Template-based rsa-crt private key recovery method and system for module reduction attack

Abstract

The embodiment of the present application discloses a method and system for recovering a private key based on a template-based RSA-CRT to realize a module reduction attack. State distribution modeling to obtain the template corresponding to the intermediate value byte by byte after modular reduction; based on the template matching method of selected ciphertext, the intermediate value r of the modular reduction operation of the RSA algorithm is obtained, and the private value used by the RSA algorithm is restored from the intermediate value r. key p; decompose the public key n to get the private key q, and thus get the RSA private keys p and q. Based on the Hamming weight model modeling of the intermediate value after modular reduction, the Hamming weight of the intermediate value after modular reduction is obtained by collecting and selecting the energy trace of the ciphertext modular reduction, and the key is recovered 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 the reduction of the modulus.

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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