Private key recovery method and system for realizing modular reduction attack based on RSA-CRT of template

Abstract

The embodiment of the invention discloses a private key recovery method and system for realizing a modular reduction attack based on RSA-CRT of a template, and the method comprises the steps: carrying out the multivariate normal distribution modeling of an energy trace of a modular reduction operation of training equipment based on a Hamming weight model, and obtaining a template corresponding to an intermediate value byte by byte after modular reduction; based on a template matching method for selecting the ciphertext, obtaining an intermediate value r of the RSA algorithm modular reduction operation, and recovering a private key p used by the RSA algorithm through the intermediate value r; decomposing the public key n to obtain a private key q, thereby obtaining private keys p and q of the RSA. Modeling is carried out based on a Hamming weight model of the intermediate value after modular reduction, template matching is carried out by collecting and selecting an energy trace of ciphertext modular reduction to obtain the Hamming weight of the intermediate value after modular reduction, key recovery is carried out according to a private key recovery algorithm, and the problem that a private key cannot be recovered through the Hamming weight of the intermediate value after modular reduction is solved.

Description

technical field [0001] The embodiment of the present application relates to the technical field of cryptography application, and specifically relates to a method and system for recovering a private key based on a template-based RSA-CRT to implement a modulus reduction attack. Background technique [0002] The differential energy analysis proposed by Kocher et al. created the research field of side-channel attack. Side-channel attack mainly studies the recovery of sensitive information by using side-channel information such as energy consumption and electromagnetic radiation leaked in the process of encrypting and decrypting messages by cryptographic equipment. Side channel attacks are mainly divided into two categories, one is modeling attacks, such as template attacks, and the other is non-modeling attacks, such as correlation energy analysis. Based on modeling attacks, the attacker needs to obtain two identical devices, one of which has sufficient control rights, trains th...

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Problems solved by technology

[0005] To this end, the embodiment of the present application provides a template-based RSA-CRT to realize a private key recovery method and system for modulus reduction attacks, based on the Hamming weight model modeling of the intermediate value after modulus reduction, and selecting ciphertext modulus reduction by collecting Perform template matching on the energy traces to obtain the Hamming weight of the intermediate value after modular reduction, and recover the key according to the private key recovery algorithm, which solves the problem that the private key cannot be recovered from the Hamming weight of the intermediate value after modular reduction

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