Scalar Regular Naf Sequence Generation Method

Abstract

The invention discloses a generation method for a regular NAF sequence of a scalar. The method includes steps of choosing a window size w of the regular NAF sequence according to demands and listing formats of the regular NAF sequence in the corresponding window size; listing all possible results of a non-zero item and re-encoding the results to a continuous positive integer set according to a size sequence; recording the parity according to the lowest order of the scalar k and adjusting the lowest order so as to obtain an odd k', if k[0]=1, k'=k, or, k'=k+1; dividing k' into groups from the lowest order to the highest order, each group containing w orders and finding the non-zero group with the highest order and adding 1 in front of the highest order, moving the new k' from the high order to the low order and removing the lowest order. Therefore, the regular NAF sequence, subjected to re-encoding and with no 0 in a prior regular NAF sequence remained, with the window size of w, is obtained. The method saves calculation time and saves storage space.

Description

technical field [0001] The invention relates to the field of information security, in particular to a method for generating a scalar regular NAF (non-adjacent expression type) sequence. Background technique [0002] Elliptic curve cryptography (ECC) has the characteristics of high security, small amount of calculation, fast processing speed, small storage space, and low bandwidth requirements. Compared with the RSA public key system, ECC is very suitable for embedded mobile environments with limited resources, such as cryptographic chips on smart cards. Traditionally, the attack on cryptographic chips is mainly to analyze the implemented algorithm from a mathematical point of view, such as differential analysis and linear analysis. However, since Side Channel Attacks (Side Channel Attacks) was proposed, more and more people began to pay attention to the implementation of the chip and the anti-attack measures taken against the attacks faced by the chip. Side-channel attack ...

AI Technical Summary

Problems solved by technology

[0004] An effective way to defend against SPA attacks is to generate regular Width-w NAF representations for scalar k. In this regular Width-w NAF sequence, non-zero bits must and will only be generated at specific positions in each w-bit sequence. Therefore, the position of the non-zero bit has no direct relationship with the value of the scalar k itself, and there is no obvious feature on the power consumption curve of the scalar multiplication that can be used by SPA

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