Modular inverse operating method and operational unit

Abstract

The invention relates to a modulo inversion operation method and an arithmetic unit. The positive integers u and m are known, and u‑1modm is calculated. In the modular inverse operation method and arithmetic unit provided by the present invention, the algorithm only needs to add one flag bit, and at most one multiplication and two subtraction operations, which can greatly improve the operation speed, and has the characteristics of versatility and high efficiency in terms of hardware implementation; Compared with the existing binary extended Euclidean algorithm, there is no need to eliminate the weight factor of the operation result, and the modulus is not limited to be an odd number, and the modulus inverse operation of any non-zero integer can be realized, and Improve the computational efficiency of modular inverse operations and reduce hardware power consumption.

Description

technical field [0001] The invention relates to the technical field of modular inverse calculation, and more specifically, relates to a modular inverse calculation 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. 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...

AI Technical Summary

Problems solved by technology

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

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

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