A CCA-PKE Secure-Cryptosystem Resilient to Randomness Reset and Secret-Key Leakage

Abstract

In recent years, several new notions of security have begun receiving consideration for public-key cryptosystems, beyond the standard of security against adaptive chosen ciphertext attack (CCA2). Among these are security against randomness reset attacks, in which the randomness used in encryption is forcibly set to some previous value, and against constant secret-key leakage attacks, wherein the constant factor of a secret key’s bits is leaked. In terms of formal security definitions, cast as attack games between a challenger and an adversary, a joint combination of these attacks means that the adversary has access to additional encryption queries under a randomness of his own choosing along with secret-key leakage queries. This implies that both the encryption and decryption processes of a cryptosystem are being tampered under this security notion. In this paper, we attempt to address this problem of a joint combination of randomness and secret-key leakage attacks through two cryptosystems that incorporate hash proof system and randomness extractor primitives. The first cryptosystem relies on the random oracle model and is secure against a class of adversaries, called non-reversing adversaries. We remove the random oracle oracle assumption and the non-reversing adversary requirement in our second cryptosystem, which is a standard model that relies on a proposed primitive called LM lossy functions. These functions allow up to M lossy branches in the collection to substantially lose information, allowing the cryptosystem to use this loss of information for several encryption and challenge queries. For each cryptosystem, we present detailed security proofs using the game-hopping procedure. In addition, we present a concrete instantation of LM lossy functions in the end of the paper—which relies on the DDH assumption.