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A New Fast Large-number Modular Multiplication Algorithm Based on Addition

Min Zhang

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Abstract

Researched on several recently widely used modular multiplication algorithms,adopted the ideal of window division,estimating quotient,and modular 2n easy to be calculated,which is used in Montgomery modular multiplication algorithm,a new fast calculating AB mod N algorithm based on addition is presented,which introduces pre-calculating by modular N.When the length of modular N is 1 024-bit and the length of window is 6,on the average,the new algorithm requires only 693 times 1 024-bit addition to calculate AB mod N.Comparing with current additional modular multiplication algorithm,the computing complexity is reduced largely.

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What this paper is about

Researched on several recently widely used modular multiplication algorithms,adopted the ideal of window division,estimating quotient,and modular 2n easy to be calculated,which is used in Montgomery modular multiplication algorithm,a new fast calculating AB mod N algorithm based on addition is presented,which introduces pre-calculating by modular N.When the length of modular N is 1 024-bit and the length of window is 6,on the average,the new algorithm requires only 693 times 1 024-bit addition to calculate AB mod N.Comparing with current additional modular multiplication algorithm,the computing complexity is reduced largely.

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Available abstract

Researched on several recently widely used modular multiplication algorithms,adopted the ideal of window division,estimating quotient,and modular 2n easy to be calculated,which is used in Montgomery modular multiplication algorithm,a new fast calculating AB mod N algorithm based on addition is presented,which introduces pre-calculating by modular N.When the length of modular N is 1 024-bit and the length of window is 6,on the average,the new algorithm requires only 693 times 1 024-bit addition to calculate AB mod N.Comparing with current additional modular multiplication algorithm,the computing complexity is reduced largely.

Key concepts: Modular arithmetic, Modular design, Computer science, Multiplication (music), Multiplication algorithm, Division (mathematics), Algorithm, Arithmetic

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