Study on building pseudorandom functions from cryptographic primitives

Abstract

A Pseudorandom function (PRF) is one of the most basic cryptographic primitives and core of variouscryptosystem. To construct PRFs, one may use pseudorandom permutations (PRPs) by truncating theoutput of a PRP (TRP) and xoring the outputs of two PRPs (XoP). In this dissertation, we prove abetter security bound upon the previous bound in indifferentiability model. We also introduce new PRFconstructions motivated from XoP, dubbed XoTP1, XoTP2, and XoIC, and prove their security boundswhich are resulted in1. multi-user security of XoP,2. constructing a highly secure PRF construction from tweakable block ciphers,3. constructing a highly secure PRF construction in the ideal cipher model and the indifferentiabilitymodel.Furthermore, to attain above results, we generalize and improve upon the previous Mirror theory, to beapplicable Mirror theory to tweakable block cipher-based or ideal cipher-based constructions.