Ameer Mohammed

On the Power of Hierarchical Identity-Based Encryption

We prove that there is no fully black-box construction of collision-resistant hash functions CRH from hierarchical identity-based encryption HIBE with arbitrary polynomial number of identity levels. To the best of our knowledge this is the first limitation proved for HIBE. As a corollary, we obtain a series of separations that are not directly about HIBE or CRH but are interesting on their own right. Namely, we show that primitives such as IBE and CCA-secure public-key encryption cannot be used in a black-box way to construct fully homomorphic encryption or any primitive that implies CRH in a black-box way. Our proof relies on the reconstruction paradigm of Gennaro and Trevisan FOCS 2000 and Haitner eti¾?al. FOCS 2007 and extends their techniques for one-way and trapdoor permutations to the setting of HIBE. A main technical challenge in the proof of our separation stems from the adaptivity of the HIBE adversary who is allowed to obtain keys for different identities before she selects the attacked identity. Our main technical contribution is to develop compression/reconstruction techniques that can be achieved relative to such adaptive attackers.

Lower Bounds on Obfuscation from All-or-Nothing Encryption Primitives

Indistinguishability obfuscation (IO) enables many heretofore out-of-reach applications in cryptography. However, currently all known constructions of IO are based on multilinear maps which are poorly understood. Hence, tremendous research effort has been put towards basing obfuscation on better-understood computational assumptions. Recently, another path to IO has emerged through functional encryption [Anath and Jain, CRYPTO 2015; Bitansky and Vaikuntanathan, FOCS 2015] but such FE schemes currently are still based on multi-linear maps. In this work, we study whether IO could be based on other powerful encryption primitives.

When Does Functional Encryption Imply Obfuscation

Realizing indistinguishablility obfuscation (IO) based on well understood computational assumptions is an important open problem. Recently, realizing functional encryption (FE) has emerged as a promising direction towards that goal. This is because: (1) compact single-key FE (where the functional secret-key is of length double the ciphertext length) is known to imply IO [Anath and Jain, CRYPTO 2015; Bitansky and Vaikuntanathan, FOCS 2015] and (2) several strong variants of single-key FE are known based on various standard computation assumptions.

Limits on the Power of Garbling Techniques for Public-Key Encryption

Understanding whether public-key encryption can be based on one-way functions is a fundamental open problem in cryptography. The seminal work of Impagliazzo and Rudich [STOC’89] shows that black-box constructions of public-key encryption from one-way functions are impossible. However, this impossibility result leaves open the possibility of using non-black-box techniques for achieving this goal.