Abstract. 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.

We present practical and realistic attacks on some standardized elliptic curve key establishment and public-key encryption protocols that are effective if the receiver of an elliptic curve point does not check that the point lies on the appropriate elliptic curve. The attacks combine ideas from the small subgroup attack of Lim and Lee, and the differential fault attack of Biehl, Meyer and Müller. Although the ideas behind the attacks are quite elementary, and there are simple countermeasures known, the attacks can have drastic consequences if these countermeasures are not taken by implementors of the protocols. We illustrate the effectiveness of such attacks on a key agreement protocol recently proposed for the IEEE 802.15 Wireless Personal Area Network (WPAN) standard.