Related papers: Categorical composable cryptography
The disastrous vulnerabilities in smart contracts sharply remind us of our ignorance: we do not know how to write code that is secure in composition with malicious code. Information flow control has long been proposed as a way to achieve…
We introduce string diagrams for graded symmetric monoidal categories. Our approach includes a definition of graded monoidal theory and the corresponding freely generated syntactic category. Also, we show how an axiomatic presentation for…
Compact categories have lately seen renewed interest via applications to quantum physics. Being essentially finite-dimensional, they cannot accomodate (co)limit-based constructions. For example, they cannot capture protocols such as quantum…
These notes offer a lightening introduction to topological quantum field theory in its functorial axiomatisation, assuming no or little prior exposure. We lay some emphasis on the connection between the path integral motivation and the…
We provide a construction for holes into which morphisms of abstract symmetric monoidal categories can be inserted, termed the polyslot construction pslot[C], and identify a sub-class srep[C] of polyslots that are single-party…
Notions of guardedness serve to delineate the admissibility of cycles, e.g. in recursion, corecursion, iteration, or tracing. We introduce an abstract notion of guardedness structure on a symmetric monoidal category, along with a…
The present work builds on previous investigations of the authors (and their collaborators) regarding bridges, a certain type of morphisms between encryption schemes, making a step forward in developing a (category theory) language for…
It is of folkloric belief that the security of classical cryptographic protocols is automatically broken if the Adversary is allowed to perform superposition queries and the honest players forced to perform actions coherently on quantum…
Automatic security protocol analysis is currently feasible only for small protocols. Since larger protocols quite often are composed of many small protocols, compositional analysis is an attractive, but non-trivial approach. We have…
By resorting to basic features of topological knot theory we propose a (classical) cryptographic protocol based on the `difficulty' of decomposing complex knots generated as connected sums of prime knots and their mutants. The scheme…
Categorical probability has recently seen significant advances through the formalism of Markov categories, within which several classical theorems have been proven in entirely abstract categorical terms. Closely related to Markov categories…
A significant branch of classical cryptography deals with the problems which arise when mistrustful parties need to generate, process or exchange information. As Kilian showed a while ago, mistrustful classical cryptography can be founded…
We propose a new symmetric cryptographic scheme based on functional invariants defined over discrete oscillatory functions with hidden parameters. The scheme encodes a secret integer through a four-point algebraic identity preserved under…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
There are two ways to describe the interaction between classical and quantum information categorically: one based on completely positive maps between Frobenius algebras, the other using symmetric monoidal 2-categories. This paper makes a…
An `obfuscation' for encrypted computing is quantified exactly here, leading to an argument that security against polynomial-time attacks has been achieved for user data via the deliberately `chaotic' compilation required for security…
The primary contribution of this paper is to give a formal, categorical treatment to Penrose's abstract tensor notation, in the context of traced symmetric monoidal categories. To do so, we introduce a typed, sum-free version of an abstract…
Measurement-device-independent quantum key distribution protocol, whose security analysis does not rely on any assumption on the detection system, can immune the attacking against detectors. We give a first composable security analysis for…
Milner's bigraphs are a general framework for reasoning about distributed and concurrent programming languages. Notably, it has been designed to encompass both the pi-calculus and the Ambient calculus. This paper is only concerned with…
The unconditional security of a quantum key distribution protocol is often defined in terms of the accessible information, that is, the maximum mutual information between the distributed key S and the outcome of an optimal measurement on…