2025

A survey of hash-based signature schemes as a post-quantum option for bitcoin, from basic building blocks to SPHINCS+ and its variants. Parameters tuned for bitcoin, with a cap on signatures per key, cut signature size well below the SPHINCS+ standard.

2023

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

2022

Bitcoin and other cryptocurrencies have recently introduced support for Schnorr signatures whose cleaner algebraic structure, as compared to ECDSA, allows for simpler and more practical constructions of highly demanded ''t-of-n'' threshold signatures. However, existing Schnorr threshold signature schemes still fall short of the needs of real-world applications due to their assumption that the network is synchronous and due to their lack of robustness, i.e., the guarantee that t honest signers are able to obtain a valid signature even in the presence of other malicious signers who try to disrupt the protocol. This hinders the adoption of threshold signatures in the cryptocurrency ecosystem, e.g., in second-layer protocols built on top of cryptocurrencies.

2017

Bitcoin is an online distributed ledger in which coins are distributed according to the unspent transaction output (UTXO) set, and transactions describe changes to this set. Every UTXO has associated to it an amount and signature verification key, representing the quantity that can be spent and the entity authorized to do so, respectively.

2017

The blockchain has fueled one of the most enthusiastic bursts of activity in applied cryptography in years, but outstanding problems in security and privacy research must be solved for blockchain technologies to go beyond the hype and reach their full potential. At the first IEEE Privacy and Security on the Blockchain Workshop (IEEE S&B), we presented peer-reviewed papers bringing together academia and industry to analyze problems ranging from deploying newer cryptographic primitives on Bitcoin to enabling use-cases like privacy-preserving file storage. We overview not only the larger problems the workshop has set out to tackle, but also outstanding unsolved issues that will require further cooperation between academia and the blockchain community.

2015

It is well-known that n-of-n Schnorr multisignatures can be produced in one round of communication by adding ordinary Schnorr signatures. As observed by Boneh, this can be extended from n-of-n to arbitrary monotone functions of the signers by use of a linear secret sharing scheme.