Offline Witness Encryption with Semi-Adaptive Security

The first construction of Witness Encryption (WE) by Garg et al. (STOC 2013) has led to many exciting avenues of research in the past years. A particularly interesting variant is Offline WE (OWE) by Abusalah et al. (ACNS 2016), as the encryption algorithm uses neither obfuscation nor multilinear maps. Current OWE schemes provide only selective security. That is, the adversary must commit to their challenge messages $m_0$ and $m_1$ before seeing the public parameters. We provide a new, generic framework to construct OWE, which achieves adaptive security in the sense that the adversary may choose their challenge messages adaptively. We call this semi-adaptive security, because - as in prior work - the instance of the considered NP language that is used to create the challenge ciphertext must be fixed before the parameters are generated in the security proof. We show that our framework gives the first OWE scheme with constant ciphertext overhead even for messages of polynomially-bounded size. We achieve this by introducing a new variant of puncturable encryption defined by Green and Miers (S&P 2015) and combining it with the iO-based approach of Abusalah et al. Finally, we show that our framework can be easily extended to construct the first Extractable Offline Witness Encryption (EOWE), by using extractability obfuscation of Boyle et al. (TCC 2014) in place of iO, opening up even more possible applications. The obfuscation is needed only for our public parameters, but its functionality can be realised with a Trusted Execution Environment (TEE), which means we have a very efficient scheme with ciphertexts consisting of only 5 group elements

Semi-Adaptively Secure Offline Witness Encryption from Puncturable Witness PRF

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 indistinguishability 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