Secure Obfuscation for Encrypted Signatures

Obfuscation is one of the most intriguing open problems in cryptography and only a few positive results are known. In TCC'07, Hohenberger et al. proposed an obfuscator for a re-encryption functionality, which takes a ciphertext for a message encrypted under Alice's public key and transforms it into a ciphertext for the same message under Bob's public key [24]. It is the first complicated cryptographic functionality that can be securely obfuscated, but obfuscators for such cryptographic functionalities are still elusive. In this paper, we consider obfuscation for encrypted signature (ES) functionalities, which generate a signature on a given message under Alice's secret signing key and encrypt the signature under Bob's public encryption key. We propose a special ES functionality, which is the sequential composition of Waters's signature scheme [33] and the linear encryption scheme proposed by Boneh, Boyen, and Shoehorn [5], and construct a secure obfuscator for it. We follow the security argument by Hohenberger et al. to prove that our proposed obfuscator satisfies a virtual black-box property (VBP), which guarantees that the security of the signature scheme is preserved even when adversaries are given an obfuscated program. Our security argument is in the standard model.