Publication

The Security of DSA and ECDSA

Serge Vaudenay
2003
Conference Papers

Abstract

DSA and ECDSA are well established standards for digital signature based on the discrete logarithm problem. In this paper we survey known properties, certification issues regarding the public parameters, and security proofs. ECDSA also includes a standard certification scheme for elliptic curve which is assumed to guarantee that the elliptic curve was randomly selected, preventing from any potential malicious choice. In this paper we show how to bypass this scheme and certify any elliptic curve in characteristic two. The prime field case is also studied. Although this does not lead to any attack at this time since all possible malicious choices which are known at this time are specifically checked, this demonstrates that some part of the standard is not well designed. We finally propose a tweak.

Official source

https://infoscience.epfl.ch/entities/publication/0fe8db49-1573-4c69-8980-62dbcd1457e2

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Serge Vaudenay
2003
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/0fe8db49-1573-4c69-8980-62dbcd1457e2

About this result

Related concepts (32)

Elliptic Curve Digital Signature Algorithm

In cryptography, the Elliptic Curve Digital Signature Algorithm (ECDSA) offers a variant of the Digital Signature Algorithm (DSA) which uses elliptic-curve cryptography. As with elliptic-curve cryptography in general, the bit size of the private key believed to be needed for ECDSA is about twice the size of the security level, in bits. For example, at a security level of 80 bits—meaning an attacker requires a maximum of about operations to find the private key—the size of an ECDSA private key would be 160 bits.

Certification

Certification is part of testing, inspection and certification and the provision by an independent body of written assurance (a certificate) that the product, service or system in question meets specific requirements. It is the formal attestation or confirmation of certain characteristics of an object, person, or organization. This confirmation is often, but not always, provided by some form of external review, education, assessment, or audit. Accreditation is a specific organization's process of certification.

Elliptic-curve cryptography

Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC allows smaller keys compared to non-EC cryptography (based on plain Galois fields) to provide equivalent security. Elliptic curves are applicable for key agreement, digital signatures, pseudo-random generators and other tasks. Indirectly, they can be used for encryption by combining the key agreement with a symmetric encryption scheme.

Related publications (10)

The Security of DSA and ECDSA

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