### Interesting papers on HMAC and NMAC

Steve Bellovin forwarded me the following links (which he got from Eric Rescorla). Note the bit at the end about a path to second preimage attacks: http://eprint.iacr.org/2006/187 On the Security of HMAC and NMAC Based on HAVAL, MD4, MD5, SHA-0 and SHA-1 Jongsung Kim and Alex Biryukov and Bart Preneel and Seokhie Hong Abstract. HMAC is a widely used message authentication code and a pseudorandom function generator based on cryptographic hash functions such as MD5 and SHA-1. It has been standardized by ANSI, IETF, ISO and NIST. HMAC is proved to be secure as long as the compression function of the underlying hash function is a pseudorandom function. In this paper we devise two new distinguishers of the structure of HMAC, called {\em differential} and {\em rectangle distinguishers}, and use them to discuss the security of HMAC based on HAVAL, MD4, MD5, SHA-0 and SHA-1. We show how to distinguish HMAC with reduced or full versions of these cryptographic hash functions from a random function or from HMAC with a random function. We also show how to use our differential distinguisher to devise a forgery attack on HMAC. Our distinguishing and forgery attacks can also be mounted on NMAC based on HAVAL, MD4, MD5, SHA-0 and SHA-1. Furthermore, we show that our differential and rectangle distinguishers can lead to second-preimage attacks on HMAC and NMAC. Also of interest, this somewhat earlier paper, which shows that HMAC can be secure if the underlying hash is merely a pseudorandom function even if it is not collision resistant: http://eprint.iacr.org/2006/043 New Proofs for NMAC and HMAC: Security Without Collision-Resistance Mihir Bellare Abstract. HMAC was proved by Bellare, Canetti and Krawczyk [2] to be a PRF assuming that (1) the underlying compression function is a PRF, and (2) the iterated hash function is weakly collision-resistant. However, recent attacks show that assumption (2) is false for MD5 and SHA-1, removing the proof-based support for HMAC in these cases. This paper proves that HMAC is a PRF under the sole assumption that the compression function is a PRF. This recovers a proof based guarantee since no known attacks compromise the pseudorandomness of the compression function, and it also helps explain the resistance-to-attack that HMAC has shown even when implemented with hash functions whose (weak) collision resistance is compromised. We also show that an even weaker-than-PRF condition on the compression function, namely that it is a privacy-preserving MAC, suffices to establish HMAC is a MAC as long as the hash function meets the very weak requirement of being computationally almost universal, where again the value lies in the fact that known attacks do not invalidate the assumptions made. - The Cryptography Mailing List Unsubscribe by sending unsubscribe cryptography to [EMAIL PROTECTED]

### cryptanalysis of Galileo satellite navigation signals

The EU Galileo navigation satellite uses a set of pseudo-random numbers to secure access to its data. Galileo is partially investor-funded; part of the business model is to sell access to the data. Some researchers at Cornell took a different approach -- they cryptanalyzed the algorithm... Better yet, they got an opinion from their university lawyer that the DMCA didn't apply. See http://www.newswise.com/articles/view/521790/?sc=rsla for details. --Steven M. Bellovin, http://www.cs.columbia.edu/~smb - The Cryptography Mailing List Unsubscribe by sending unsubscribe cryptography to [EMAIL PROTECTED]

### RE: Factorization polynomially reducible to discrete log - known fact or not?

I believe this has been known for a long time, though I have never seen the proof. I could imagine constructing one based on quadratic sieve. I believe that a proof that the discrete log problem is polynomially reducible to the factorization problem is much harder and more recent (as in sometime in the last 20 years). I've never seen that proof either. --Charlie -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Ondrej Mikle Sent: Sunday, July 09, 2006 12:22 PM To: cryptography@metzdowd.com Subject: Factorization polynomially reducible to discrete log - known fact or not? Hello. I believe I have the proof that factorization of N=p*q (p, q prime) is polynomially reducible to discrete logarithm problem. Is it a known fact or not? I searched for such proof, but only found that the two problems are believed to be equivalent (i.e. no proof). I still might have some error in the proof, so it needs to be checked by someone yet. I'd like to know if it is already known (in that case there would be no reason to bother with it). Thanks O. Mikle - The Cryptography Mailing List Unsubscribe by sending unsubscribe cryptography to [EMAIL PROTECTED] - The Cryptography Mailing List Unsubscribe by sending unsubscribe cryptography to [EMAIL PROTECTED]

### NIST hash function design competition

I was registering today for the Crypto conference and discovered that immediately afterwards, and at the same site in Santa Barbara, CA, NIST is holding a two-day workshop on hash function design. The information is here: http://www.csrc.nist.gov/pki/HashWorkshop/index.html In response to the SHA-1 vulnerability that was announced in Feb. 2005, NIST held a Cryptographic Hash Workshop on Oct. 31-Nov. 1, 2005 to solicit public input on its cryptographic hash function policy and standards. NIST continues to recommend a transition from SHA-1 to the larger approved hash functions (SHA-224, SHA-256, SHA-384, and SHA-512). In response to the workshop, NIST has also decided that it would be prudent in the long-term to develop an additional hash function through a public competition, similar to the development process for the block cipher in the Advanced Encryption Standard (AES). I had not heard that there had been an official decision to hold a new competition for hash functions similar to AES. That is very exciting! The AES process was one of the most interesting events to have occured in the last few years in our field. Seemed like one of the lessons of that effort was that, even though it was successful in terms of attracting the interest and hard work of some of the top researchers in the field, in the end we have learned considerably more about Rijndael's vulnerabilities only after the process was over. Perhaps the intrinsic difficulty of cryptography makes this kind of outcome inevitable. But hopefully the hashing competition will learn from the AES experience and make sure that it takes as much time as it needs to take. Hal Finney - The Cryptography Mailing List Unsubscribe by sending unsubscribe cryptography to [EMAIL PROTECTED]