Elliptic Curve Cryptography in Practice

The recent paper Elliptic Curve Cryptography in Practice by Joppe W. Bos and J. Alex Halderman and Nadia Heninger and Jonathan Moore and Michael Naehrig and Eric Wustrow is well worth reading. The discovery in 2012 of a large number of RSA public keys with common factors showed that public key cryptography can go badly wrong in the real world. This paper reports on a thorough evaluation of ECC systems in the real world. Some of them, for example the Austrian e-ID citizen card, are found to have no weaknesses. However, serious issues are discovered with some other systems. In particular, the paper gives evidence that a theft of 59 bitcoins was achieved by an attacker exploiting duplicated nonces in ECDSA signatures. Further issues with bitcoin are discussed. The paper also reports some potentially serious bugs in TLS implementations in some commercially available devices. The paper does not reveal details of any companies or individuals affected by these issues.

— Steven Galbraith

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