Improved binary-system left-shifting modular inversion algorithm
An inverse algorithm and binary technology, which is applied to calculations using non-numerical representations, calculations using residual algorithms, etc., can solve problems such as unfavorable computer processing and complex division operations, and meet the requirements of low power consumption and less storage units. , the effect of streamlining the operation steps
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[0039] The implementation of the present invention will be described in detail below in conjunction with the drawings and examples.
[0040] An improved binary left-shift modular inverse algorithm of the present invention, the modular inverse of an integer a on the prime number field GF(p) is defined as: for a prime number p and an integer a∈[1,p-1], there is a unique integer i∈[ 1,p-1], so that i·a≡1(mod p), then the integer i is the inverse of a, recorded as: i≡a -1 (mod p), characterized in that, for a given modulus p (the number of bits of p is recorded as ), in the process of calculating the modular inverse, the condition for jumping out of the loop is c_u=n-1 or c_v=n-1, that is, the comparison between c_u, c_v and the constant n-1. In this way, fewer storage units will be used ( bit), and the operation is relatively simple. In addition, it is necessary to increase The bit variable d is used to record the number of left shifts. The improved algorithm must be shif...
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