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- We show how to derive compact HIBE by instantiating the dual system framework in Waters (Crypto \'09) and Lewko and Waters (TCC \'10) with dual system groups. Our construction provides a unified treatment of the prior compact HIBE schemes from static assumptions.
- We show how to instantiate dual system groups under the decisional subgroup assumption in composite-order groups and the decisional linear assumption ($d$-LIN) in prime-order groups. Along the way, we provide new tools for simulating properties of composite-order bilinear groups in prime-order groups. In particular, we present new randomization and parameter-hiding techniques in prime-order groups.
Combining the two, we obtain a number of new encryption schemes, notably
- a new construction of IBE in prime-order groups with shorter parameters;
- a new construction of compact HIBE in prime-order
groups whose structure closely mirrors the selectively secure HIBE
scheme of Boneh, Boyen and Goh (Eurocrypt \'05);
- a new construction of compact spatial encryption in prime-order groups.
In this work, we present a novel T-PAKE protocol which solves the above fault management problem by employing a batched and offline phase of distributed key generation (DKG). Our protocol is secure against any malicious behavior from up to any t < n servers under the decisional Diffie-Hellman assumption in the random oracle model, and it ensures protocol completion for t < n/2. Moreover, it is efficient (16n + 7 exponentiations per client, 20n + 14 per server), performs explicit authentication in three communication rounds, and requires a significantly lesser number of broadcast rounds compared to previous secure T-PAKE constructions. We have implemented our protocol, and have verified its efficiency using micro-benchmark experiments. Our experimental results show that the protocol only introduces a computation overhead of few milliseconds at both the client and the server ends, and it is practical for use in real-life authentication scenarios.
To this end, we first formalize the requirements of ZKPPC protocols and propose a general framework for their construction in the standard model using randomised password hashing and set membership proofs. We design a suitable encoding scheme for password characters and show how to express password policies to allow the adoption of set membership proofs. Finally, we present a concrete ZKPPC-based registration protocol that is based on efficient Pedersen commitments and corresponding proofs, and analyse its performance.
To complete the ZKPPC-based registration and authentication framework we propose a concrete VPAKE protocol, where the server can use the obtained verification information from the ZKPPC-based registration phase to subsequently setup secure communication sessions with the client. Our VPAKE protocol follows the recent framework for the construction of such protocols and is secure in the standard model.
We construct the first fuzzy extractors that work for a large class of distributions that have negative minimum usable entropy. Their security is computational. They correct Hamming errors over a large alphabet. In order to avoid the worst-case loss, they necessarily restrict distributions for which they work.
Our first construction requires high individual entropy of a constant fraction of symbols, but permits symbols to be dependent. Our second construction requires a constant fraction of symbols to have a constant amount of entropy conditioned on prior symbols. The constructions can be implemented efficiently based on number-theoretic assumptions or assumptions on cryptographic hash functions.