Cryptology ePrint Archive: Report 2014/376

How Secure is Deterministic Encryption?

Mihir Bellare and Rafael Dowsley and Sriram Keelveedhi

Abstract: This paper presents three curious findings about deterministic public-key encryption (D-PKE) that further our understanding of its security, in particular because of the contrast with standard, randomized public-key encryption (R-PKE):

(1) It would appear to be a triviality, for any primitive, that security in the standard model implies security in the random-oracle model, and it is certainly true, and easily proven, for R-PKE. For D-PKE it is not clear and depends on details of the definition. In particular we can show it in the non-uniform case but not in the uniform case.

(2) The power of selective-opening attacks (SOA) comes from an adversary's ability, upon corrupting a sender, to learn not just the message but also the coins used for encryption. For R-PKE, security is achievable. For D-PKE, where there are no coins, one's first impression may be that SOAs are vacuous and security should be easily achievable. We show instead that SOA-security is impossible, meaning no D-PKE scheme can achieve it.

(3) For R-PKE, single-user security implies multi-user security, but we show that there are D-PKE schemes secure for a single user and insecure with two users.

Category / Keywords: public-key cryptography / Deterministic public-key encryption, random-oracle model, selective-opening attack

Date: received 27 May 2014

Contact author: mihir at eng ucsd edu

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Version: 20140528:163702 (All versions of this report)

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