original modulus. By means of the transformation according to the invention, iterative working off of the modular multiplication is simplified so that the modular multiplication can be performed faster.
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Walter C. D.: “Faster Modular Multiplication by Operand Scaling”, Editor: Feigenbaum, J.: “Advances in Cryptology-CRYPTO '91”, Springer Verlag, Aug. 1991, pp. 1991, pp. 313-323.
Walter, C. D.: “Space/Time Trade-Offs for Higher Radix Modular Multiplication Using Repeated Addition”, IEEE, vol. 46, No. 2, Feb. 1997, pp. 139-141.
Elbe Astrid
Janssen Norbert
Sedlak Holger
Seifert Jean-Pierre
Dickstein & Shapiro LLP
Infineon - Technologies AG
Mai Tan V
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