arXiv subjects

Christopher Battarbee

Publications and source records attributed to Christopher Battarbee.

9 recordsLinked to original sources

arXiv2026

Authentication in Quantum Networks

In this review, we survey the cryptographic task of authentication from the perspective of quantum communication. We review three main flavours of authentication that are often conflated in the literature: authentication of classical messages, authentication of quantum messages, and entity authentication, also covering recent hardware-assisted approaches. We compare representative protocols for each functionality in terms of their security assumptions, set-up requirements, composability, and scalability in large or dynamic networks, and use these criteria to identify and recommend suitable candidates. Finally, applications are surveyed: we provide a detailed case study of authentication and quantum key distribution (QKD), then extend the discussion to protocols beyond QKD, where the role of authentication is more complex. Our take-home message is that an authentication requirement is not an intrinsic limitation of quantum networks: as with all secure communication, each protocol relies on a particular authentication resource, and the security claim of that protocol is meaningful only once the authentication resource and its deployment assumptions are made explicit. At the same time, the existing classical and quantum literature already offers a range of quantum-secure authentication schemes, which can support different applications when carefully matched to the required functionality, assumptions, and security guarantees.

quant-ph↗

arXiv2025

Hard Instances of Discrete Logarithm Problem and Cryptographic Applications

Let f be an arbitrary positive integer valued function. The goal of this note is to show that one can construct a finitely generated group in which the discrete log problem is polynomially equivalent to computing the function f. In particular, we provide infinite, but finitely generated groups, in which the discrete logarithm problem is arbitrarily hard. As another application, we construct a family of two-generated groups that have polynomial time word problem and NP-complete discrete log problem. Additionally, using our framework, we propose a generic scheme of cryptographic protocols, which might be of independent interest.

math.GR↗

arXiv2024

Quantum-Safe Hybrid Key Exchanges with KEM-Based Authentication

Authenticated Key Exchange (AKE) between any two entities is one of the most important security protocols available for securing our digital networks and infrastructures. In PQCrypto 2023, Bruckner, Ramacher and Striecks proposed a novel hybrid AKE (HAKE) protocol, dubbed Muckle+, that is particularly useful in large quantum-safe networks consisting of a large number of nodes. Their protocol is hybrid in the sense that it allows key material from conventional and post-quantum primitives, as well as from quantum key distribution, to be incorporated into a single end-to-end shared key. To achieve the desired authentication properties, Muckle+ utilizes post-quantum digital signatures. However, available instantiations of such signatures schemes are not yet efficient enough compared to their post-quantum key-encapsulation mechanism (KEM) counterparts, particularly in large networks with potentially several connections in a short period of time. To mitigate this gap, we propose Muckle# that pushes the efficiency boundaries of currently known HAKE constructions. Muckle# uses post-quantum key-encapsulating mechanisms for implicit authentication inspired by recent works done in the area of Transport Layer Security (TLS) protocols, particularly, in KEMTLS (CCS'20). We port those ideas to the HAKE framework and develop novel proof techniques on the way. Due to our novel KEM-based approach, the resulting protocol has a slightly different message flow compared to prior work that we carefully align with the HAKE framework and which makes our changes to the Muckle+ non-trivial.

cs.CR↗

arXiv2023

SPDH-Sign: towards Efficient, Post-quantum Group-based Signatures

In this paper, we present a new diverse class of post-quantum group-based Digital Signature Schemes (DSS). The approach is significantly different from previous examples of group-based digital signatures and adopts the framework of group action-based cryptography: we show that each finite group defines a group action relative to the semidirect product of the group by its automorphism group, and give security bounds on the resulting signature scheme in terms of the group-theoretic computational problem known as the Semidirect Discrete Logarithm Problem (SDLP). Crucially, we make progress towards being able to efficiently compute the novel group action, and give an example of a parameterised family of groups for which the group action can be computed for any parameters, thereby negating the need for expensive offline computation or inclusion of redundancy required in other schemes of this type.

cs.CR↗

arXiv2022

A Subexponential Quantum Algorithm for the Semidirect Discrete Logarithm Problem

Group-based cryptography is a relatively unexplored family in post-quantum cryptography, and the so-called Semidirect Discrete Logarithm Problem (SDLP) is one of its most central problems. However, the complexity of SDLP and its relationship to more well-known hardness problems, particularly with respect to its security against quantum adversaries, has not been well understood and was a significant open problem for researchers in this area. In this paper we give the first dedicated security analysis of SDLP. In particular, we provide a connection between SDLP and group actions, a context in which quantum subexponential algorithms are known to apply. We are therefore able to construct a subexponential quantum algorithm for solving SDLP, thereby classifying the complexity of SDLP and its relation to known computational problems.

cs.CR↗

arXiv2022

Post-quantum hash functions using $\mathrm{SL}_n(\mathbb{F}_p)$

We define new families of Tillich-Z\'emor hash functions, using higher dimensional special linear groups over finite fields as platforms. The Cayley graphs of these groups combine fast mixing properties and high girth, which together give rise to good preimage and collision resistance of the corresponding hash functions. We justify the claim that the resulting hash functions are post-quantum secure.

cs.CR↗

arXiv2022

Semidirect Product Key Exchange: the State of Play

Of the many families of cryptographic schemes proposed to be post-quantum, a relatively unexplored set of examples comes from group-based cryptography. One of the more central schemes from this area is the so-called Semidirect Product Key Exchange (SDPKE), a generalisation of Diffie-Hellman Key Exchange that is plausibly post-quantum. In this report we survey the state of the literature relating to SDPKE, providing a high-level discussion of security, as well as a comprehensive overview of the proposed platforms and the main cryptanalytic ideas relevant to each.

cs.CR↗

arXiv2021

On the efficiency of a general attack against the MOBS cryptosystem

All instances of the semidirect key exchange protocol, a generalisation of the famous Diffie-Hellman key exchange protocol, satisfy the so-called "telescoping equality"; in some cases, this equality has been used to construct an attack. In this report we present computational evidence suggesting that an instance of the scheme called `MOBS' is an example of a scheme where the telescoping equality has too many solutions to be a practically viable means to conduct an attack.

cs.CR↗

arXiv2021

Cryptanalysis of Semidirect Product Key Exchange Using Matrices Over Non-Commutative Rings

It was recently demonstrated that the Matrix Action Key Exchange (MAKE) algorithm, a new type of key exchange protocol using the semidirect product of matrix groups, is vulnerable to a linear algebraic attack if the matrices are over a commutative ring. In this note, we establish conditions under which protocols using matrices over a non-commutative ring are also vulnerable to this attack. We then demonstrate that group rings $R[G]$ are examples of non-commutative rings that satisfy these conditions.

cs.CR↗