Fast Multiparty Threshold ECDSA with Fast Trustless Setup

A threshold signature scheme enables distributed signing among $n$ players such that any subgroup of size $t+1$ can sign, whereas any group with $t$ or fewer players cannot. While there exist previous threshold schemes for the ECDSA signature scheme, we present the first protocol that supports multiparty signatures for any $t \leq n$ with efficient, dealerless key generation. Our protocol is faster than previous solutions and significantly reduces the communication complexity as well. We prove our scheme secure against malicious adversaries with a dishonest majority. We implemented our protocol, demonstrating its efficiency and suitability to be deployed in practice

One Round Threshold ECDSA with Identifiable Abort

Threshold ECDSA signatures have received much attention in recent years due to the widespread use of ECDSA in cryptocurrencies. While various protocols now exist that admit efficient distributed key generation and signing, these protocols have two main drawbacks. Firstly, if a player misbehaves, the protocol will abort, but all current protocols give no way to detect which player is responsible for the abort. In distributed settings, this can be catastrophic as any player can cause the protocol to fail without any consequence. General techniques to realize dishonest-majority MPC with identifiable abort add a prohibitive overhead, but we show how to build a tailored protocol for threshold ECDSA with minimal overhead. Secondly, current threshold ECDSA protocols (that do not rely on generic MPC) have numerous rounds of interaction. We present a highly efficient protocol with a non-interactive online phase allowing for players to asynchronously participate in the protocol without the need to be online simultaneously. We benchmark our protocols and find that our protocol simultaneously reduces the rounds and computations of current protocols, while adding significant functionality: identifiable abort and noninteractivity

Publicly Verifiable Delegation of Large Polynomials and Matrix Computations, with Applications

Outsourced computations (where a client requests a server to perform some computation on its behalf) are becoming increasingly important due to the rise of Cloud Computing and the proliferation of mobile devices. Since cloud providers may not be trusted, a crucial problem is the verification of the integrity and correctness of such computation, possibly in a {\em public} way, i.e., the result of a computation can be verified by any third party, and requires no secret key -- akin to a digital signature on a message. We present new protocols for publicly verifiable secure outsourcing of {\em Evaluation of High Degree Polynomials} and {\em Matrix Multiplication}. Compared to previously proposed solutions, ours improve in efficiency and offer security in a stronger model. The paper also discusses several practical applications of our protocols

LNCS

NMAC is a mode of operation which turns a fixed input-length keyed hash function f into a variable input-length function. A practical single-key variant of NMAC called HMAC is a very popular and widely deployed message authentication code (MAC). Security proofs and attacks for NMAC can typically be lifted to HMAC. NMAC was introduced by Bellare, Canetti and Krawczyk [Crypto'96], who proved it to be a secure pseudorandom function (PRF), and thus also a MAC, assuming that (1) f is a PRF and (2) the function we get when cascading f is weakly collision-resistant. Unfortunately, HMAC is typically instantiated with cryptographic hash functions like MD5 or SHA-1 for which (2) has been found to be wrong. To restore the provable guarantees for NMAC, Bellare [Crypto'06] showed its security based solely on the assumption that f is a PRF, albeit via a non-uniform reduction. - Our first contribution is a simpler and uniform proof for this fact: If f is an ε-secure PRF (against q queries) and a δ-non-adaptively secure PRF (against q queries), then NMAC f is an (ε+ℓqδ)-secure PRF against q queries of length at most ℓ blocks each. - We then show that this ε+ℓqδ bound is basically tight. For the most interesting case where ℓqδ ≥ ε we prove this by constructing an f for which an attack with advantage ℓqδ exists. This also violates the bound O(ℓε) on the PRF-security of NMAC recently claimed by Koblitz and Menezes. - Finally, we analyze the PRF-security of a modification of NMAC called NI [An and Bellare, Crypto'99] that differs mainly by using a compression function with an additional keying input. This avoids the constant rekeying on multi-block messages in NMAC and allows for a security proof starting by the standard switch from a PRF to a random function, followed by an information-theoretic analysis. We carry out such an analysis, obtaining a tight ℓq2/2 c bound for this step, improving over the trivial bound of ℓ2q2/2c. The proof borrows combinatorial techniques originally developed for proving the security of CBC-MAC [Bellare et al., Crypto'05]

Tag-KEM/DEM: A New Framework for Hybrid Encryption

This paper presents a novel framework for the generic construction of hybrid encryption schemes which produces more efficient schemes than the ones known before. A previous framework introduced by Shoup combines a key encapsulation mechanism (KEM) and a data encryption mechanism (DEM). While it is sufficient to require both components to be secure against chosen ciphertext attacks (CCA-secure), Kurosawa and Desmedt showed a particular example of KEM that is not CCA-secure but can be securely combined with a specific type of CCA-secure DEM to obtain a more efficient, CCA-secure hybrid encryption scheme. There are also many other efficient hybrid encryption schemes in the literature that do not fit Shoup\u27s framework. These facts serve as motivation to seek another framework. The framework we propose yields more efficient hybrid scheme, and in addition provides insightful explanation about existing schemes that do not fit into the previous framework. Moreover, it allows immediate conversion from a class of threshold public-key encryption to a hybrid one without considerable overhead, which may not be possible in the previous approach

Threshold-optimal DSA/ECDSA signatures and an application to Bitcoin wallet security

While threshold signature schemes have been presented before, there has never been an optimal threshold signature algorithm for DSA. Due to the properties of DSA, it is far more difficult to create a threshold scheme for it than for other signature algorithms. In this paper, we present a breakthrough scheme that provides a threshold DSA algorithm that is efficient and optimal. We also present a compelling application to use our scheme: securing Bitcoin wallets. Bitcoin thefts are on the rise, and threshold DSA is necessary to secure Bitcoin wallets. Our scheme is the first general threshold DSA scheme that does not require an honest majority and is useful for securing Bitcoin wallets

Okamoto-Tanaka Revisited: Fully Authenticated Diffie-Hellman with Minimal Overhead

Okamoto-Tanaka Revisited: Fully Authenticated Diffie-Hellman with Minimal Overhead The Diffie-Hellman protocol (DHP) is one of the most studied protocols in cryptography. Much work has been dedicated to armor the original protocol against active attacks while incurring a minimal performance overhead relative to the basic (unauthenticated) DHP. This line of work has resulted in some remarkable protocols, e.g., MQV, where the protocol\u27s communication cost is identical to that of the basic DHP and the computation overhead is small. Unfortunately, MQV and similar 2-message ``implicitly authenticated protocols do not achieve full security against active attacks since they cannot provide forward secrecy (PFS), a major security goal of DHP, against active attackers. In this paper we investigate the question of whether one can push the limits of authenticated DHPs even further, namely, to achieve communication complexity as in the original DHP (two messages with a single group element per message), maintain low computational overhead, and yet achieve full PFS against active attackers in a provable way. We answer this question in the affirmative by resorting to an old and elegant key agreement protocol: the Okamoto-Tanaka protocol \cite{okta}. We present a variant of the protocol (denoted mOT) which achieves the above minimal communication, incurs a computational overhead relative to the basic DHP that is practically negligible, and yet achieves full provable key agreement security, including PFS, against active attackers. Moreover, due to the identity-based properties of mOT, even the sending of certificates (typical for authenticated DHPs) can be avoided in the protocol. As additional contributions, we apply our analysis to prove the security of a recent multi-domain extension of the Okamoto-Tanaka protocol by Schridde et al. and show how to adapt mOT to the (non id-based) certificate-based setting

Secure Hashed Diffie-Hellman over Non-DDH Groups

We show that in applications that use the Diffie-Hellman (DH) transform but take care of hashing the DH output (as required, for example, for secure DH-based encryption and key exchange) the usual requirement to work over a DDH group (i.e., a group in which the Decisional Diffie-Hellman assumption holds) can be relaxed to only requiring that the DH group contains a large enough DDH subgroup. In particular, this implies the security of (hashed) Diffie-Hellman over non-prime order groups such as $Z_p^*$. Moreover, our results show that one can work directly over $Z_p^*$ without requiring any knowledge of the prime factorization of $p-1$ and without even having to find a generator of $Z_p^*$. These results are obtained via a general characterization of DDH groups in terms of their DDH subgroups, and a relaxation (called $t$-DDH) of the DDH assumption via computational entropy. We also show that, under the short-exponent discrete-log assumption, the security of the hashed Diffie-Hellman transform is preserved when replacing full exponents with short exponents