acm-header
Sign In

Communications of the ACM

Research highlights

Technical Perspective: Attacking Cryptographic Key Exchange with Precomputation


The Diffie-Hellman key exchange protocol is at the heart of many cryptographic protocols widely used on the Internet. It is used for session setup in HTTPS (TLS), in SSH, in IPsec, and others. The original protocol, as described by Diffie and Hellman, operates by choosing a large prime p and computing certain exponentiations modulo this prime. For the protocol to be secure one needs, at the very least, that the discrete-log problem modulo the prime p be difficult to solve. This problem is quite easy to state: fix a large prime p, and an integer 0 < g < p (a generator). Next, choose an integer 0 < x < p and compute h = gx modulo p. The discrete-log problem is to compute x given only p, g and h. If this problem could be solved efficiently, for most h, then the Diffie-Hellman protocol for the chosen (p, g) would be insecure.

The authors of the following paper show that, in practice, implementations that use Diffie-Hellman tend to choose a universally fixed prime p (and fixed g). For example, many SSH servers and IPsec VPNs use a fixed universal 1,024 bit prime p. The same is true for HTTPS Web servers, although to a lesser extent.


 

No entries found

Log in to Read the Full Article

Sign In

Sign in using your ACM Web Account username and password to access premium content if you are an ACM member, Communications subscriber or Digital Library subscriber.

Need Access?

Please select one of the options below for access to premium content and features.

Create a Web Account

If you are already an ACM member, Communications subscriber, or Digital Library subscriber, please set up a web account to access premium content on this site.

Join the ACM

Become a member to take full advantage of ACM's outstanding computing information resources, networking opportunities, and other benefits.
  

Subscribe to Communications of the ACM Magazine

Get full access to 50+ years of CACM content and receive the print version of the magazine monthly.

Purchase the Article

Non-members can purchase this article or a copy of the magazine in which it appears.
Sign In for Full Access
» Forgot Password? » Create an ACM Web Account