Universal Hash Proofs and a Paradigm for Adaptive Chosen Ciphertext Secure Public-Key Encryption

Abstract

We present several new and fairly practical public-key encryption schemes and prove them secure against adaptive chosen ciphertext attack. One scheme is based on Paillier's Decision Composite Residuosity (DCR) assumption, while another is based in the classical Quadratic Residuosity (QR) assumption. The analysis is in the standard cryptographic model, i.e., the security of our schemes does not rely on the Random Oracle model.<br /> <br />We also introduce the notion of a universal hash proof system. Essentially, this is a special kind of non-interactive zero-knowledge proof system for an NP language. We do not show that universal hash proof systems exist for all NP languages, but we do show how to construct very efficient universal hash proof systems for a general class of group-theoretic language membership problems.<br /> <br />Given an efficient universal hash proof system for a language with certain natural cryptographic indistinguishability properties, we show how to construct an efficient public-key encryption schemes secure against adaptive chosen ciphertext attack in the standard model. Our construction only uses the universal hash proof system as a primitive: no other primitives are required, although even more efficient encryption schemes can be obtained by using hash functions with appropriate collision-resistance properties. We show how to construct efficient universal hash proof systems for languages related to the DCR and QR assumptions. From these we get corresponding public-key encryption schemes that are secure under these assumptions. We also show that the Cramer-Shoup encryption scheme (which up until now was the only practical encryption scheme that could be proved secure against adaptive chosen ciphertext attack under a reasonable assumption, namely, the Decision Diffie-Hellman assumption) is also a special case of our general theory.

A New Paradigm of Hybrid Encryption Scheme

“…Our result gives new light to Cramer-Shoup encryption schemes [3,4,6] and opens a door to design more efficient hybrid encryption schemes.…”

“…Our KEM is essentially a universal 2 projective hash family [4]. We present a generalization of our scheme to universal 2 projective hash families also.…”

“…It is secure against adaptive chosen ciphertext attack (IND-CCA) under the Decisional Diffie-Hellman (DDH) assumption. They further generalized their scheme to projective hash families [4]. (In the random oracle model [1], many practical schemes have been proven to be IND-CCA, for example, OAEP+ [13], SAEP [2] , RSA-OAEP [8], etc.…”

Spreading Alerts Quietly and the Subgroup Escape Problem

“…Various subgroup membership problems have been extensively studied in the literature, and examples include the Decision Diffie-Hellman problem [11], the quadratic residue problem [18], among others [28,31,33]. Our constructions however are more related to the problems described in [16,29].…”

“…The subgroup membership problem has appeared in many different forms in the literature [11,18,28,31,33,16,29]. The subgroup escape problem has not been studied before.…”