相关论文: Studies in Cryptological Combinatorics

Motivated by a desire to test the security of the pubic key exchange protocol of I. Anshel, M. Anshel, and D. Goldfeld, (``An Algebraic Method for Public-Key Cryptography'', Mathematical Research Letters, vol. 6, pp. 1-5, 1999), we study…

We introduce explicit schemes based on the polarization phenomenon for the tasks of one-way secret key agreement from common randomness and private channel coding. For the former task, we show how to use common randomness and insecure…

A secret key shared through quantum key distribution between two cooperative players is secure against any eavesdropping attack allowed by the laws of physics. Yet, such a key can be established only when the quantum channel error rate due…

In a recent work (Ghazi et al., SODA 2016), the authors with Komargodski and Kothari initiated the study of communication with contextual uncertainty, a setup aiming to understand how efficient communication is possible when the…

We consider a pair-wise independent network where every pair of terminals in the network observes a common pair-wise source that is independent of all the sources accessible to the other pairs. We propose a method for secret key agreement…

This paper investigates a reconciliation method in order to establish an errorless secret key in a QKD protocol. Classical key distribution protocols are no longer unconditionally secure because computational complexity of mathematical…

We study the role of interaction in the Common Randomness Generation (CRG) and Secret Key Generation (SKG) problems. In the CRG problem, two players, Alice and Bob, respectively get samples $X_1,X_2,\dots$ and $Y_1,Y_2,\dots$ with the pairs…

In a random key graph (RKG) of $n$ nodes each node is randomly assigned a key ring of $K_n$ cryptographic keys from a pool of $P_n$ keys. Two nodes can communicate directly if they have at least one common key in their key rings. We assume…

Secret sharing schemes based on the idea of hidden multipliers in encryption are proposed. As a platform, one can use both multiplicative groups of finite fields and groups of invertible elements of commutative rings, in particular,…

Quantum key distribution (QKD) allows for communication with security guaranteed by quantum theory. The main theoretical problem in QKD is to calculate the secret key rate for a given protocol. Analytical formulas are known for protocols…

We prove that the equivalence of two fundamental problems in the theory of computing. For every polynomial $t(n)\geq (1+\varepsilon)n, \varepsilon>0$, the following are equivalent: - One-way functions exists (which in turn is equivalent to…

We propose a symmetric key homomorphic encryption scheme based on the evaluation of multivariate polynomials over a finite field. The proposed scheme is somewhat homomorphic with respect to addition and multiplication. Further, we define a…

Quantum key distribution (QKD) allows Alice and Bob to share a secret key over an insecure channel with proven information-theoretic security against an adversary whose strategy is bounded only by the laws of physics. Composability-based…

In key agreement protocols, the user will send a request to the server and the server will respond to that message. After two-way authentication, a secure session key will be created between them. They use the session key to create a secure…

Classical correlation can be locked via quantum means--quantum data locking. With a short secret key, one can lock an exponentially large amount of information, in order to make it inaccessible to unauthorized users without the key. Quantum…

Akiyama et al. (Int. J. Math. Indust., 2019) proposed a post-quantum key exchange protocol that is based on the hardness of solving a system of multivariate non-linear polynomial equations but has a design strategy different from ordinary…

The subset cover problem for $k \geq 1$ hash functions, which can be seen as an extension of the collision problem, was introduced in 2002 by Reyzin and Reyzin to analyse the security of their hash-function based signature scheme HORS. The…

In 1976, Whitfield Diffie and Martin Hellman introduced the public key cryptography or asymmetric cryptography standards. Two years later, an asymmetric cryptosystem was published by Ralph Merkle and Martin Hellman called MH, based on a…

Bogopolski, Martino and Ventura in [BMV10] introduced a general criteria to construct groups extensions with unsolvable conjugacy problem using short exact sequences. We prove that such extensions have always solvable word problem. This…

Recently, Aaronson et al. (arXiv:2009.07450) showed that detecting interference between two orthogonal states is as hard as swapping these states. While their original motivation was from quantum gravity, we show its applications in quantum…