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

Inactive Publication Date: 2013-10-02
TSINGHUA UNIV
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Problems solved by technology

[0004] The extended Euclidean algorithm realizes the solution of the modular inverse by using the method of rolling and dividing, but

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  • Improved binary-system left-shifting modular inversion algorithm

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Embodiment Construction

[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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Abstract

The invention relates to an improved binary-system left-shifting modular inversion algorithm. For a given modulus p, during a process of calculating the modular inversion, the condition of skipping out of circulation of the bits of the p is c_u=n-1 or c_v=n-1, namely, the comparison between c_u as well as c_v and the constant n-1, wherein u and v are intermediate variables of n bits for storing left-shifted data and are respectively initialized as p and a; r is the intermediate variable for obtaining modular inversion through left shifting and is initialized as 0; after the algorithm is ended, the value in r is a resolved modular inversion result; c_u shows the times of the left shifting; and c_v shows the times of the left shifting of the v. The invention also provides a circuit structure for realizing the algorithm. The algorithm provided by the invention has simpler operation steps and occupies fewer storing units, so that the circuit area and the circuit power consumption are reduced, and a low power consumption requirement of a low-end code system is preferably met.

Description

technical field [0001] The invention relates to an improved binary left-shift modular inverse algorithm. Background technique [0002] With the rapid development of information security, the public key cryptosystem based on mathematical problems has been widely used. Elliptic curve cryptography (ECC, elliptic curve cryptography) is widely used in mobile communication, e-commerce and other fields because of its short key, high speed, high security, resource saving and other advantages. The modular inverse operation of large numbers, as a kind of modular operation, is an indispensable operation in elliptic curve cryptography in the field of prime numbers. In the elliptic curve cryptosystem, both point addition and point doubling operations need to use the inverse operation. With the industrial upgrading of bank IC cards, non-contact financial IC cards will gradually increase, and the application of low-end cryptographic systems is becoming more and more urgent. Therefore, th...

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Application Information

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IPC IPC(8): G06F7/72
Inventor 李树国马帅
Owner TSINGHUA UNIV
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