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All anonymous identity-based encryption (IBE) schemes that are group homomorphic (to the best of our knowledge) require knowledge of the identity to compute the homomorphic operation. This paper is motivated by this open problem, namely to construct an anonymous group-homomorphic IBE scheme that does not sacrifice anonymity to perform homomorphic operations. Note that even when strong assumptions, such as indistinguishability obfuscation (iO), are permitted, no schemes are known. We succeed in solving this open problem by assuming iO and the hardness of the DBDH problem over rings (specifically, ZN2 for RSA modulus N). We then use the existence of such a scheme to construct an IBE scheme with re-randomizable anonymous encryption keys, which we prove to be IND-ID-RCCA secure. Finally, we use our results to construct identity-based anonymous aggregation protocols.

The evolution of smart contracts in recent years inspired a crucial question: do smart contract evaluation protocols provide the required level of privacy when executing contracts on the blockchain? The Hawk (IEEE S&P ’16) paper introduces a way to solve the problem of privacy in smart contracts by evaluating the contracts off-chain, albeit with the trust assumption of a manager. To avoid the partially trusted manager altogether, a novel approach named zkHawk (IEEE BRAINS ’21) explains how we can evaluate the contracts privately off-chain using a multi-party computation (MPC) protocol instead of trusting said manager. This paper dives deeper into the detailed construction of a variant of the zkHawk protocol titled V-zkHawk using formal proofs to construct the said protocol and model its security in the universal composability (UC) framework (FOCS ’01). The V-zkHawk protocol discussed here does not support immediate closure, i.e., all the parties (n) have to send a message to inform the blockchain that the contract has been executed with corruption allowed for up to t parties, where t