Imperfect Forward Secrecy
Speaker: J. Alex Halderman, University of Michigan
Diffie-Hellman key exchange is a cornerstone of modern cryptography at the core of protocols like HTTPS and SSH. Last year, we discovered that Diffie-Hellman, as used in practice, is significantly less secure than widely believed. An adversary who performs a large precomputation for a prime p can then quickly calculate arbitrary discrete logs in groups modulo that prime, amortizing the cost over all targets that share this parameter. Although this fact is well known among mathematical cryptographers, it seems to have been lost among practitioners.
Using these observations, we developed Logjam, an attack on TLS in which a man-in-the-middle can downgrade a connection to 512-bit “export-grade’’ Diffie-Hellman. After a week-long precomputation for a specified 512-bit group, we can compute arbitrary discrete logs in that group in about a minute. We found that 82% of vulnerable servers use a single 512-bit group, allowing us to compromise connections to 7% of Alexa Top Million HTTPS sites. In response, major browsers have been changed to reject short groups. In the more widespread case of 1024-bit Diffie-Hellman, we estimate that discrete log computations are plausible given nation-state resources, and a close reading of published NSA leaks shows that the agency’s attacks on VPNs are consistent with having achieved such a break. We conclude that the security community should prioritize moving to stronger key exchange methods.
Bio: J. Alex Halderman is an Associate Professor of Computer Science and Engineering at the University of Michigan and Director of Michigan’s Center for Computer Security and Society. His interests include computer and network security, Internet security measurement, censorship resistance, and electronic voting, as well as the interaction of technology with law and international affairs. Named one of Popular Science’s “Brilliant 10” for 2015, his recent projects include ZMap, Let’s Encrypt, and the Telex censorship resistance system.
For more information, please contact Prof. Damon McCoy.