In this paper we systematically consider examples representative of the various families of public-key cryptosystems to see if it would be possible to incorporate them into trapdoor hash functions, and we attempt to evaluate the resulting strengths and weaknesses of the functions we are able to construct. We are motivated by the following question:
Question 1.2 How likely is it that the discoverer of a heretofore unknown public-key cryptosystem could subvert it for use in a plausible secure trapdoor hash algorithm?
In subsequent sections, our investigations will lead to a variety of constructions and bring to light the non-adaptability of public-key cryptosystems that are of a \low density." More importantly, we will be led to consider from a new point of view the effects of the unsigned addition, shift, exclusive-or and other logical bit string operators that are presently used in constructing secure hash algorithms: We will show how the use of publickey cryptosystems leads to \fragile" secure hash algorithms, and we will argue that circular shift operators are largely responsible for the security of modern high-speed secure hash algorithms.
Gary R. Greenfield and Sarah A. Spence. Secure Trapdoor Hash Functions Based on Public-Key Cryptosystems. Technical paper (TR-95-02). Math and Computer Science Technical Report Series. Richmond, Virginia: Department of Mathematics and Computer Science, University of Richmond, December, 1995.