Daniel R. L. Brown

Accelerated verification of ECDSA signatures

Verification of ECDSA signatures is considerably slower than generation of ECDSA signatures. This paper describes a method that can be used to accelerate verification of ECDSA signatures by more than 40% with virtually no added implementation complexity. The method can also be used to accelerate verification for other ElGamal-like signature algorithms, including DSA.

A security analysis of the NIST SP 800-90 elliptic curve random number generator

An elliptic curve random number generator (ECRNG) has been approved in a NIST standard and proposed for ANSI and SECG draft standards. This paper proves that, if three conjectures are true, then the ECRNG is secure. The three conjectures are hardness of the elliptic curve decisional Diffie-Hellman problem and the hardness of two newer problems, the x-logarithm problem and the truncated point problem. The x-logarithm problem is shown to be hard if the decisional Diffie-Hellman problem is hard, although the reduction is not tight. The truncated point problem is shown to be solvable when the minimum amount of bits allowed in NIST standards are truncated, thereby making it insecure for applications such as stream ciphers. Nevertheless, it is argued that for nonce and key generation this distinguishability is harmless.