Adaptively Secure BLS Threshold Signatures from DDH and co-CDH

Threshold signature is one of the most important cryptographic primitives in distributed systems. A popular choice of threshold signature scheme is the BLS threshold signature introduced by Boldyreva (PKC\u2703). Some attractive properties of Boldyreva\u27s threshold signature are that the signatures are unique and short, the signing process is non-interactive, and the verification process is identical to that of non-threshold BLS. These properties have resulted in its practical adoption in several decentralized systems. However, despite its popularity and wide adoption, up until recently, the Boldyreva scheme has been proven secure only against a static adversary. Very recently, Bacho and Loss (CCS\u2722) presented the first proof of adaptive security for Boldyreva\u27s threshold signature, but they have to rely on strong and non-standard assumptions such as the hardness of one-more discrete log (OMDL) and the Algebraic Group Model~(AGM). In this paper, we present the first adaptively secure threshold BLS signature scheme that relies on the hardness of DDH and co-CDH in asymmetric pairing group in the Random Oracle Model (ROM). Our signature scheme also has non-interactive signing, compatibility with non-threshold BLS verification, and practical efficiency like Boldyreva\u27s scheme. Moreover, to achieve static security, our scheme only needs the hardness of CDH in the ROM, which is the same as the standard non-threshold BLS signature. These properties make our protocol a suitable candidate for practical adoption with the added benefit of provable adaptive security. We also present an efficient distributed key generation (DKG) protocol to set up the signing keys for our signature scheme. We implement our scheme in Go and evaluate its signing and aggregation costs

Fully Adaptive Schnorr Threshold Signatures

We prove adaptive security of a simple three-round threshold Schnorr signature scheme, which we call Sparkle. The standard notion of security for threshold signatures considers a static adversary – one who must declare which parties are corrupt at the beginning of the protocol. The stronger adaptive adversary can at any time corrupt parties and learn their state. This notion is natural and practical, yet not proven to be met by most schemes in the literature. In this paper, we demonstrate that Sparkle achieves several levels of security based on different corruption models and assumptions. To begin with, Sparkle is statically secure under minimal assumptions: the discrete logarithm assumption (DL) and the random oracle model (ROM). If an adaptive adversary corrupts fewer than t/2 out of a threshold of t + 1 signers, then Sparkle is adaptively secure under a weaker variant of the one-more discrete logarithm assumption (AOMDL) in the ROM. Finally, we prove that Sparkle achieves full adaptive security, with a corruption threshold of t, under AOMDL in the algebraic group model (AGM) with random oracles. Importantly, we show adaptive security without requiring secure erasures. Ours is the first proof achieving full adaptive security without exponential tightness loss for any threshold Schnorr signature scheme; moreover, the reduction is tight

Security of a biometric identity-based encryption scheme

Biometric identity-based encryption (Bio-IBE) is a kind of fuzzy identity-based encryption (fuzzy IBE) where a ciphertext encrypted under an identity w' can be decrypted using a secret key corresponding to the identity w which is close to w' as measured by some metric. Recently, Yang et al. proposed a constant-size Bio-IBE scheme and proved that it is secure against adaptive chosen-ciphertext attack (CCA2) in the random oracle model. Unfortunately, in this paper, we will show that their Bio-IBE scheme is even not chosen-plaintext secure. Specifically, user w using his secret key is able to decrypt any ciphertext encrypted under an identity w' even though w is not close to w'.Comment: Journal version of the paper will be appearing in International Journal of Network Securit

Born and Raised Distributively: Fully Distributed Non-Interactive Adaptively-Secure Threshold Signatures with Short Shares

International audienceThreshold cryptography is a fundamental distributed computational paradigm for enhancing the availability and the security of cryptographic public-key schemes. It does it by dividing private keys into $n$ shares handed out to distinct servers. In threshold signature schemes, a set of at least $t+1 \leq n$ servers is needed to produce a valid digital signature. Availability is assured by the fact that any subset of $t+1$ servers can produce a signature when authorized. At the same time, the scheme should remain robust (in the fault tolerance sense) and unforgeable (cryptographically) against up to $t$ corrupted servers; {\it i.e.}, it adds quorum control to traditional cryptographic services and introduces redundancy. Originally, most practical threshold signatures have a number of demerits: They have been analyzed in a static corruption model (where the set of corrupted servers is fixed at the very beginning of the attack), they require interaction, they assume a trusted dealer in the key generation phase (so that the system is not fully distributed), or they suffer from certain overheads in terms of storage (large share sizes). In this paper, we construct practical {\it fully distributed} (the private key is born distributed), non-interactive schemes -- where the servers can compute their partial signatures without communication with other servers -- with adaptive security ({\it i.e.}, the adversary corrupts servers dynamically based on its full view of the history of the system). Our schemes are very efficient in terms of computation, communication, and scalable storage (with private key shares of size $O(1)$, where certain solutions incur $O(n)$ storage costs at each server). Unlike other adaptively secure schemes, our schemes are erasure-free (reliable erasure is a hard to assure and hard to administer property in actual systems). To the best of our knowledge, such a fully distributed highly constrained scheme has been an open problem in the area. In particular, and of special interest, is the fact that Pedersen's traditional distributed key generation (DKG) protocol can be safely employed in the initial key generation phase when the system is born -- although it is well-known not to ensure uniformly distributed public keys. An advantage of this is that this protocol only takes one round optimistically (in the absence of faulty player)