Method and device for realizing scalar multiplication in chip and computer readable storage medium

Abstract

The invention discloses a Method and device for realizing scalar multiplication in chip and computer readable storage medium. The method comprises the steps that parameters of a first scalar k, a fixed coordinate point P, a window width w and an elliptic curve E (Fp) are acquired; The method comprises the following steps: obtaining a positive integer r, generating a positive integer r which belongs to Fp, calculating the number of windows, m being binary bit lengths k and r respectively, adding r * n to k, and subtracting (2d-n) from the k, The method comprises the following steps: 1) assigning a second scalar k'to an obtained result, wherein n is an order of an elliptic curve base point; Encoding k'into an array C 'comprising d elements corresponding to a binary bit sequence of each column in a matrix of w rows and d columns converted from k'; And using the element C '[i] in the array C' and the fixed coordinate point P to circularly execute a multiple point operation Q2Q and a pointaddition operation QQ + C '[i] P + P, and outputting a circulation result. According to the method, the SPA attack resistance and the fault attack resistance are completely realized by setting the point multiplication operation and the point addition operation once in each cyclic calculation process.

Description

technical field [0001] The present invention relates to but not limited to the technical field of information security, and in particular relates to a scalar multiplication implementation method and device in a chip, and a computer-readable storage medium. Background technique [0002] With the development of computer technology and the continuous improvement of social informatization, information security issues have been paid more and more attention by people. Elliptic curve cryptography (Elliptic curve cryptography, ECC) has the advantages of high security, fast calculation speed, small storage space, low bandwidth requirements, and few calculation parameters compared with traditional public key encryption algorithms, and has been widely used in field of information security. [0003] The scalar multiplication operation is a core operation step in the elliptic curve public key cryptosystem, and it is also the most time-consuming operation step. Comb method is a fast alg...

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Problems solved by technology

However, during the execution of the existing comb algorithm, "non-zero window" and "zero window" will appear, and the attacker can observe the difference between the "non-zero window" and "zero window" on the power consumption curve through an oscilloscope. Analysis to obtain partial scalar information, so the existing comb algorithm cannot resist Simple Power Analysis (SPA) attack

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