On the One-Per-Message Unforgeability of (EC)DSA and Its Variants

The American signature standards DSA and ECDSA, as well as their Russian and Chinese counterparts GOST 34.10 and SM2, are of utmost importance in the current security landscape. The mentioned schemes are all rooted in the Elgamal signature scheme and use a hash function and a cyclic group as building blocks. Unfortunately, authoritative security guarantees for the schemes are still due: All existing positive results on their security use aggressive idealization approaches, like the generic group model, leading to debatable overall results. In this work we conduct security analyses for a set of classic signature schemes, including the ones mentioned above, providing positive results in the following sense: If the hash function is modeled as a random oracle, and the signer issues at most one signature per message, then the schemes are unforgeable if and only if they are key-only unforgeable, where the latter security notion captures that the adversary has access to the verification key but not to sample signatures. Put differently, for the named signature schemes, in the one-signature-per-message setting the signature oracle is redundant

Shorter Double-Authentication Preventing Signatures for Small Address Spaces

A recent paper by Derler, Ramacher, and Slamanig (IEEE EuroS&P 2018) constructs double-authentication preventing signatures ( DAP signatures , a specific self-enforcement enabled variant of signatures where messages consist of an address and a payload) that have---if the supported address space is not too large---keys and signatures that are considerably more compact than those of prior work. We embark on their approach to restrict attention to small address spaces and construct novel DAP schemes that beat their signature size by a factor of five and reduce the signing key size from linear to constant (the verification key size remains almost the same). We construct our DAP signatures generically from identification protocols, using a transform similar to but crucially different from that of Fiat and Shamir. We use random oracles. We don\u27t use pairings

Tweakable Sleeve: A Novel Sleeve Construction based on Tweakable Hash Functions

Recently, Chaum et al. (ACNS\u2721) introduced $\mathcal{S}_{leeve}$, which describes an extra security layer for signature schemes, i.e., ECDSA. This distinctive feature is a new key generation mechanism, allowing users to generate a \u27\u27back up key\u27\u27 securely nested inside the secret key of a signature scheme. Using this novel construction, the \u27\u27back up key\u27\u27, which is secret, can be used to generate a \u27\u27proof of ownership\u27\u27, i.e., only the rightful owner of this secret key can generate such a proof. This design offers a quantum secure fallback, i.e., a brand new quantum resistant signature, ready to be used, nested in the ECDSA secret key. In this work, we rely on the original $\mathcal{S}_{leeve}$ definition to generalize the construction to a modular design based on Tweakable Hash Functions, thus yielding a cleaner design of the primitive. Furthermore, we provide a thorough security analysis taking into account the security of the ECDSA signature scheme, which is lacking in the original work. Finally, we provide an analysis based on formal methods using Verifpal assuring the security guarantees our construction provides

Security Analysis of Signature Schemes with Key Blinding

Digital signatures are fundamental components of public key cryptography. They allow a signer to generate verifiable and unforgeable proofs---signatures---over arbitrary messages with a private key, and allow recipients to verify the proofs against the corresponding and expected public key. These properties are used in practice for a variety of use cases, ranging from identity or data authenticity to non-repudiation. Unsurprisingly, signature schemes are widely used in security protocols deployed on the Internet today. In recent years, some protocols have extended the basic syntax of signature schemes to support key blinding, a.k.a., key randomization. Roughly speaking, key blinding is the process by which a private signing key or public verification key is blinded (randomized) to hide information about the key pair. This is generally done for privacy reasons and has found applications in Tor and Privacy Pass. Recently, Denis, Eaton, Lepoint, and Wood proposed a technical specification for signature schemes with key blinding in an IETF draft. In this work, we analyze the constructions in this emerging specification. We demonstrate that the constructions provided satisfy the desired security properties for signature schemes with key blinding. We experimentally evaluate the constructions and find that they introduce a very reasonable 2-3x performance overhead compared to the base signature scheme. Our results complement the ongoing standardization efforts for this primitive

Limits in the Provable Security of ECDSA Signatures

Digital Signatures are ubiquitous in modern computing. One of the most widely used digital signature schemes is ECDSA due to its use in TLS, various Blockchains such as Bitcoin and Etherum, and many other applications. Yet the formal analysis of ECDSA is comparatively sparse. In particular, all known security results for ECDSA rely on some idealized model such as the generic group model or the programmable (bijective) random oracle model. In this work, we study the question whether these strong idealized models are necessary for proving the security of ECDSA. Specifically, we focus on the programmability of ECDSA\u27s conversion function which maps an elliptic curve point into its $x$-coordinate modulo the group order. Unfortunately, our main results are negative. We establish, by means of a meta reductions, that an algebraic security reduction for ECDSA can only exist if the security reduction is allowed to program the conversion function. As a consequence, a meaningful security proof for ECDSA is unlikely to exist without strong idealization

Digital Signatures with Memory-Tight Security in the Multi-Challenge Setting

The standard security notion for digital signatures is single-challenge (SC) EUF-CMA security, where the adversary outputs a single message-signature pair and wins if it is a forgery. Auerbach et al. (CRYPTO 2017) introduced memory-tightness of reductions and argued that the right security goal in this setting is actually a stronger multi-challenge (MC) definition, where an adversary may output many message-signature pairs and wins if at least one is a forgery. Currently, no construction from simple standard assumptions is known to achieve full tightness with respect to time, success probability, and memory simultaneously. Previous works showed that memory-tight signatures cannot be achieved via certain natural classes of reductions (Auerbach et al., CRYPTO 2017; Wang et al., EUROCRYPT 2018). These impossibility results may give the impression that the construction of memory-tight signatures is difficult or even impossible. We show that this impression is false, by giving the first constructions of signature schemes with full tightness in all dimensions in the MC setting. To circumvent the known impossibility results, we first introduce the notion of canonical reductions in the SC setting. We prove a general theorem establishing that every signature scheme with a canonical reduction is already memory-tightly secure in the MC setting, provided that it is strongly unforgeable, the adversary receives only one signature per message, and assuming the existence of a tightly-secure pseudorandom function. We then achieve memory-tight many-signatures-per-message security in the MC setting by a simple additional generic transformation. This yields the first memory-tightly, strongly EUF-CMA-secure signature schemes in the MC setting. Finally, we show that standard security proofs often already can be viewed as canonical reductions. Concretely, we show this for signatures from lossy identification schemes (Abdalla et al., EUROCRYPT 2012), two variants of RSA Full-Domain Hash (Bellare and Rogaway, EUROCRYPT 1996), and two variants of BLS signatures (Boneh et al., ASIACRYPT 2001)

Concurrently Secure Blind Schnorr Signatures

Many applications of blind signatures (notably in blockchains) require the resulting signatures to be compatible with the existing system. This makes schemes that produce Schnorr signatures (now being standardized and supported by major cryptocurrencies like Bitcoin) desirable. Unfortunately, the existing blind-signing protocol has been shown insecure when users can open signing sessions concurrently (Eurocrypt\u2721). On the other hand, only allowing sequential sessions opens the door to denial-of-service attacks. We present the first practical, concurrently secure blind-signing protocol for Schnorr signatures, using the standard primitives NIZK and PKE and assuming that Schnorr signatures themselves are unforgeable. We cast our scheme as a generalization of blind and partially blind signatures: we introduce the notion of predicate blind signatures, in which the signer can define a predicate that the blindly signed message must satisfy. We provide proof-of-concept implementations and benchmarks for various choices of primitives and scenarios, including blindly signing Bitcoin transactions conditioned on certain properties