Public Key Compression and Modulus Switching for Fully Homomorphic Encryption over the Integers

Abstract : We describe a compression technique that reduces the public key size of van Dijk, Gentry, Halevi and Vaikuntanathan’s (DGHV) fully homomorphic scheme over the integers from O~(λ^7) to O~(λ^5). Our variant remains semantically secure, but in the random oracle model. We obtain an implementation of the full scheme with a 10.1 MB public key instead of 802 MB using similar parameters as in [7]. Additionally we show how to extend the quadratic encryption technique of [7] to higher degrees, to obtain a shorter public-key for the basic scheme. This paper also describes a new modulus switching technique for the DGHV scheme that enables to use the new FHE framework without bootstrapping from Brakerski, Gentry and Vaikuntanathan with the DGHV scheme. Finally we describe an improved attack against the Approximate GCD Problem on which the DGHV scheme is based, with complexity O~(2^ρ) instead of O~(2^3ρ/2).
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Communication dans un congrès
David Pointcheval; Thomas Johansson. EUROCRYPT 2012 - 31st Annual International Conference on the Theory and Applications of Cryptographic Techniques, Apr 2012, Cambridge, UK, United Kingdom. Springer, LNCS - Lecture Notes in Computer Science, 7237, pp.446-464, 2012, Advances in Cryptology – EUROCRYPT 2012. 〈10.1007/978-3-642-29011-4_27〉
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Contributeur : Brigitte Briot <>
Soumis le : vendredi 30 janvier 2015 - 15:14:37
Dernière modification le : vendredi 25 mai 2018 - 12:02:05

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Jean-Sébastien Coron, David Naccache, Mehdi Tibouchi. Public Key Compression and Modulus Switching for Fully Homomorphic Encryption over the Integers. David Pointcheval; Thomas Johansson. EUROCRYPT 2012 - 31st Annual International Conference on the Theory and Applications of Cryptographic Techniques, Apr 2012, Cambridge, UK, United Kingdom. Springer, LNCS - Lecture Notes in Computer Science, 7237, pp.446-464, 2012, Advances in Cryptology – EUROCRYPT 2012. 〈10.1007/978-3-642-29011-4_27〉. 〈hal-01111541〉

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