Semi-Adaptively Secure Offline Witness Encryption from Puncturable Witness PRF

摘要

In this work, we introduce the notion of puncturable witness pseudorandom, function (pWPRF) which is a stronger variant of WPRF proposed by Zhandry, TCC 2016. The punctured technique is similar to what we have seen for puncturable PRFs and is capable of extending the applications of WPRF. Specifically, we construct a semi-adaptively secure offline witness encryption (OWE) scheme using a pWPRF, an indistin-guishability obfuscation (iO) and a symmetric-key encryption (SKE), which enables us to encrypt messages along with NP statements. We show that replacing iO with extractability obfuscation, the OWE turns out to be an extractable offline witness encryption scheme. To gain finer control over data, we further demonstrate how to convert our OWEs into offline functional witness encryption (OFWE) and extractable OFWE. All of our OWEs and OFWEs produce an optimal size ciphertext, in particular, encryption of a message is as small as the size of the message plus the security parameter multiplied with a constant, which is optimal for any public-key encryption scheme. On the other hand, in any previous OWE, the size of a ciphertext increases polynomially with the size of messages. Finally, we show that the WPRF of Pal et al. (ACISP 2019) can be extended to a pWPRF and an extractable pWPRF.