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Evaluation of Homomorphic Signature Schemes

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Part of the SpringerBriefs in Computer Science book series (BRIEFSCOMPUTER)

Abstract

Together with security, there are many other properties that should be taken into account when evaluating a homomorphic signature scheme. In fact it might be important that a signature generated according to an admissible function is indistinguishable from the original ones. In other scenarios a post-quantum signature scheme is needed. In this case we have to make sure that the underlying hardness assumption is expected to face quantum computer attacks. Furthermore, there are situations where computation efficiency and shortness of the generated signatures are important features. In this chapter we discuss and define formally all the above features.

Keywords

Homomorphic Signature Schemes Hardness Assumptions Asymmetric Bilinear Map Integer Factorization Problem Diffie-Hellman Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Abe M, Haralambiev K, Ohkubo M (2010) Signing on elements in bilinear groups for modular protocol design. IACR Cryptology ePrint Archive, 2010:133Google Scholar
  2. 4.
    Ahn JH, Boneh D, Camenisch J, Hohenberger S, Waters B et al (2012) Computing on authenticated data. In: Theory of cryptography. Springer, Berlin, pp 1–20CrossRefGoogle Scholar
  3. 5.
    Attrapadung N, Libert B (2011) Homomorphic network coding signatures in the standard model. In: Public key cryptography–PKC 2011. Springer, Berlin, pp 17–34CrossRefGoogle Scholar
  4. 6.
    Attrapadung N, Libert B, Peters T (2012) Computing on authenticated data: new privacy definitions and constructions. In: Advances in cryptology–ASIACRYPT 2012. Springer, Berlin, pp 367–385CrossRefGoogle Scholar
  5. 7.
    Attrapadung N, Libert B, Peters T (2013) Efficient completely context-hiding quotable and linearly homomorphic signatures. In: Public-key cryptography–PKC 2013. Springer, Berlin, pp 386–404CrossRefGoogle Scholar
  6. 8.
    Bernstein DJ, Buchmann J, Dahmen E (2009) Post-quantum cryptography. Springer, BerlinCrossRefzbMATHGoogle Scholar
  7. 9.
    Blake IF, Seroussi G, Smart N (1999) Elliptic curves in cryptography, vol 265. Cambridge University Press, CambridgeCrossRefzbMATHGoogle Scholar
  8. 12.
    Boneh D, Boyen X (2008) Short signatures without random oracles and the SDH assumption in bilinear groups. J Cryptol 21(2):149–177MathSciNetCrossRefzbMATHGoogle Scholar
  9. 14.
    Boneh D, Freeman DM (2011) Homomorphic signatures for polynomial functions. In: Advances in cryptology–EUROCRYPT 2011. Springer, Berlin, pp 149–168CrossRefGoogle Scholar
  10. 16.
    Boneh D, Boyen X, Shacham H (2004) Short group signatures. In: Advances in cryptology–CRYPTO 2004. Springer, Berlin, pp 41–55CrossRefGoogle Scholar
  11. 18.
    Boneh D, Freeman D, Katz J, Waters B (2009) Signing a linear subspace: signature schemes for network coding. In: Public key cryptography–PKC 2009. Springer, Berlin, pp 68–87CrossRefGoogle Scholar
  12. 22.
    Catalano D, Fiore D, Warinschi B (2012) Efficient network coding signatures in the standard model. In: Public key cryptography–PKC 2012. Springer, Berlin, pp 680–696CrossRefGoogle Scholar
  13. 29.
    Cramer R, Shoup V (2000) Signature schemes based on the strong RSA assumption. ACM Trans Inf Syst Secur 3(3):161–185CrossRefGoogle Scholar
  14. 32.
    Dutta R, Barua R, Sarkar P (2004) Pairing-based cryptographic protocols: a survey. IACR Cryptology ePrint Archive, 2004:64Google Scholar
  15. 34.
    Freeman DM (2012) Improved security for linearly homomorphic signatures: a generic framework. In: Public key cryptography–PKC 2012. Springer, Berlin, pp 697–714CrossRefGoogle Scholar
  16. 38.
    Gentry C, Peikert C, Vaikuntanathan V (2008) Trapdoors for hard lattices and new cryptographic constructions. In: Proceedings of the fortieth annual ACM symposium on theory of computing. ACM, New York, pp 197–206Google Scholar
  17. 45.
    Jing Z (2014) An efficient homomorphic aggregate signature scheme based on lattice. Math Probl EngGoogle Scholar
  18. 48.
    Katz J (2010) Digital signatures. Springer, BerlinCrossRefzbMATHGoogle Scholar
  19. 49.
    Katz J, Waters B (2008) Compact signatures for network codingGoogle Scholar
  20. 52.
    Libert B, Peters T, Joye M, Yung M (2013) Linearly homomorphic structure-preserving signatures and their applications. In: Advances in cryptology–CRYPTO 2013. Springer, Berlin, pp 289–307CrossRefGoogle Scholar
  21. 55.
    Menezes AJ, Okamoto T, Vanstone S et al (1993) Reducing elliptic curve logarithms to logarithms in a finite field. IEEE Trans Inf Theory 39(5):1639–1646MathSciNetCrossRefzbMATHGoogle Scholar
  22. 60.
    Rivest RL, Shamir A, Adleman L (1978) A method for obtaining digital signatures and public-key cryptosystems. Commun ACM 21(2):120–126MathSciNetCrossRefzbMATHGoogle Scholar
  23. 63.
    Shor PW (1994) Algorithms for quantum computation: discrete logarithms and factoring. In: 35th annual symposium on foundations of computer science, 1994 proceedings. IEEE, New York, pp 124–134CrossRefGoogle Scholar
  24. 73.
    Zhang N (2010) Signatures for network codingGoogle Scholar

Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.Theoretische InformatikTechnische Universität DarmstadtDarmstadtGermany

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