ECC (Error Correction Code) authentication method and system for reducing modular inversion calculation

Abstract

The invention discloses an ECC authentication method and system for reducing modular inversion calculation, and the method comprises the steps: receiving an authentication request of a slave through a host, and enabling the slave to store a public key and private key pair; enabling the host to verify the legality of the access request; and after the verification is passed, enabling the host to perform identity authentication on the slave, and if the authentication is passed, allowing the slave to access the host resources. The method has the advantages that the Z coordinate value and the X or Y coordinate value of the calculation result of the ECC jacobian coordinate are used instead of the x and y coordinate values of the projective coordinate, so that only modular multiplication operation can be carried out during authentication, modular inverse operation is avoided, point multiplication operation only needs to be carried out once, complex and time-consuming modular inverse operation is avoided for the slave end, the area of the slave end is optimized, the computing time of the slave end is reduced, the cost is minimum, the time is shortest, and therefore the method is most suitable for hardware implementation.

Description

technical field [0001] The invention relates to the technical field of security authentication, in particular to an ECC authentication method and system that reduces modular inverse calculation. Background technique [0002] Elliptic curve cryptography, referred to as ECC, is an asymmetric encryption algorithm based on elliptic curve mathematical theory. structure. According to this method, the trapdoor function is the solution of a discrete logarithm over a finite field. This problem is known in the art as the "discrete logarithm problem", and in the case of elliptic curves over finite fields, the "elliptic curve discrete logarithm problem", and has been shown to be more efficient than the problem on which other public-key methods are based trickier. Compared with RSA, the advantage of ECC is that a shorter key can be used to achieve equivalent or higher security than RSA. According to research, a 160-bit ECC key will provide a security level equivalent to a 1024-bit RS...

AI Technical Summary

Problems solved by technology

[0006] To sum up, the current solution requires matrix inversion, which requires a large amount of calculation, difficult to reuse calculation units, long calculation time, and large hardware overhead.

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