Faster Fully Homomorphic Encryption View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2010

AUTHORS

Damien Stehlé , Ron Steinfeld

ABSTRACT

We describe two improvements to Gentry’s fully homomorphic scheme based on ideal lattices and its analysis: we provide a more aggressive analysis of one of the hardness assumptions (the one related to the Sparse Subset Sum Problem) and we introduce a probabilistic decryption algorithm that can be implemented with an algebraic circuit of low multiplicative degree. Combined together, these improvements lead to a faster fully homomorphic scheme, with a Õ(λ3.5) bit complexity per elementary binary add/mult gate, where λ is the security parameter. These improvements also apply to the fully homomorphic schemes of Smart and Vercauteren [PKC’2010] and van Dijk et al. [Eurocrypt’2010]. More... »

PAGES

377-394

References to SciGraph publications

  • 2010. Toward Basing Fully Homomorphic Encryption on Worst-Case Hardness in ADVANCES IN CRYPTOLOGY – CRYPTO 2010
  • 2001. Improving Lattice Based Cryptosystems Using the Hermite Normal Form in CRYPTOGRAPHY AND LATTICES
  • 2009. Lattice-based Cryptography in POST-QUANTUM CRYPTOGRAPHY
  • 1986-03. On Lovász’ lattice reduction and the nearest lattice point problem in COMBINATORICA
  • 2011. Implementing Gentry’s Fully-Homomorphic Encryption Scheme in ADVANCES IN CRYPTOLOGY – EUROCRYPT 2011
  • 2008. Predicting Lattice Reduction in ADVANCES IN CRYPTOLOGY – EUROCRYPT 2008
  • 2002. Complexity of Lattice Problems, A Cryptographic Perspective in NONE
  • 2010. Fully Homomorphic Encryption over the Integers in ADVANCES IN CRYPTOLOGY – EUROCRYPT 2010
  • 1991-07. On fast multiplication of polynomials over arbitrary algebras in ACTA INFORMATICA
  • 2003. A Faster Lattice Reduction Method Using Quantum Search in ALGORITHMS AND COMPUTATION
  • 2001. On the Insecurity of a Server-Aided RSA Protocol in ADVANCES IN CRYPTOLOGY — ASIACRYPT 2001
  • 2010. Fully Homomorphic Encryption with Relatively Small Key and Ciphertext Sizes in PUBLIC KEY CRYPTOGRAPHY – PKC 2010
  • 1982-12. Factoring polynomials with rational coefficients in MATHEMATISCHE ANNALEN
  • 1971-09. Schnelle Multiplikation großer Zahlen in COMPUTING
  • Book

    TITLE

    Advances in Cryptology - ASIACRYPT 2010

    ISBN

    978-3-642-17372-1
    978-3-642-17373-8

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-642-17373-8_22

    DOI

    http://dx.doi.org/10.1007/978-3-642-17373-8_22

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1021970215


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