modular inverse operator

Abstract

The invention provides a modular inverse operation method and an arithmetic device. The modular inversion operation method and the arithmetic device are used for calculating Z=Y<-1>mod X, wherein Z is a result of a modular inverse operation, X is a first operand and Y is a second operand. The modular inverse operation method comprises the following steps of calculating and acquiring a binary bit length Xlen of the first operand X and a binary bit length Ylen of the second operand Y; initializing a first variable R and a second variable S; when Xlen is greater than and equal to Ylen, calculating X <-1>modY; and when Xlen is smaller than and equal to Ylen, calculating Y <-1>modX. When the updated X is equal to 0 and the updated Y is equal to 1, a result of the modular inverse operation is the updated second variable S; when the updated X is equal to 1 and the updated Y is equal to 0, a result of the modular inverse operation is a difference between an X initial value and the updated first variable R; and when one of the updated X and the updated Y is equal to 0 and the other of the updated X and the updated Y is not equal to 1, a result of the modular inverse operation does not exist. By using the method and the arithmetic device, the modular inverse operation, in which the module is any non-zero integer can be realized, the calculation efficiency of the modular inverse operation is improved and the power consumption of hardware is reduced.

Description

technical field [0001] The invention relates to the field of information security, in particular to a modular inverse operation method and a computing device. Background technique [0002] Modular inverse operations are widely used in public key cryptosystems. For example, modular inverse operations are used in the generation of decryption keys in the RSA algorithm. Modular inverse operations can also be used in point addition and point multiplication in elliptic curve cryptographic algorithms. [0003] At present, the methods for solving modular inverse operations mainly include modular exponentiation algorithm, extended Euclidean algorithm, and binary extended Euclidean algorithm. [0004] The modular exponentiation algorithm is based on Fermat's little theorem, and converts the modular inversion operation into a modular exponentiation operation, but the modular exponentiation algorithm cannot determine whether the modular inversion result exists. Using a modular multipli...

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Problems solved by technology

[0004] The modular exponentiation algorithm is based on Fermat's little theorem, and converts the modular inversion operation into a modular exponentiation operation, but the modular exponentiation algorithm cannot determine whether the modular inversion result exists

The modular multiplier is used as the hardware operation unit, which is relatively complex and consumes a lot of power

[0005] The extended Euclidean algorithm solves the modular inverse by calculating the greatest common factor by rolling and dividing. When the greatest common factor is a non-1 integer, the calculation result of the modular inverse cannot be obtained

Using the divider as the hardware operation unit, the implementation is still relatively complicated

[0006] The binary extended Euclidean algorithm converts division into shift and addition and subtraction. However, in the process of shifting, the weight of the operand changes, and the final operation result contains 2 n (n is the bit length of the operand) item weight factor, removing the weight factor requires multiple operations of dividing by 2, therefore, the modulus must be an odd number

[0007] The existing binary extended Euclidean algorithm method still has certain limitations in the modular inverse operation, it cannot be used to calculate the modulus for any non-zero integer, and the calculation process is relatively complicated

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