Related papers: A New Cryptosystem Based On Hidden Order Groups

In classical cryptography, one-way functions (OWFs) are the minimal assumption, while it is not the case in quantum cryptography. Several new primitives have been introduced such as pseudorandom state generators (PRSGs), one-way state…

In this paper, a new key-agreement scheme is proposed and analyzed. In addition to being provably secure in shared secret key indistinguishability model, the scheme has an interesting feature: while using exponentiation over a cyclic…

This paper presents a new efficient protocol for k-out-of-n oblivious transfer which is a generalization of Parakh's 1-out-of-2 oblivious transfer protocol based on Diffie-Hellman key exchange. In the proposed protocol, the parties involved…

We revisit the problem of designing scalable protocols for private statistics and private federated learning when each device holds its private data. Locally differentially private algorithms require little trust but are (provably) limited…

The square root modulo problem is a known primitive in designing an asymmetric cryptosystem. It was first attempted by Rabin. Decryption failure of the Rabin cryptosystem caused by the 4-to-1 decryption output is overcome efficiently in…

In 1998, Blaze, Bleumer, and Strauss suggested a cryptographic primitive named proxy re-signatures where a proxy turns a signature computed under Alice's secret key into one from Bob on the same message. The semi-trusted proxy does not…

We give an algorithm to solve the quantum hidden subgroup problem for maximal cyclic non-normal subgroups of the affine group of a finite field (if the field has order $q$ then the group has order $q(q-1)$) with probability $1-\varepsilon$…

In quantum cryptography, there could be a new world, Microcrypt, where cryptography is possible but one-way functions (OWFs) do not exist. Although many fundamental primitives and useful applications have been found in Microcrypt, they lack…

We consider actions of a group or a semigroup on a set, which generalize the setup of discrete logarithm based cryptosystems. Such cryptographic group actions have gained increasing attention recently in the context of isogeny-based…

In discrete logarithm based cryptography, a method by Pohlig and Hellman allows solving the discrete logarithm problem efficiently if the group order is known and has no large prime factors. The consequence is that such groups are avoided.…

Difficulty of calculation of discrete logarithm for any arbitrary Field is the basis for security of several popular cryptographic solutions. Pohlig-Hellman method is a popular choice to calculate discrete logarithm in finite field $F_p^*$.…

The discrete logarithm is a problem that surfaces frequently in the field of cryptography as a result of using the transformation g^a mod n. This paper focuses on a prime modulus, p, for which it is shown that the basic structure of the…

When working with joint collections of confidential data from multiple sources, e.g., in cloud-based multi-party computation scenarios, the ownership relation between data providers and their inputs itself is confidential information.…

The quantum Fourier transform (QFT) has emerged as the primary tool in quantum algorithms which achieve exponential advantage over classical computation and lies at the heart of the solution to the abelian hidden subgroup problem, of which…

The semidirect discrete logarithm problem (SDLP) is the following analogue of the standard discrete logarithm problem in the semidirect product semigroup $G\rtimes \mathrm{End}(G)$ for a finite semigroup $G$. Given $g\in G, \sigma\in…

Fully homomorphic encryption (FHE) enables an entity to perform arbitrary computation on encrypted data without decrypting the ciphertexts. An ongoing group-theoretical approach to construct an FHE scheme uses a certain "compression"…

This paper introduces a newly developed private key cryptosystem and a public key cryptosystem. In the first one, each letter is encrypted with a different key. Therefore, it is a kind of a one-time pad. The second one is inspired by the…

We investigate security properties of the Anshel-Anshel-Goldfeld commutator key-establishment protocol used with certain polycyclic groups. We show that despite low success of the length based attack the protocol can be broken by a…

We provide a survey on the Hidden Subgroup Problem (HSP), which plays an important role in studying the security of public-key cryptosystems. We first review the abelian case, where Kitaev's algorithm yields an efficient quantum solution to…

Encryption schemes often derive their power from the properties of the underlying algebra on the symbols used. Inspired by group theoretic tools, we use the centralizer of a subgroup of operations to present a private-key quantum…