TARDIS: A Foundation of Time-Lock Puzzles in UC
Time-based primitives like time-lock puzzles (TLP) are finding widespread use in practical protocols, partially due to the surge of interest in the blockchain space where TLPs and related primitives are perceived to solve many problems. Unfortunately, the security claims are often shaky or plainly wrong since these primitives are used under composition. One reason is that TLPs are inherently not UC secure and time is tricky to model and use in the UC model. On the other hand, just specifying standalone notions of the intended task, left alone correctly using standalone notions like non-malleable TLPs only, might be hard or impossible for the given task. And even when possible a standalone secure primitive is harder to apply securely in practice afterwards as its behavior under composition is unclear. The ideal solution would be a model of TLPs in the UC framework to allow simple modular proofs. In this paper we provide a foundation for proving composable security of practical protocols using time-lock puzzles and related timed primitives in the UC model. We construct UC-secure TLPs based on random oracles and show that using random oracles is necessary. In order to prove security, we provide a simple and abstract way to reason about time in UC protocols. Finally, we demonstrate the usefulness of this foundation by constructing applications that are interesting in their own right, such as UC-secure two-party computation with output-independent abort.
Efficient UC Commitment Extension with Homomorphism for Free (and Applications)
Homomorphic universally composable (UC) commitments allow for the sender to reveal the result of additions and multiplications of values contained in commitments without revealing the values themselves while assuring the receiver of the correctness of such computation on committed values. In this work, we construct essentially optimal additively homomorphic UC commitments from any (not necessarily UC or homomorphic) extractable commitment, while the previous best constructions require oblivious transfer. We obtain amortized linear computational complexity in the length of the input messages and rate 1. Next, we show how to extend our scheme to also obtain multiplicative homomorphism at the cost of asymptotic optimality but retaining low concrete complexity for practical parameters. Moreover, our techniques yield public coin protocols, which are compatible with the Fiat-Shamir heuristic. These results come at the cost of realizing a restricted version of the homomorphic commitment functionality where the sender is allowed to perform any number of commitments and operations on committed messages but is only allowed to perform a single batch opening of a number of commitments. Although this functionality seems restrictive, we show that it can be used as a building block for more efficient instantiations of recent protocols for secure multiparty computation and zero knowledge non-interactive arguments of knowledge.
On the Impossibility of Structure-Preserving Deterministic Primitives
In structure-preserving cryptography over bilinear groups, cryptographic schemes are restricted to exchange group elements only, and their correctness must be verifiable only by evaluating pairing product equations. Several primitives, such as structure-preserving signatures, commitments, and encryption schemes, have been proposed. Although deterministic primitives, such as verifiable pseudorandom functions or verifiable unpredictable functions, play an important role in the construction of cryptographic protocols, no structure-preserving realizations of them are known. This is not coincident: In this paper, we show that it is impossible to construct algebraic structure-preserving deterministic primitives that provide provability, uniqueness, and unpredictability. This includes verifiable random functions, unique signatures, and verifiable unpredictable functions as special cases. The restriction of structure-preserving primitives to be algebraic is natural, otherwise it would not be known how to verify correctness only by evaluating pairing product equations. We further extend our negative result to pseudorandom functions and deterministic public key encryption as well as non-strictly structure-preserving primitives, where target group elements are also allowed in their ranges and public keys.
A Two-Party Protocol with Trusted Initializer for Computing the Inner Product
We propose the first protocol for securely computing the inner product modulo an integer $m$ between two distrustful parties based on a trusted initializer, i.e. a trusted party that interacts with the players solely during a setup phase. We obtain a very simple protocol with universally composable security. As an application of our protocol, we obtain a solution for securely computing linear equations.
Oblivious Transfer based on the McEliece Assumptions}
We implement one-out-of-two bit oblivious transfer (OT) based on the assumptions used in the McEliece cryptosystem: the hardness of decoding random binary linear codes, and the difficulty of distinguishing a permuted generating matrix of Goppa codes from a random matrix. To our knowledge this is the first OT reduction to these problems only.
A CCA2 Secure Public Key Encryption Scheme Based on the McEliece Assumptions in the Standard Model
We show that a recently proposed construction by Rosen and Segev can be used for obtaining the first public key encryption scheme based on the McEliece assumptions which is secure against adaptive chosen ciphertext attacks in the standard model.
- Masayuki Abe (2)
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- Sriram Keelveedhi (2)
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