Fully leakage-resilient signatures revisited: Graceful degradation, noisy leakage, and construction in the bounded-retrieval model

We construct new leakage-resilient signature schemes. Our schemes remain unforgeable against an adversary leaking arbitrary (yet bounded) information on the entire state of the signer (sometimes known as fully leakage resilience), including the random coin tosses of the signing algorithm. The main feature of our constructions is that they offer a graceful degradation of security in situations where standard existential unforgeability is impossible

Fiat-Shamir for highly sound protocols is instantiable

The Fiat–Shamir (FS) transformation (Fiat and Shamir, Crypto '86) is a popular paradigm for constructing very efficient non-interactive zero-knowledge (NIZK) arguments and signature schemes from a hash function and any three-move interactive protocol satisfying certain properties. Despite its wide-spread applicability both in theory and in practice, the known positive results for proving security of the FS paradigm are in the random oracle model only, i.e., they assume that the hash function is modeled as an external random function accessible to all parties. On the other hand, a sequence of negative results shows that for certain classes of interactive protocols, the FS transform cannot be instantiated in the standard model. We initiate the study of complementary positive results, namely, studying classes of interactive protocols where the FS transform does have standard-model instantiations. In particular, we show that for a class of “highly sound” protocols that we define, instantiating the FS transform via a q-wise independent hash function yields NIZK arguments and secure signature schemes. In the case of NIZK, we obtain a weaker “q-bounded” zero-knowledge flavor where the simulator works for all adversaries asking an a-priori bounded number of queries q; in the case of signatures, we obtain the weaker notion of random-message unforgeability against q-bounded random message attacks. Our main idea is that when the protocol is highly sound, then instead of using random-oracle programming, one can use complexity leveraging. The question is whether such highly sound protocols exist and if so, which protocols lie in this class. We answer this question in the affirmative in the common reference string (CRS) model and under strong assumptions. Namely, assuming indistinguishability obfuscation and puncturable pseudorandom functions we construct a compiler that transforms any 3-move interactive protocol with instance-independent commitments and simulators (a property satisfied by the Lapidot–Shamir protocol, Crypto '90) into a compiled protocol in the CRS model that is highly sound. We also present a second compiler, in order to be able to start from a larger class of protocols, which only requires instance-independent commitments (a property for example satisfied by the classical protocol for quadratic residuosity due to Blum, Crypto '81). For the second compiler we require dual-mode commitments. We hope that our work inspires more research on classes of (efficient) 3-move protocols where Fiat–Shamir is (efficiently) instantiable

LNCS

We extend a commitment scheme based on the learning with errors over rings (RLWE) problem, and present efficient companion zeroknowledge proofs of knowledge. Our scheme maps elements from the ring (or equivalently, n elements fro

Trapdoor commitment schemes and their applications

Informally, commitment schemes can be described by lockable steely boxes. In the commitment phase, the sender puts a message into the box, locks the box and hands it over to the receiver. On one hand, the receiver does not learn anything about the message. On the other hand, the sender cannot change the message in the box anymore. In the decommitment phase the sender gives the receiver the key, and the receiver then opens the box and retrieves the message. One application of such schemes are digital auctions where each participant places his secret bid into a box and submits it to the auctioneer. In this thesis we investigate trapdoor commitment schemes. Following the abstract viewpoint of lockable boxes, a trapdoor commitment is a box with a tiny secret door. If someone knows the secret door, then this person is still able to change the committed message in the box, even after the commitment phase. Such trapdoors turn out to be very useful for the design of secure cryptographic protocols involving commitment schemes. In the first part of the thesis, we formally introduce trapdoor commitments and extend the notion to identity-based trapdoors, where trapdoors can only be used in connection with certain identities. We then recall the most popular constructions of ordinary trapdoor protocols and present new solutions for identity-based trapdoors. In the second part of the thesis, we show the usefulness of trapdoors in commitment schemes. Deploying trapdoors we construct efficient non-malleable commitment schemes which basically guarantee indepency of commitments. Furthermore, applying (identity-based) trapdoor commitments we secure well-known identification protocols against a new kind of attack. And finally, by means of trapdoors, we show how to construct composable commitment schemes that can be securely executed as subprotocols within complex protocols

Non-Malleable Vector Commitments via Local Equivocability

Vector commitments (VCs), enabling to commit to a vector and locally reveal any of its entries, play a key role in a variety of both classic and recently-evolving applications. However, security notions for VCs have so far focused on passive attacks, and non-malleability notions considering active attacks have not been explored. Moreover, existing frameworks that may enable to capture the non-malleability of VCs seem either too weak (non-malleable non-interactive commitments that do not account for the security implications of local openings) or too strong (non-malleable zero-knowledge sets that support both membership and non-membership proofs). We put forward a rigorous framework capturing the non-malleability of VCs, striking a careful balance between the existing weaker and stronger frameworks: We strengthen the framework of non-malleable non-interactive commitments by considering attackers that may be exposed to local openings, and we relax the framework of non-malleable zero-knowledge sets by focusing on membership proofs. In addition, we strengthen both frameworks by supporting (inherently-private) updates to entries of committed vectors, and discuss the benefits of non-malleable VCs in the context of both UTXO-based and account-based stateless blockchains, and in the context of simultaneous multi-round auctions (that have been adopted by the US Federal Communications Commission as the standard auction format for selling spectrum ranges). Within our framework we present a direct approach for constructing non-malleable VCs whose efficiency essentially matches that of the existing standard VCs. Specifically, we show that any VC can be transformed into a non-malleable one, relying on a new primitive that we put forth. Our new primitive, locally-equivocable commitments with all-but-one binding, is evidently both conceptually and technically simpler compared to multi-trapdoor mercurial trapdoor commitments (the main building block underlying existing non-malleable zero-knowledge sets), and admits more efficient instantiations based on the same number-theoretic assumptions

Efficient non-malleable commitment schemes

We present efficient non-malleable commitment schemes based on standard assumptions such as RSA and Discrete-Log, and under the condition that the network provides publicly available RSA or Discrete-Log parameters generated by a trusted party. Our protocols require only three rounds and a few modular exponentiations. We also discuss the difference between the notion of non-malleable commitment schemes used by Dolev, Dwork and Naor [DDN00] and the one given by Di Crescenzo, Ishai and Ostrovsky [DIO98]

Functional Commitment Schemes: From Polynomial Commitments to Pairing-Based Accumulators from Simple Assumptions

International audienceWe formalize a cryptographic primitive called functional commitment (FC) which can be viewed as a generalization of vector commitments (VCs), polynomial commitments and many other special kinds of commitment schemes. A non-interactive functional commitment allows committing to a message in such a way that the committer has the flexibility of only revealing a function F (M) of the committed message during the opening phase. We provide constructions for the functionality of linear functions, where messages consist of a vectors of n elements over some domain D (e.g., m = (m_1,. .. , m_n) ∈ D_n) and commitments can later be opened to a specific linear function of the vector coordinates. An opening for a function F : D_n → R thus generates a witness for the fact that F (m) indeed evaluates to y ∈ R. One security requirement is called function binding and requires that no adversary be able to open a commitment to two different evaluations y, y for the same function F. We propose a construction of functional commitment for linear functions based on constant-size assumptions in composite order groups endowed with a bilinear map. The construction has commitments and openings of constant size (i.e., independent of n or function description) and is perfectly hiding – the underlying message is information theoretically hidden. Our security proofs builds on the Déjà Q framework of Chase and Meiklejohn (Eurocrypt 2014) and its extension by Wee (TCC 2016) to encryption primitives, thus relying on constant-size subgroup decisional assumptions. We show that the FC for linear functions are sufficiently powerful to solve four open problems. They, first, imply polynomial commitments, and, then, give cryptographic accumulators (i.e., an algebraic hash function which makes it possible to efficiently prove that some input belongs to a hashed set). In particular, specializing our FC construction leads to the first pairing-based polynomial commitments and accumulators for large universes known to achieve security under simple assumptions. We also substantially extend our pairing-based accumulator to handle subset queries which requires a non-trivial extension of the Déjà Q framework

Cryptography in the Multi-string Model

The common random string model introduced by Blum, Feldman, and Micali permits the construction of cryptographic protocols that are provably impossible to realize in the standard model. We can think of this model as a trusted party generating a random string and giving it to all parties in the protocol. However, the introduction of such a third party should set alarm bells going off: Who is this trusted party? Why should we trust that the string is random? Even if the string is uniformly random, how do we know it does not leak private information to the trusted party? The very point of doing cryptography in the first place is to prevent us from trusting the wrong people with our secrets. In this paper, we propose the more realistic multi-string model. Instead of having one trusted authority, we have several authorities that generate random strings. We do not trust any single authority; we only assume a majority of them generate random strings honestly. Our results also hold even if different subsets of these strings are used in different instances, as long as a majority of the strings used at any particular invocation is honestly generated. This security model is reasonable and at the same time very easy to implement. We could for instance imagine random strings being provided on the Internet, and any set of parties that want to execute a protocol just need to agree on which authorities’ strings they want to use. We demonstrate the use of the multi-string model in several fundamental cryptographic tasks. We define multi-string non-interactive zero-knowledge proofs and prove that they exist under general cryptographic assumptions. Our multi-string NIZK proofs have very strong security properties such as simulation-extractability and extraction zero-knowledge, which makes it possible to compose them with arbitrary other protocols and to reuse the random strings. We also build efficient simulation-sound multi-string NIZK proofs for circuit satisfiability based on groups with a bilinear map. The sizes of these proofs match the best constructions in the single common random string model. We also suggest a universally composable commitment scheme in the multi-string model. It has been proven that UC commitment does not exist in the plain model without setup assumptions. Prior to this work, constructions were only known in the common reference string model and the registered public key model. The UC commitment scheme can be used in a simple coin-flipping protocol to create a uniform random string, which in turn enables the secure realization of any multi-party computation protocol