Related papers: Aperiodic logarithmic signatures
S. S. Magliveras et al. have described symmetric and public key cryptosystems based on logarithmic signatures (also known as group bases) for finite permutation groups. In this paper we show that if $G$ is a nontrivial finite group which is…
On the basis of the signatures scheme without trapdoors from lattice, which is proposed by Vadim Lyubashevsky in 2012, we present a new ring signature scheme from lattice. The proposed ring signature scheme is an extension of the signatures…
Biggs proposed the sandpile group of certain modified wheel graphs for cryptosystems relying on the difficulty of the discrete logarithm problem. Blackburn and independently Shokrieh showed that the discrete logarithm problem is efficiently…
We establish that the sequences formed by logarithms and by "fractional" powers of integers, as well as the sequence of prime numbers, are non-holonomic, thereby answering three open problems of Gerhold [Electronic Journal of Combinatorics…
We design the first efficient polynomial identity testing algorithms over the nonassociative polynomial algebra. In particular, multiplication among the formal variables is commutative but it is not associative. This complements the strong…
In this paper, we explain a procedure based on a classical result of Sturm that can be used to determine rigorously whether a given trigonometric polynomial is nonnegative in a certain interval or not. Many examples are given. This…
We prove a structural result for measure preserving systems naturally associated with any finite collection of multiplicative functions that take values on the complex unit disc. We show that these systems have no irrational spectrum and…
We describe an algorithm for the factorization of non-commutative polynomials over a field. The first sketch of this algorithm appeared in an unpublished manuscript (literally hand written notes) by James H. Davenport more than 20 years…
Post-Quantum Cryptography PQC attempts to find cryptographic protocols resistant to attacks using Shors polynomial time algorithm for numerical field problems or Grovers algorithm to find the unique input to a black-box function that…
This article presents an encryption scheme based on the small Ree groups. We propose utilizing the small Ree group structure to enhance the overall security parameters of the encryption scheme. By extending the logarithmic signature to…
The strong factorization conjecture states that a proper birational map between smooth algebraic varieties over a field of characteristic zero can be factored as a sequence of smooth blowups followed by a sequence of smooth blowdowns. We…
The notion of aggregate signature has been motivated by applications and it enables any user to compress different signatures signed by different signers on different messages into a short signature. Sequential aggregate signature, in turn,…
We investigate S^3/Z_n partition function of 3d N = 2 supersymmetric field theories. In a gauge theory the partition function is the sum of the contributions of sectors specified by holonomies, and we should carefully choose the relative…
This paper proposes uni-orthogonal and bi-orthogonal nonnegative matrix factorization algorithms with robust convergence proofs. We design the algorithms based on the work of Lee and Seung [1], and derive the converged versions by utilizing…
Linear (or differential) cryptanalysis may seem dull topics for a mathematician: they are about super simple invariants characterized by say a word on n=64 bits with very few bits at 1, the space of possible attacks is small, and basic…
We survey three methods for proving that the characteristic polynomial of a finite lattice factors over the nonnegative integers and indicate how they have evolved recently. The first technique uses geometric ideas and is based on…
This work revisits the security of classical signatures and ring signatures in a quantum world. For (ordinary) signatures, we focus on the arguably preferable security notion of blind-unforgeability recently proposed by Alagic et al.…
In an earlier article [3], we presented an algorithm that can be used to rigorously check whether a specific cosine or sine polynomial is nonnegative in a given interval or not. The algorithm proves to be an indispensable tool in…
We provide a recursive classification of meander graphs, showing that each meander is identified by a unique sequence of fundamental graph-theoretic moves. This sequence is called the meander's signature. The signature not only provides a…
We present a new algorithm to decompose generic spinor polynomials into linear factors. Spinor polynomials are certain polynomials with coefficients in the geometric algebra of dimension three that parametrize rational conformal motions.…