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Method and device for attacking elliptic curve signature algorithm, equipment and storage medium

A technology based on elliptic curves and algorithms, applied in secure communication devices, public keys for secure communications, digital transmission systems, etc., can solve problems such as difficulty in obtaining partial values ​​of temporary keys, and achieve the effect of increasing feasibility

Active Publication Date: 2022-05-10
SHANGHAI FUDAN MICROELECTRONICS GROUP
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  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

Problems solved by technology

[0006] The technical problem solved by the present invention is how to solve the problems such as the difficulty in obtaining the partial value of the temporary key when applying the lattice attack method

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  • Method and device for attacking elliptic curve signature algorithm, equipment and storage medium
  • Method and device for attacking elliptic curve signature algorithm, equipment and storage medium
  • Method and device for attacking elliptic curve signature algorithm, equipment and storage medium

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Embodiment Construction

[0026] In an embodiment of the present invention, the elliptic curve signature algorithm includes a conventional elliptic curve digital signature algorithm (Elliptic Curve Digital Signature Algorithm, ECDSA), an elliptic curve public key cryptographic algorithm SM2, and the like.

[0027]In an embodiment of the present invention, the temporary key is composed of several bits, wherein zero bits and non-zero bits indicate that a certain bit of the temporary key is 0 and 1, respectively.

[0028] In the embodiment of the present invention, it is considered that the elliptic curve signature algorithm involves a point product algorithm, and no matter which point product algorithm is used (for example, always point doubling point algorithm, Montgomery point product algorithm), the signature parameters are related to the temporary key The effective length of the key is related.

[0029] For example, the signature parameter is the signature time required for a temporary key to perform...

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Abstract

The embodiment of the invention provides a method and device for attacking an elliptic curve signature algorithm, equipment and a storage medium, and the method comprises the steps: obtaining a plurality of signature parameters for carrying out the multiple times of signature based on the elliptic curve signature algorithm, and enabling each signature in the multiple times of signature to correspond to one signature parameter; obtaining a threshold value related to N zero bits before a first non-zero bit in a temporary key of the elliptic curve signature algorithm, N being an integer; respectively comparing each signature parameter corresponding to at least one part of signatures in the multiple signatures with a threshold value to obtain effective signatures in the multiple signatures, and further obtaining a set of the effective signatures; performing lattice cracking on the set based on an LLL algorithm to obtain a specific temporary key corresponding to at least one effective signature in the set; and obtaining a private key of the elliptic curve signature algorithm based on the specific temporary key. Therefore, the private key can be conveniently obtained, and the feasibility of the attack elliptic curve signature algorithm is improved.

Description

technical field [0001] The invention relates to the technical field of data encryption, in particular to a method, device, equipment and storage medium for attacking an elliptic curve signature algorithm. Background technique [0002] Compared with traditional signature algorithms (such as RSA algorithm), the elliptic curve signature algorithm only needs a shorter key length under the same security strength, so it is more suitable for applications in chips with limited resources. However, attack methods against the elliptic curve signature algorithm are also constantly emerging. [0003] In 2001, Romer (Romer) proposed a grid attack method against the Elliptic Curve Signature Algorithm, which can be referred to in Document 1 (Romer, Information Leakage Attacks against Smart Card Implementations of the Elliptic Curve Digital Signature Algorithm, I.Attali and T.Jensen (Eds .): E-smart 2001, LNCS 2140, pp.211–219, 2001), where the attacker obtains part of the value of the ephe...

Claims

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Application Information

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IPC IPC(8): H04L9/32H04L9/30
CPCH04L9/3247H04L9/3066
Inventor 王立辉闫守礼单伟君刘枫张纲李清俞军
Owner SHANGHAI FUDAN MICROELECTRONICS GROUP