Related papers: A note on conjugacy search and racks
The secure instantiation of the random oracle is one of the major open problems in modern cryptography. We investigate this problem using concepts and methods of algorithmic randomness. In modern cryptography, the random oracle model is…
A quantum algorithm for general combinatorial search that uses the underlying structure of the search space to increase the probability of finding a solution is presented. This algorithm shows how coherent quantum systems can be matched to…
Quantum Key Exchange (QKE, also known as Quantum Key Distribution or QKD) allows communicating parties to securely establish cryptographic keys. It is a well-established fact that all QKE protocols require that the parties have access to an…
Recursive coalgebras provide an elegant categorical tool for modelling recursive algorithms and analysing their termination and correctness. By considering coalgebras over categories of suitably indexed families, the correctness of the…
In the not so unlikely scenario of total compromise of computers accessible to a group of users, they might be tempted to resort to human-computable paper-and-pencil cryptographic methods aided by a classic Tabula Recta, which helps to…
We discuss quantum key distribution protocols using quantum continuous variables. We show that such protocols can be made secure against individual gaussian attacks regardless the transmission of the optical line between Alice and Bob. This…
Retrieval Augmented Generation (RAG) systems deployed across organizational boundaries face fundamental tensions between security, accuracy, and efficiency. Current encryption methods expose plaintext during decryption, while federated…
In this note, we describe a probabilistic attack on public key cryptosystems based on the word/conjugacy problems for finitely presented groups of the type proposed recently by Anshel, Anshel and Goldfeld. In such a scheme, one makes use of…
Recently, position-based quantum cryptography has been claimed to be unconditionally secure. In contrary, here we show that the existing proposals for position-based quantum cryptography are, in fact, insecure if entanglement is shared…
The cycling operation endows the super summit set $S_x$ of any element $x$ of a Garside group $G$ with the structure of a directed graph $\Gamma_x$. We establish that the subset $U_x$ of $S_x$ consisting of the circuits of $\Gamma_x$ can be…
This paper studies how to use relation algebras, which are useful for high-level specification and verification, for proving the correctness of lower-level array-based implementations of algorithms. We give a simple relation-algebraic…
The verification of security protocols is essential, in order to ensure the absence of potential attacks. However, verification results are only valid with respect to the assumptions under which the verification was performed. These…
We prove that Ad-semisimple conjugacy classes in a connected Lie group $G$ are closed embedded submanifolds of $G$. We also prove that if $\alpha:H\to G$ is a homomorphism of connected Lie groups such that the kernel of $\alpha$ is discrete…
This paper presents applications of the trope of the locked and sealed piggy-bank into which the secret can be easily inserted but from which it cannot be withdrawn without opening the box. We present a basic two-pass cryptographic scheme…
Though not yet widely deployed, password-authenticated key exchange (PAKE) protocols have been the subject of several recent standardization efforts, partly because of their resistance against various guessing attacks, but also because they…
The partial oracles framework is a quantum search algorithm that has the potential to exceed the quadratic speedup of Grover's algorithm, up to a theoretical maximum of an exponential speedup. Until now, however, the framework has lacked an…
The breakthrough of achieving fully homomorphic encryption sparked enormous studies on where and how to apply homomorphic encryption schemes so that operations can be performed on encrypted data without the secret key while still obtaining…
Recently, Lu et al. have proposed two image search schemes based on additive homomorphic encryption [IEEE Access, 2 (2014), 125-141]. We remark that both two schemes are flawed because: (1) the first scheme does not make use of the additive…
We propose an authentication scheme where forgery (a.k.a. impersonation) seems infeasible without finding the prover's long-term private key. The latter would follow from solving the conjugacy search problem in the platform (noncommutative)…
Based on our previous work on truly concurrent process algebras APTC, we use it to verify the security protocols. This work (called Secure APTC, abbreviated SAPTC) have the following advantages in verifying security protocols: (1) It has a…