Batch fully homomorphic encryption over the integers. (English) Zbl 1306.94040
Johansson, Thomas (ed.) et al., Advances in cryptology – EUROCRYPT 2013. 32nd annual international conference on the theory and applications of cryptographic techniques, Athens, Greece, May 26–30, 2013. Proceedings. Berlin: Springer (ISBN 978-3-642-38347-2/pbk). Lecture Notes in Computer Science 7881, 315-335 (2013).
Summary: We extend the fully homomorphic encryption scheme over the integers of M. van Dijk et al. (DGHV) [Eurocrypt 2010, Lect. Notes Comput. Sci. 6110, 24–43 (2010; Zbl 1279.94130)] into a batch fully homomorphic encryption scheme, i.e. to a scheme that supports encrypting and homomorphically processing a vector of plaintexts as a single ciphertext.
We present two variants in which the semantic security is based on different assumptions. The first variant is based on a new decisional problem, the decisional approximate-GCD problem, whereas the second variant is based on the more classical computational error-free approximate-GCD problem but requires additional public key elements.
We also show how to perform arbitrary permutations on the underlying plaintext vector given the ciphertext and the public key. Our scheme offers competitive performance even with the bootstrapping procedure: we describe an implementation of the homomorphic evaluation of AES, with an amortized cost of about 12 minutes per AES ciphertext on a standard desktop computer; this is comparable to the timings presented by C. Gentry et al. at Crypto 2012 [Lect. Notes Comput. Sci. 7417, 850–867 (2012; Zbl 1296.94117)] for their implementation of a Ring-LWE based fully homomorphic encryption scheme.
For the entire collection see [Zbl 1263.94005].
We present two variants in which the semantic security is based on different assumptions. The first variant is based on a new decisional problem, the decisional approximate-GCD problem, whereas the second variant is based on the more classical computational error-free approximate-GCD problem but requires additional public key elements.
We also show how to perform arbitrary permutations on the underlying plaintext vector given the ciphertext and the public key. Our scheme offers competitive performance even with the bootstrapping procedure: we describe an implementation of the homomorphic evaluation of AES, with an amortized cost of about 12 minutes per AES ciphertext on a standard desktop computer; this is comparable to the timings presented by C. Gentry et al. at Crypto 2012 [Lect. Notes Comput. Sci. 7417, 850–867 (2012; Zbl 1296.94117)] for their implementation of a Ring-LWE based fully homomorphic encryption scheme.
For the entire collection see [Zbl 1263.94005].
MSC:
| 94A60 | Cryptography |
