Categorical composable cryptography

Abstract

We formalize the simulation paradigm of cryptography in terms of category theory and show that protocols secure against abstract attacks form a symmetric monoidal category, thus giving an abstract model of composable security definitions in cryptography. Our model is able to incorporate computational security, set-up assumptions and various attack models such as colluding or independently acting subsets of adversaries in a modular, flexible fashion. We conclude by using string diagrams to rederive the security of the one-time pad and no-go results concerning the limits of bipartite and tripartite cryptography, ruling out e.g., composable commitments and broadcasting.

Quantum Oblivious Transfer: A Short Review

“…However, most of the discord has ended with Ariano et al proof [ 60 ] in 2007, giving an impossibility proof covering all conceivable protocols based on classical and quantum information theory. Subsequent work digested Ariano et al [ 60 ] work, trying to present more succinct proofs [ 61 , 62 , 63 ] and to translate it into categorical quantum mechanics language [ 64 , 65 , 66 ].…”

“…Maurer and Renner [ 102 ] developed a more general composability framework that does not depend on the models of computation, communication, and adversary behaviour. More recently, Broadbent and Karvonen [ 66 ] created an abstract model of composable security in terms of category theory. Up until now, and to the best of our knowledge, the composable security of the protocol was only proven in the Fehr and Schaffner model [ 79 ] by Damgård et al [ 9 ] and in the quantum-UC by Unruh [ 86 ].…”

Quantum oblivious transfer: a short review

“…However, most of the discord has ended with Ariano et al proof [DKSW07] in 2007, giving an impossibility proof covering all conceivable protocols based on classical and quantum information theory. Subsequent work digested Ariano et al [DKSW07] work, trying to present more succinct proofs [CDP10, CDP + 13, He13] and to translate it into categorical quantum mechanics language [CG12, SHW20,BK22].…”

Quantum Oblivious Transfer: a Short Review

“…However, most of the discord has ended with Ariano's et al proof [55] in 2007, giving an impossibility proof covering all conceivable protocols based on classical and quantum information theory. Subsequent work digested Ariano et al [55] work, trying to present more succinct proofs [56][57][58] and to translate it into categorical quantum mechanics language [59][60][61].…”

“…In the literature there have been some proposals for such a framework. In summary, Fehr and Schaffner [74] developed a composability framework that allows sequential composition of quantum protocols in a classical environment; the works developed by Ben-Or and Mayers [95] and Unruh [81,96] extended the classical Universal Composability model [97] to a quantum setting (quantum-UC model) which, allowing concurrent composability; Maurer and Renner [98] developed a more general composability framework which does not depend on the models of computation, communication, and adversary behavior; and, more recently, Broadbent and Karvonen [61] created an abstract model of composable security definitions in terms of category theory. Up until now, and to the best of our knowledge, the composable security of the protocol Π BBCS F com was only proven in the Fehr and Schaffner model [74] by Damgård et al [9] and in the quantum-UC by Unruh [81].…”