Homomorphic Encryption

• Papers
  • Secure Circuit Evaluation: A Protocol Based on Hiding Information from an Oracle (Abadi, Feigenbaum, 1990)
  • Naccache-Stern cryptosystem
    • A New Public Key Cryptosystem Based on Higher Residues (David Naccache and Jacques Stern)
  • Fujisaki-Okamoto cryptosystem & friends
    • Accelerating Okamoto-Uchiyama's Public-Key Cryptosystem (Jean-Sbastien Coron, David Naccache and Pascal Paillier)
    • EPOC: Efficient Probabilistic Public-Key Encryption (Okamoto, Uchiyama, Fujisaki, 1998)
  • Paillier cryptosystem
    • Public-Key Cryptosystems Based on Composite Degree Residuosity Classes (Pascal Paillier, EUROCRYPT 1999)
    • Efficient Protocols based on Probabilistic Encryption using Composite Degree Residue Classes (Damgård, Jurik, eprint 2000/008)
    • Paillier's Cryptosystem Revisited (Dario Catalano and Rosario Gennaro and Nick Howgrave-Graham and Phong Q. Nguyen , ACM CCS 2001)
    • Trapdooring Discrete Logarithms on Elliptic Curves over Rings (Pascal Paillier, ASIACRYPT 2000)
    • Use of high degree residues in other settings
      S. Park and D. Won, "A Generalization of Public-Key Residue Cryptosystem,", In Proceedings of 1993 Korean-Japan Joint Workshop on Information Security and Cryptology, pp. 202-206, 1993 [ResearchIndex]
      S. Vanstone and R. Zuccherato, "Elliptic Curve Cryptosystem Using Curves of Smooth Order Over the Ring Z_n", IEEE Trans. Inf. Theory, Vol. 43, No 4, July 1997 [ResearchIndex]
  • Damgård-Jurik cryptosystem (PKC 2001)
    • A Generalisation, a Simplification and some Applications of Paillier's Probabilistic Public-Key System (Ivan Damgård and Mads Jurik, 2001)
    • A Generalization of Paillier's Public-Key System with Applications to Electronic Voting (Ivan Damgaard, Mads Jurik, Jesper Buus Nielsen, 2003)
  • Multiparty Computation from Threshold Homomorphic Encryption ( Ronald Cramer, Ivan Damgard, Jesper Buus Nielsen, 2000)
  • Homomorphic Encryption on Non-Abelian Groups and Applications (Eberhard Becker, Dörte Rappe, Tomas Sander, 2002 (preprint))
  • The previous schmeme has been broken
  • Homomorphic public-key cryptosystems and encrypting boolean circuits (Dima Grigoriev, Ilia Ponomarenko, cs.CR/0301022)
  • Homomorphic public-key cryptosystems over groups and rings (Dima Grigoriev, Ilia Ponomarenko, cs.CR/0309010)
  • A Length-Flexible Threshold Cryptosystem with Application (Damgård-Jurik, ACISP 2003)
  • Encoding-Free ElGamal Encryption Without Random Oracles (by Benoît Chevallier-Mames, Pascal Paillier and David Pointcheval, PKC 2006)
  • [scholar]Towards a DL-based Additively Homomorphic Encryption Scheme (Guilhem Castagnos, Benoît Chevallier-Mames, ISC 2007)
  • Negative Results
    • Algorithms for black box fields and their application to cryptography (Dan Boneh, Richard Lipton, Crypto 96)
    • A quantum algorithm that breaks algebraically homomorphic encryption (Wim van Dam, 2002)
    • Algebraic Lower Bounds for Computing on Encrypted Data (Rafail Ostrovsky and William E. Skeith III, eprint 2007/064)
  • @Fully-Homomorphic Encryption (29.05.11)
• Theses
  • Homomorphic Cryptosystems and their Applications (Dörte Rappe, Ph.D. Thesis, University of Dortmund, Germany, August 2004)
  • Alternative download
    • Homomorphic Cryptosystems and their Applications (Doerte K. Rappe, PhD thesis (eprint 2006/001))
  • Cryptanalysis of a Homomorphic Public-Key Cryptosystem (Su-Jeong Choi, Royal Holloway, PhD thesis, 2006)
• Privacy Homomorphism []
  • [scholar]On Data Banks and Privacy Homomorphisms (R. Rivest, L. Adlernan, and M. Dertouzos, 1978)
  • Processing encrypted data (Niv Ahituv, Yeheskel Lapid, Seev Neumann, 1987)
  • Applications of Cryptographic "Zero-Knowledge" Techniques in Computerized Secret Ballot Election Schemes (Kenneth Roar Iversen, 1991)
  • A Provably Secure Additive and Multiplicative Privacy Homomorphism (Josep Domingo-Ferrer, ISC 2002)
• Usage areas
  • @Electronic Voting
  • @Electronic Auctions
  • @Oblivious transfer
• Related things
  • Order-preserving Encryption []
    • Multi-application smart cards and encrypted data processing (Josep Domingo-Ferrer, FGCS 1997)
      • Alternative download
    • Dike: A Prototype for Secure Delegation of Statistical Data (Josep Domingo-Ferrer, Ricardo X. Sánchez DelCastillo, Javier Castilla)
    • Usage areas
      • Executing SQL over Encrypted Data in the Database-service-provider model
        (Hakan Hacigumus, Dala Iyer, Chen Li, Sharad Mehorta)
      • Privacy in Database-as-a-Service (DAM) model
        (Maithili Narasimha)
      • Anti-Tamper Databases
        ( Querying Encrypted Databases)
      • Balancing Confidentiality and Efficiency in Untrusted Relational DBMSs
        (E. Damiani, S. De Capitani di Vimercati, S. Jajodia, S. Paraboschi, P. Samarati, ACM CCS 2003)

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(C) Helger Lipmaa 1997-2009.