In Search of CurveSwap: Measuring Elliptic Curve Implementations in the Wild

Presented at Black Hat Europe 2018, Dec. 6, 2018, 9 a.m. (30 minutes)

We survey elliptic curve implementations from several vantage points. We perform internet-wide scans for TLS on a large number of ports, as well as SSH and IPsec to measure elliptic curve support and implementation behaviors, as well as collect passive measurements of client curve support for TLS. We also perform active measurements to estimate server vulnerability to known attacks against elliptic curve implementations, including support for weak curves, invalid curve attacks, and curve twist attacks. We estimate that 0.77% of HTTPS hosts, 0.04% of SSH hosts, and 4.04% of IKEv2 hosts that support elliptic curves do not perform curve validity checks as specified in elliptic curve standards. We describe how such vulnerabilities could be used to construct an elliptic curve parameter downgrade attack called CurveSwap for TLS, and observe that there do not appear to be combinations of weak behaviors we examined enabling a feasible CurveSwap attack in the wild. We also analyze source code for elliptic curve implementations, and find that a number of libraries fail to perform point validation for JSON Web Encryption, and find a flaw in the Java and NSS multiplication algorithms.


  • Luke Valenta - PhD Student, University of Pennsylvania
    Luke is a PhD student in the Department of Computer and Information Science at the University of Pennsylvania. He works with Nadia Heninger in the Security Laboratory, and helps organize the Security Reading group. He is broadly interested in applied cryptography, computer security, privacy, elliptic curve cryptography, cryptocurrencies, and distributed systems.
  • Nick Sullivan - Head of Cryptography, Cloudflare
    Nick Sullivan is a leading cryptography and security technologist. As head of Cryptography at Cloudflare he is responsible for overseeing all cryptographic products and strategy.


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