Threshold Homomorphic Encryption in the Universally Composable Cryptographic Library

The universally composable cryptographic library by Backes, Pfitzmann and Waidner provides Dolev-Yao-like, but cryptographically sound abstractions to common cryptographic primitives like encryptions and signatures. The library has been used to give the correctness proofs of various protocols; while the arguments in such proofs are similar to the ones done with the Dolev-Yao model that has been researched for a couple of decades already, the conclusions that such arguments provide are cryptographically sound. Various interesting protocols, for example e-voting, make extensive use of primitives that the library currently does not provide. The library can certainly be extended, and in this paper we provide one such extension -- we add threshold homomorphic encryption to the universally composable cryptographic library and demonstrate its usefulness by (re)proving the security of a well-known e-voting protocol.

[1]  Michael Backes,et al.  A cryptographically sound Dolev-Yao style security proof of an electronic payment system , 2005, 18th IEEE Computer Security Foundations Workshop (CSFW'05).

[2]  Ivan Damgård,et al.  Efficient Concurrent Zero-Knowledge in the Auxiliary String Model , 2000, EUROCRYPT.

[3]  Birgit Pfitzmann,et al.  Limits of the BRSIM/UC Soundness of Dolev-Yao Models with Hashes , 2006, ESORICS.

[4]  Birgit Pfitzmann,et al.  A composable cryptographic library with nested operations , 2003, CCS '03.

[5]  Silvio Micali,et al.  Proofs that yield nothing but their validity and a methodology of cryptographic protocol design , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[6]  Peeter Laud,et al.  Secrecy types for a simulatable cryptographic library , 2005, CCS '05.

[7]  Vitaly Shmatikov,et al.  Probabilistic Polynomial-Time Semantics for a Protocol Security Logic , 2005, ICALP.

[8]  Vitaly Shmatikov,et al.  Is it possible to decide whether a cryptographic protocol is secure or not , 2002 .

[9]  Birgit Pfitzmann,et al.  A Cryptographically Sound Security Proof of the Needham-Schroeder-Lowe Public-Key Protocol , 2003, FSTTCS.

[10]  David Pointcheval,et al.  Threshold Cryptosystems Secure against Chosen-Ciphertext Attacks , 2001, ASIACRYPT.

[11]  Bruce M. Kapron,et al.  Logics for reasoning about cryptographic constructions , 2003, 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings..

[12]  Birgit Pfitzmann,et al.  Relating Symbolic and Cryptographic Secrecy , 2005, IEEE Trans. Dependable Secur. Comput..

[13]  Mihir Bellare,et al.  The Security of Triple Encryption and a Framework for Code-Based Game-Playing Proofs , 2006, EUROCRYPT.

[14]  Cédric Fournet,et al.  Cryptographically Sound Implementations for Communicating Processes , 2006, ICALP.

[15]  Peeter Laud,et al.  Computationally sound secrecy proofs by mechanized flow analysis , 2006, CCS '06.

[16]  Birgit Pfitzmann,et al.  On the Cryptographic Key Secrecy of the Strengthened Yahalom Protocol , 2006, SEC.

[17]  Rafail Ostrovsky,et al.  Perfect Non-Interactive Zero Knowledge for NP , 2006, IACR Cryptol. ePrint Arch..

[18]  Birgit Pfitzmann,et al.  Cryptographically sound theorem proving , 2006, 19th IEEE Computer Security Foundations Workshop (CSFW'06).

[19]  Douglas Wikström,et al.  Universally Composable DKG with Linear Number of Exponentiations , 2004, SCN.

[20]  Jens Groth.  Evaluating Security of Voting Schemes in the Universal Composability Framework , 2004, ACNS.

[21]  Roberto Zunino,et al.  Models for Cryptographic Protocol Analysis , 2006 .

[22]  Bruno Blanchet,et al.  Computationally Sound Mechanized Proofs of Correspondence Assertions , 2007, 20th IEEE Computer Security Foundations Symposium (CSF'07).

[23]  Birgit Pfitzmann,et al.  A Universally Composable Cryptographic Library , 2003, IACR Cryptol. ePrint Arch..

[24]  Birgit Pfitzmann,et al.  Limits of the Reactive Simulatability/UC of Dolev-Yao Models with Hashes , 2006, IACR Cryptol. ePrint Arch..

[25]  Oded Goldreich.  Foundations of Cryptography: Volume 1 , 2006 .

[26]  Oded Goldreich,et al.  Foundations of Cryptography: List of Figures , 2001 .

[27]  Birgit Pfitzmann,et al.  Symmetric encryption in a simulatable Dolev-Yao style cryptographic library , 2004, Proceedings. 17th IEEE Computer Security Foundations Workshop, 2004..

[28]  Catherine A. Meadows,et al.  Formal methods for cryptographic protocol analysis: emerging issues and trends , 2003, IEEE J. Sel. Areas Commun..

[29]  Mihir Bellare,et al.  A concrete security treatment of symmetric encryption , 1997, Proceedings 38th Annual Symposium on Foundations of Computer Science.

[30]  Oded Goldreich.  Foundations of Cryptography: Index , 2001 .

[31]  Oded Goldreich,et al.  Foundations of Cryptography: Volume 1, Basic Tools , 2001 .

[32]  Pascal Paillier,et al.  Public-Key Cryptosystems Based on Composite Degree Residuosity Classes , 1999, EUROCRYPT.

[33]  Silvio Micali,et al.  The knowledge complexity of interactive proof-systems , 1985, STOC '85.

[34]  Jacques Stern,et al.  Sharing Decryption in the Context of Voting or Lotteries , 2000, Financial Cryptography.

[35]  Peeter Laud,et al.  Symmetric encryption in automatic analyses for confidentiality against active adversaries , 2004, IEEE Symposium on Security and Privacy, 2004. Proceedings. 2004.

[36]  Serge Fehr,et al.  Adaptively Secure Feldman VSS and Applications to Universally-Composable Threshold Cryptography , 2004, CRYPTO.

[37]  Ran Canetti,et al.  Universally composable security: a new paradigm for cryptographic protocols , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[38]  Peeter Laud,et al.  Application of Dependency Graphs to Security Protocol Analysis , 2007, TGC.

[39]  Ivan Damgård,et al.  A Generalisation, a Simplification and Some Applications of Paillier's Probabilistic Public-Key System , 2001, Public Key Cryptography.

[40]  P. Cogn,et al.  A Computationally Sound Mechanized Prover for Security Protocols , 2009 .

[41]  Martín Abadi,et al.  Reconciling Two Views of Cryptography (The Computational Soundness of Formal Encryption) , 2007, Journal of Cryptology.

[42]  John C. Mitchell,et al.  Protocol Composition Logic (PCL) , 2007, Computation, Meaning, and Logic.

[43]  Ran Canetti.  A unified framework for analyzing security of protocols , 2001, Electron. Colloquium Comput. Complex..

[44]  Birgit Pfitzmann,et al.  Soundness Limits of Dolev-Yao Models , 2006 .

[45]  Birgit Pfitzmann,et al.  A model for asynchronous reactive systems and its application to secure message transmission , 2001, Proceedings 2001 IEEE Symposium on Security and Privacy. S&P 2001.

[46]  Danny Dolev,et al.  On the security of public key protocols , 1981, 22nd Annual Symposium on Foundations of Computer Science (sfcs 1981).

[47]  Michael Backes,et al.  A Cryptographically Sound Dolev-Yao Style Security Proof of the Otway-Rees Protocol , 2004, ESORICS.

[48]  Birgit Pfitzmann,et al.  Symmetric Authentication within a Simulatable Cryptographic Library , 2003, ESORICS.

[49]  Helger Lipmaa.  Secure Electronic Voting Protocols , 2005 .

[50]  Birgit Pfitzmann,et al.  Limits of the Cryptographic Realization of Dolev-Yao-Style XOR , 2005, ESORICS.

[51]  Ralf Küsters,et al.  Conditional Reactive Simulatability , 2006, ESORICS.

[52]  Birgit Pfitzmann,et al.  A General Composition Theorem for Secure Reactive Systems , 2004, TCC.