Multi-signature schemes are gaining significant interest due to their blockchain applications. Of particular interest are two-round schemes in the plain public-key model that offer key aggregation, and whose security is based on the hardness of the DLOG problem. Unfortunately, despite substantial recent progress, the security proofs of the proposed schemes provide rather insufficient concrete guarantees (especially for 256-bit groups). This frustrating situation has so far been approached...

With the demand of cryptocurrencies, threshold ECDSA recently regained popularity. So far, several methods have been proposed to construct threshold ECDSA, including the usage of OT and homomorphic encryptions (HE). Due to the mismatch between the plaintext space and the signature space, HE-based threshold ECDSA always requires zero-knowledge range proofs, such as Paillier and Joye-Libert (JL) encryptions. However, the overhead of range proofs constitutes a major portion of the total...

T-out-of-N threshold signatures have recently seen a renewed interest, with various types now available, each offering different tradeoffs. However, one property that has remained elusive is adaptive security. When we target thresholdizing existing efficient signatures schemes based on the Fiat-Shamir paradigm such as Schnorr, the elusive nature becomes clear. This class of signature schemes typically rely on the forking lemma to prove unforgeability. That is, an adversary is rewound and...

In this work we first present an explicit forking lemma that distills the information-theoretic essence of the high-moment technique introduced by Rotem and Segev (CRYPTO '21), who analyzed the security of identification protocols and Fiat-Shamir signature schemes. Whereas the technique of Rotem and Segev was particularly geared towards two specific cryptographic primitives, we present a stand-alone probabilistic lower bound, which does not involve any underlying primitive or idealized...

Blind signatures serve as a foundational tool for privacy-preserving applications and have recently seen renewed interest due to new applications in blockchains and privacy-authentication tokens. With this, constructing practical round-optimal (i.e., signing consists of the minimum two rounds) blind signatures in the random oracle model (ROM) has been an active area of research, where several impossibility results indicate that either the ROM or a trusted setup is inherent. In this work,...

Existing proofs of adaptive security (e.g., in settings in which decryption keys are adaptively revealed) often rely on guessing arguments. Such guessing arguments can be simple (and, e.g., just involve guessing which keys are revealed), or more complex "partitioning'' arguments. Since guessing directly and negatively impacts the loss of the corresponding security reduction, this leads to black-box lower bounds for a number of cryptographic scenarios that involve adaptive security. In...

Multi-signatures have been drawing lots of attention in recent years, due to their applications in cryptocurrencies. Most early constructions require three-round signing, and recent constructions have managed to reduce the round complexity to two. However, their security proofs are mostly based on non-standard, interactive assumptions (e.g. one-more assumptions) and come with a huge security loss, due to multiple uses of rewinding (aka the Forking Lemma). This renders the quantitative...

Partially blind signatures, an extension of ordinary blind signatures, are a primitive with wide applications in e-cash and electronic voting. One of the most efficient schemes to date is the one by Abe and Okamoto (CRYPTO 2000), whose underlying idea - the OR-proof technique - has served as the basis for several works. We point out several subtle flaws in the original proof of security, and provide a new detailed and rigorous proof, achieving similar bounds as the original work. We...

Commit-and-open Sigma-protocols are a popular class of protocols for constructing non-interactive zero-knowledge arguments and digital-signature schemes via the Fiat-Shamir transformation. Instantiated with hash-based commitments, the resulting non-interactive schemes enjoy tight online-extractability in the random oracle model. Online extractability improves the tightness of security proofs for the resulting digital-signature schemes by avoiding lossy rewinding or forking-lemma based...

The Schnorr identification and signature schemes have been amongst the most influential cryptographic protocols of the past three decades. Unfortunately, although the best-known attacks on these two schemes are via discrete-logarithm computation, the known approaches for basing their security on the hardness of the discrete logarithm problem encounter the ``square-root barrier''. In particular, in any group of order $p$ where Shoup's generic hardness result for the discrete logarithm problem...

Multi-signatures are used to attest that a fixed collection of $n$ parties, represented by their respective public keys, have all signed a given message. An emerging application of multi-signatures is to be found in consensus protocols to attest that a qualified subset of a global set of $n$ validators have reached agreement. In this paper, we point out that the traditional security model for multi-signatures is insufficient for this new application, as it assumes that every party in the...

Multi-signatures enable a group of signers to produce a joint signature on a joint message. Recently, Drijvers et al. (S&P'19) showed that all thus far proposed two-round multi-signature schemes in the pure DL setting (without pairings) are insecure under concurrent signing sessions. While Drijvers et al. proposed a secure two-round scheme, this efficiency in terms of rounds comes with the price of having signatures that are more than twice as large as Schnorr signatures, which are becoming...

This paper studies concrete security with respect to expected-time adversaries. Our first contribution is a set of generic tools to obtain tight bounds on the advantage of an adversary with expected-time guarantees. We apply these tools to derive bounds in the random-oracle and generic-group models, which we show to be tight. As our second contribution, we use these results to derive concrete bounds on the soundness of public-coin proofs and arguments of knowledge. Under the lens of...

We introduce an efficient post-quantum signature scheme that relies on the one-wayness of the Legendre PRF. This "LEGendRe One-wAyness SignaTure" (LegRoast) builds upon the MPC-in-the-head technique to construct an efficient zero-knowledge proof, which is then turned into a signature scheme with the Fiat-Shamir transform. Unlike many other Fiat-Shamir signatures, the security of LegRoast can be proven without using the forking lemma, and this leads to a tight (classical) ROM proof. We also...

We bypass impossibility results for the deterministic encryption of public-key-dependent messages, showing that, in this setting, the classical Encrypt-with-Hash scheme provides message-recovery security, across a broad range of message distributions. The proof relies on a new variant of the forking lemma in which the random oracle is reprogrammed on just a single fork point rather than on all points past the fork.

Modern cryptocurrencies such as Bitcoin and Ethereum achieve decentralization by replacing a trusted center with a distributed and append-only ledger (known as blockchain). However, removing this trusted center comes at significant cost of privacy due to the public nature of blockchain. Many existing cryptocurrencies fail to provide transaction anonymity and confidentiality, meaning that addresses of sender, receiver and transfer amount are publicly accessible. As the privacy concerns...

We propose a modular security treatment of blind signatures derived from linear identification schemes in the random oracle model. To this end, we present a general framework that captures several well known schemes from the literature and allows to prove their security. Our modular security reduction introduces a new security notion for identification schemes called One-More-Man In the Middle Security which we show equivalent to the classical One-More-Unforgeability notion for blind...

We describe a new Schnorr-based multi-signature scheme (i.e., a protocol which allows a group of signers to produce a short, joint signature on a common message) called MuSig, provably secure in the plain public-key model (meaning that signers are only required to have a public key, but do not have to prove knowledge of the private key corresponding to their public key to some certification authority or to other signers before engaging the protocol), which improves over the state-of-art...

Attribute-based signature (ABS), originally introduced by Maji et al. (CT-RSA'11), represents an essential mechanism to allow for fine-grained authentication. A user associated with an attribute $x$ can sign w.r.t. a given public policy $C$ only if his attribute satisfies $C$, i.e., $C(x)=1$. So far, much effort on constructing bilinear map-based ABS schemes have been made, where the state-of-the-art scheme of Sakai et al. (PKC'16) supports the very wide class of unbounded circuits as...

This paper presents MQDSS, the first signature scheme with a security reduction based on the problem of solving a multivariate system of quadratic equations (MQ problem). In order to construct this scheme we give a new security reduction for the Fiat-Shamir transform from a large class of $5$-pass identification schemes and show that a previous attempt from the literature to obtain such a proof does not achieve the desired goal. We give concrete parameters for MQDSS and provide a detailed...

Boldyreva et al. introduced the notion of multiple forking (MF) as an extension of (general) forking to accommodate nested oracle replay attacks. The primary objective of a (multiple) forking algorithm is to separate out the oracle replay attack from the actual simulation of protocol to the adversary, and this is achieved through the intermediary of a so-called wrapper algorithm. Multiple forking has turned out to be a useful tool in the security argument of several cryptographic protocols....

In Africacrypt 2009, Galindo-Garcia proposed a lightweight identity-based signature (IBS) scheme based on the Schnorr signature. The construction is simple and claimed to be the most efficient IBS till date. The security is based on the discrete-log assumption and the security argument consists of two reductions: B1 and B2, both of which use the multiple-forking lemma to solve the discrete-log problem (DLP). In this work, we revisit the security argument given in. Our contributions are two...

The well-known forking lemma by Pointcheval and Stern has been used to prove the security of the so-called generic signature schemes. These signature schemes are obtained via the Fiat-Shamir transform from three-pass identication schemes. A number of five-pass identification protocols have been proposed in the last few years. Extending the forking lemma and the Fiat-Shamir transform would allow to obtain new signature schemes since, unfortunately, these newly proposed schemes fall outside...

The Schnorr signature scheme has been known to be provably secure in the Random Oracle Model under the Discrete Logarithm (DL) assumption since the work of Pointcheval and Stern (EUROCRYPT '96), at the price of a very loose reduction though: if there is a forger making at most $q_h$ random oracle queries, and forging signatures with probability $\varepsilon_F$, then the Forking Lemma tells that one can compute discrete logarithms with constant probability by rewinding the forger...

Digital signature is one of the basic primitives in cryptography. A common paradigm of obtaining signatures, known as the Fiat-Shamir (FS) paradigm, is to collapse any Σ-protocol (which is 3-round public-coin honest-verifier zero-knowledge) into a non-interactive scheme with hash functions that are modeled to be random oracles (RO). The Digital Signature Standard (DSS) and Schnorr’s signature schemes are two salient examples following the FS-paradigm. In this work, we present a...

Since the discovery of identity based cryptography, a number of identity based signature schemes were reported in the literature. Although, a lot of identity based signature schemes were proposed, the only identity based deterministic signature scheme was given by Javier Herranz. This signature scheme uses Schnorr signature scheme for generating the private key of the users and uses BLS short signature scheme for generating users signature. The security of this scheme was proved in the...

In this paper, we present a new authenticated key exchange(AKE) protocol, called NETS, and prove its security in the extended Canetti-Krawczyk model under the random oracle assumption and the gap Diffie-Hellman(GDH) assumption. Our protocol enjoys a simple and tight security reduction compared to those of HMQV and CMQV without using the Forking Lemma. Each session of the NETS protocol requires only three exponentiations per party, which is comparable to the efficiency of MQV, HMQV and CMQV.

Provable security based on complexity theory provides an efficient way for providing the convincing evidences of security. In this paper, we present a definition of generic ID-based signature schemes (GIBSS) by extending the definition of generic signature schemes, and prove the Forking lemma for GIBSS. That is, we provide the Forking lemma for ID-based signature schemes. The theoretical result can be viewed as an extension of the Forking Lemma due to Pointcheval and Stern for ID-based...

Rewinding techniques form the essence of many security reductions including proofs for identification and signature schemes. We propose a simple and modular approach for the construction of such proofs. Straightforward applications of our central result include, but are not limited to, the security of identification schemes, generic signatures and ring signatures. These results are well known, however, we generalise them in such a way that our technique can be used off-the-shelf for future...

In this paper, we propose an efficient ID-based signature scheme based on pairing. The number of paring operation involved in the verification procedure is one. Our scheme is proved secure against existential forgery on adaptively chosen message and ID attack under the hardness assumption of computational Diffie-Hellman problem, in the random oracle model.

Identity-based (ID-based) cryptosystems eliminate the need for validity checking of the certificates and the need for registering for a certificate before getting the public key. These two features are desirable especially for the efficiency and the real spontaneity of ring signature, where a user can anonymously sign a message on behalf of a group of spontaneously conscripted users including the actual signer. In this paper, we propose a novel construction of ID-based ring signature which...