Abstract : We investigate the security of Diffie-Hellman key exchange as used in popular Internet protocols and find it to be less secure than widely believed. First, we present Logjam, a novel flaw in TLS that lets a man-in-the-middle downgrade connections to " export-grade " Diffie-Hellman. To carry out this attack, we implement the number field sieve discrete log algorithm. 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 find 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 are being changed to reject short groups. We go on to consider Diffie-Hellman with 768-and 1024-bit groups. A small number of fixed or standardized groups are in use by millions of servers. Performing precomputations for just ten of these groups would allow a passive eavesdropper to decrypt traffic to up to 66% of IPsec VPN servers, 26% of SSH servers, 24% of popular HTTPS sites, or 16% of SMTP servers. In the 1024-bit case, we estimate that such 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 moving to stronger key exchange methods should be a priority for the Internet community.