Transferable E-cash: A Cleaner Model and the First Practical Instantiation 📺
Transferable e-cash is the most faithful digital analog of physical cash, as it allows users to transfer coins between them in isolation, that is, without interacting with a bank or a ``ledger''. Appropriate protection of user privacy and, at the same time, providing means to trace fraudulent behavior (double-spending of coins) have made instantiating the concept notoriously hard. Baldimtsi et al.\ (PKC'15) gave a first instantiation, but, as it relies on a powerful cryptographic primitive, the scheme is not practical. We also point out a flaw in their scheme. In this paper we revisit the model for transferable e-cash and propose simpler yet stronger security definitions. We then provide the first concrete construction, based on bilinear groups, give rigorous proofs that it satisfies our model, and analyze its efficiency in detail.
The One-More Discrete Logarithm Assumption in the Generic Group Model 📺
The one more-discrete logarithm assumption (OMDL) underlies the security analysis of identification protocols, blind signature and multi-signature schemes, such as blind Schnorr signatures and the recent MuSig2 multi-signatures. As these schemes produce standard Schnorr signatures, they are compatible with existing systems, e.g. in the context of blockchains. OMDL is moreover assumed for many results on the impossibility of certain security reductions. Despite its wide use, surprisingly, OMDL is lacking any rigorous analysis; there is not even a proof that it holds in the generic group model (GGM). (We show that a claimed proof is flawed.) In this work we give a formal proof of OMDL in the GGM. We also prove a related assumption, the one-more computational Diffie-Hellman assumption, in the GGM. Our proofs deviate from prior GGM proofs and replace the use of the Schwartz-Zippel Lemma by a new argument.
A Classification of Computational Assumptions in the Algebraic Group Model 📺
We give a taxonomy of computational assumptions in the algebraic group model (AGM). We first analyze the Uber assumption family for bilinear groups defined by Boyen and then extend it in multiple ways to cover assumptions such as Gap Diffie-Hellman and the LRSW assumption. We show that in the AGM every member of these families reduces to the q-discrete logarithm (DL) problem, for some q that depends on the degrees of the polynomials defining the assumption. Using the meta-reduction technique, we then separate (q+1)-DL from q-DL, which thus yields a classification of all members of the extended Uber-assumption families. We finally show that there are strong assumptions, such as one-more DL, that provably fall outside our classification, as we prove that they cannot be reduced to q-DL even in the AGM.
Combiners for Backdoored Random Oracles 📺
We formulate and study the security of cryptographic hash functions in the backdoored random-oracle (BRO) model, whereby a big brother designs a “good” hash function, but can also see arbitrary functions of its table via backdoor capabilities. This model captures intentional (and unintentional) weaknesses due to the existence of collision-finding or inversion algorithms, but goes well beyond them by allowing, for example, to search for structured preimages. The latter can easily break constructions that are secure under random inversions.BROs make the task of bootstrapping cryptographic hardness somewhat challenging. Indeed, with only a single arbitrarily backdoored function no hardness can be bootstrapped as any construction can be inverted. However, when two (or more) independent hash functions are available, hardness emerges even with unrestricted and adaptive access to all backdoor oracles. At the core of our results lie new reductions from cryptographic problems to the communication complexities of various two-party tasks. Along the way we establish a communication complexity lower bound for set-intersection for cryptographically relevant ranges of parameters and distributions and where set-disjointness can be easy.