In order to achieve a meaningful level of security, a deterministic encryption algorithm should be typically used for encrypting rather long plaintexts for ensuring a sufficient amount of entropy. This requirement may be at odds with efficiency constraints, such as communication complexity and computation complexity in the presence of small updates. Thus, a highly desirable property of deterministic encryption algorithms is incrementality: small changes in the plaintext translate into small changes in the corresponding ciphertext.
We present a framework for modeling the incrementality of deterministic public-key encryption. Within our framework we propose two schemes, which we prove to enjoy an optimal tradeoff between their security and incrementality up to small polylogarithmic factors. Our first scheme is a generic method which can be based on any deterministic public-key encryption scheme, and in particular, can be instantiated with any semantically-secure (randomized) public-key encryption scheme in the random oracle model. Our second scheme is based on the Decisional Diffie-Hellman assumption in the standard model.
The approach underpinning our schemes is inspired by the fundamental ``sample-then-extract'' technique due to Nisan and Zuckerman (JCSS '96) and refined by Vadhan (J. Cryptology '04), and by the closely related notion of ``locally-computable extractors'' due to Vadhan. Most notably, whereas Vadhan used such extractors to construct private-key encryption schemes in the bounded-storage model, we show that techniques along these lines can also be used to construct incremental public-key encryption schemes.Category / Keywords: public-key cryptography / Publication Info: EUROCRYPT 2012. This is the full version. Date: received 30 Jan 2012 Contact author: gil segev at microsoft com Available formats: PDF | BibTeX Citation Version: 20120201:041416 (All versions of this report) Discussion forum: Show discussion | Start new discussion