Aggregate signatures are digital signatures that compress multiple signatures from different parties into a single signature, thereby reducing storage and bandwidth requirements. BLS aggregate signatures are a popular kind of aggregate signature, deployed by Ethereum, Dfinity, and Cloudflare amongst others, currently undergoing standardization at the IETF. However, BLS aggregate signatures are difficult to use correctly, with nuanced requirements that must be carefully handled by protocol developers. In this work, we design the first models of aggregate signatures that enable formal verification tools, such as Tamarin and ProVerif, to be applied to protocols using these signatures. We introduce general models that are based on the cryptographic security definition of generic aggregate signatures, allowing the attacker to exploit protocols where the security requirements are not satisfied. We also introduce a second family of models formalizing BLS aggregate signatures in particular. We demonstrate our approach's practical relevance by modelling and analyzing in Tamarin a device attestation protocol called SANA. Despite SANA's claimed correctness proof, with Tamarin we uncover undocumented assumptions that, when omitted, lead to attacks.

A standard requirement for a signature scheme is that it is existentially unforgeable under chosen message attacks (EUF-CMA), alongside other properties of interest such as strong unforgeability (SUF-CMA), and resilience against key substitution attacks.Remarkably, no detailed proofs have ever been given for these security properties for EdDSA, and in particular its Ed25519 instantiations. Ed25519 is one of the most efficient and widely used signature schemes, and different instantiations of Ed25519 are used in protocols such as TLS 1.3, SSH, Tor, ZCash, and WhatsApp/Signal. The differences between these instantiations are subtle, and only supported by informal arguments, with many works assuming results can be directly transferred from Schnorr signatures. Similarly, several proofs of protocol security simply assume that Ed25519 satisfies properties such as EUF-CMA or SUF-CMA.In this work we provide the first detailed analysis and security proofs of Ed25519 signature schemes. While the design of the schemes follows the well-established Fiat-Shamir paradigm, which should guarantee existential unforgeability, there are many side cases and encoding details that complicate the proofs, and all other security properties needed to be proven independently.Our work provides scientific rationale for choosing among several Ed25519 variants and understanding their properties, fills a much needed proof gap in modern protocol proofs that use these signatures, and supports further standardisation efforts.

The standard definition of security for digital signatures - existential unforgeability - does not ensure certain properties that protocol designers might expect. For example, in many modern signature schemes, one signature may verify against multiple distinct public keys. It is left to protocol designers to ensure that the absence of these properties does not lead to attacks.

Diffie-Hellman groups are a widely used component in cryptographic protocols in which a shared secret is needed. These protocols are typically proven to be secure under the assumption they are implemented with prime order Diffie Hellman groups. However, in practice, many implementations either choose to use non-prime order groups for reasons of efficiency, or can be manipulated into operating in non-prime order groups. This leaves a gap between the proofs of protocol security, which assume prime order groups, and the real world implementations. This is not merely a theoretical possibility: many attacks exploiting small subgroups or invalid curve points have been found in the real world. While many advances have been made in automated protocol analysis, modern tools such as Tamarin and ProVerif represent DH groups using an abstraction of prime order groups. This means they, like many cryptographic proofs, may miss practical attacks on real world protocols. In this work we develop a novel extension of the symbolic model of Diffie-Hellman groups. By more accurately modelling internal group structure, our approach captures many more differences between prime order groups and their actual implementations. The additional behaviours that our models capture are surprisingly diverse, and include not only attacks using small subgroups and invalid curve points, but also a range of proposed mitigation techniques, such as excluding low order elements, single coordinate ladders, and checking the elliptic curve equation. Our models thereby capture a large family of attacks that were previously outside the symbolic model. We implement our improved models in the Tamarin Prover. We find a new attack on the Secure Scuttlebutt Gossip protocol, independently discover a recent attack on the Tendermint protocol, and show how our analysis finds previous Bluetooth attacks and evaluate the effectiveness of the proposed countermeasures.