Cocks' Identity-Based Encryption in the Standard Model, via Obfuscation Techniques (Short Paper)

Identity-based encryption (IBE) is an attractive primitive in modern cryptography. Cocks first gave an elegant construction of IBE under Quadratic Residuosity (QR) assumption. Unfortunately, its security works only in the Random Oracle (RO) model. In this work, we aim at providing Cock's scheme with provable security in the standard model. Specifically, we modify Cocks' scheme by explicitly instantiating the hash function using indistinguishability obfuscation in two different ways which yield two variants of Cocks' scheme. Their security are promised under well-defined selective-ID and adaptive-ID model respectively. As an additional contribution, we adapt the same method into the Boneh, LaVigne, Sabin (BLS) e(th) residuosity based IBE cryptosystem and obtain an adaptive chosen-ID secure scheme under Modified e(th) Residuosity (MER) assumption.