Security Analysis of Randomize-Hash-then-Sign Digital Signatures

At CRYPTO 2006, Halevi and Krawczyk proposed two randomized hash function modes and analyzed the security of digital signature algorithms based on these constructions. They showed that the security of signature schemes based on the two randomized hash function modes relies on properties similar to the second preimage resistance rather than on the collision resistance property of the hash functions. One of the randomized hash function modes was named the RMX hash function mode and was recommended for practical purposes. The National Institute of Standards and Technology (NIST), USA standardized a variant of the RMX hash function mode and published this standard in the Special Publication (SP) 800-106. In this article, we first discuss a generic online birthday existential forgery attack of Dang and Perlner on the RMX-hash-then-sign schemes. We show that a variant of this attack can be applied to forge the other randomize-hash-then-sign schemes. We point out practical limitations of the generic forgery attack on the RMX-hash-then-sign schemes. We then show that these limitations can be overcome for the RMX-hash-then-sign schemes if it is easy to find fixed points for the underlying compression functions, such as for the Davies-Meyer construction used in the popular hash functions such as MD5 designed by Rivest and the SHA family of hash functions designed by the National Security Agency (NSA), USA and published by NIST in the Federal Information Processing Standards (FIPS). We show an online birthday forgery attack on this class of signatures by using a variant of Dean's method of finding fixed point expandable messages for hash functions based on the Davies-Meyer construction. This forgery attack is also applicable to signature schemes based on the variant of RMX standardized by NIST in SP 800-106. We discuss some important applications of our attacks and discuss their applicability on signature schemes based on hash functions with 'built-in' randomization. Finally, we compare our attacks on randomize-hash-then-sign schemes with the generic forgery attacks on the standard hash-based message authentication code (HMAC).