Paper 2001/085

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

Ronald Cramer and Victor Shoup


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. 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. 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 systemas 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.

Available format(s)
Public-key cryptography
Publication info
Published elsewhere. Unknown where it was published
public-key encryptionadaptive chosen ciphertext security
Contact author(s)
cramer @ brics dk
sho @ zurich ibm com
2001-12-12: last of 3 revisions
2001-10-12: received
See all versions
Short URL
Creative Commons Attribution


      author = {Ronald Cramer and Victor Shoup},
      title = {Universal Hash Proofs and a Paradigm for Adaptive Chosen Ciphertext Secure Public-Key Encryption},
      howpublished = {Cryptology ePrint Archive, Paper 2001/085},
      year = {2001},
      note = {\url{}},
      url = {}
Note: In order to protect the privacy of readers, does not use cookies or embedded third party content.