On pseudo-random oracles

Abstract

Many cryptographic systems which involve hash functions have
proof of their security in a so called random oracle model. Behavior of hash
functions used in such cryptographic systems should be as close as possible to
the behavior of a random function. There are several properties of hash functions
dealing with a random behavior. A hash function is pseudo-random oracle if it
is indifferentiable from a random oracle. However, it is well known that hash
functions based on the popular Merkle-Damg°ard domain extension transform do
not satisfy the pseudo-random oracle property. On the other hand no attack is
known for many concrete applications utilizing Merkle-Damg°ard hash functions.
Hence, a weakened notion called public-use pseudo random oracle was introduced.
The property can be met by the Merkle-Damg°ard construction and is sufficient
for several important applications. A hash function is public use pseudo-random
oracle if it is indifferentiable from a random oracle with public messages (i.e. all
messages hashed so far are available to all parties). This is is the case of most
hash based signature schemes.
In this paper we analyze relationship between the property pseudo-random or-
acle and its variant public image pseudo-random oracle. Roughly, a hash function
is public image pseudo-random oracle if it is indifferentiable from a random oracle
with public images (i.e. all images of messages hashed so far are available to all
parties, messages are kept secret). We prove that the properties are equivalent.