ABSTRACT
In Chapter 11 we saw several examples of public-key encryption schemes used in practice. Here, we explore some schemes that are currently more of theoretical interest-although in some cases it is possible that these schemes (or variants thereof) will be used more widely in the future. We begin with a treatment of trapdoor permutations, a generalization of
one-way permutations, and show how to use them to construct public-key encryption schemes. Trapdoor permutations neatly encapsulate the key characteristics of the RSA permutation that make it so useful. As such, they often provide a useful abstraction for designing new cryptosystems. Next, we present three schemes based on problems related to factoring:
• The Paillier encryption scheme is an example of an encryption scheme that is homomorphic. This property turns out to be useful for constructing more-complex cryptographic protocols, something we touch on briefly in Section 13.3.
