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A new method for multiplication of large integersand designed for efficient software implementation is presented and compared with the well-known "schoolbook" method that is currently used for both software and hardware implementations of public-key cryptographic techniques. The comparison for the software-efficient method is made in terms of the required number of basic operations on small integers. It is shown that a significant performance gain is achieved by the new software-efficient method for integersfrom 192 to 1024 bitsin length, which isthe range of interest for all current public-key implementations. For 1024-bit integer multiplication, the savings over the schoolbook method is conservatively estimated to be about 33%. A new method for multiplication of large integers, which isanalogousto the new softwareefficient method but isdes igned for efficient hardware implementation, is also presented and compared to the schoolbook method in terms of the number of processor clock cycles required.

Fast Multiplication of Integers for Public-Key Applications