Improved Security for a Ring-Based Fully Homomorphic Encryption Scheme View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2013

AUTHORS

Joppe W. Bos , Kristin Lauter , Jake Loftus , Michael Naehrig

ABSTRACT

In 1996, Hoffstein, Pipher and Silverman introduced an efficient lattice based encryption scheme dubbed NTRUEncrypt. Unfortunately, this scheme lacks a proof of security. However, in 2011, Stehlé and Steinfeld showed how to modify NTRUEncrypt to reduce security to standard problems in ideal lattices. In 2012, López-Alt, Tromer and Vaikuntanathan proposed a fully homomorphic scheme based on this modified system. However, to allow homomorphic operations and prove security, a non-standard assumption is required. In this paper, we show how to remove this non-standard assumption via techniques introduced by Brakerski and construct a new fully homomorphic encryption scheme from the Stehlé and Steinfeld version based on standard lattice assumptions and a circular security assumption. The scheme is scale-invariant and therefore avoids modulus switching and the size of ciphertexts is one ring element. Moreover, we present a practical variant of our scheme, which is secure under stronger assumptions, along with parameter recommendations and promising implementation results. Finally, we present an approach for encrypting larger input sizes by extending ciphertexts to several ring elements via the CRT on the message space. More... »

PAGES

45-64

References to SciGraph publications

  • 2011. Better Key Sizes (and Attacks) for LWE-Based Encryption in TOPICS IN CRYPTOLOGY – CT-RSA 2011
  • 2011. BKZ 2.0: Better Lattice Security Estimates in ADVANCES IN CRYPTOLOGY – ASIACRYPT 2011
  • 2009. Lattice-based Cryptography in POST-QUANTUM CRYPTOGRAPHY
  • 2012. Homomorphic Evaluation of the AES Circuit in ADVANCES IN CRYPTOLOGY – CRYPTO 2012
  • 2011. Implementing Gentry’s Fully-Homomorphic Encryption Scheme in ADVANCES IN CRYPTOLOGY – EUROCRYPT 2011
  • 2014-04. Fully homomorphic SIMD operations in DESIGNS, CODES AND CRYPTOGRAPHY
  • 2009. Fast Cryptographic Primitives and Circular-Secure Encryption Based on Hard Learning Problems in ADVANCES IN CRYPTOLOGY - CRYPTO 2009
  • 2011. Making NTRU as Secure as Worst-Case Problems over Ideal Lattices in ADVANCES IN CRYPTOLOGY – EUROCRYPT 2011
  • 1998. NTRU: A ring-based public key cryptosystem in ALGORITHMIC NUMBER THEORY
  • 2010. On Ideal Lattices and Learning with Errors over Rings in ADVANCES IN CRYPTOLOGY – EUROCRYPT 2010
  • 2010. Fully Homomorphic Encryption over the Integers in ADVANCES IN CRYPTOLOGY – EUROCRYPT 2010
  • 2011. Fully Homomorphic Encryption over the Integers with Shorter Public Keys in ADVANCES IN CRYPTOLOGY – CRYPTO 2011
  • 2013. Batch Fully Homomorphic Encryption over the Integers in ADVANCES IN CRYPTOLOGY – EUROCRYPT 2013
  • 2011. Fully Homomorphic Encryption from Ring-LWE and Security for Key Dependent Messages in ADVANCES IN CRYPTOLOGY – CRYPTO 2011
  • 2010. Fully Homomorphic Encryption with Relatively Small Key and Ciphertext Sizes in PUBLIC KEY CRYPTOGRAPHY – PKC 2010
  • 2012. Fully Homomorphic Encryption without Modulus Switching from Classical GapSVP in ADVANCES IN CRYPTOLOGY – CRYPTO 2012
  • Book

    TITLE

    Cryptography and Coding

    ISBN

    978-3-642-45238-3
    978-3-642-45239-0

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-642-45239-0_4

    DOI

    http://dx.doi.org/10.1007/978-3-642-45239-0_4

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1042526343


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