Related papers: A new multivariate primitive from CCZ equivalence
New cryptographic techniques such as homomorphic encryption (HE) allow computations to be outsourced to and evaluated blindfolded in a resourceful cloud. These computations often require private data owned by multiple participants, engaging…
Quantum homomorphic encryption (QHE) is an encryption method that allows quantum computation to be performed on one party's private data with the program provided by another party, without revealing much information about the data nor about…
Fully Homomorphic Encryption (FHE) emerges one of the most promising solutions to privacy-preserving computing in an untrusted cloud. FHE can be implemented by various schemes, each of which has distinctive advantages, i.e., some are good…
Voting is a primary democratic activity through which voters select representatives or approve policies. Conventional paper ballot elections have several drawbacks that might compromise the fairness, effectiveness, and accessibility of the…
We study the interaction between two structures on the group of polynomial automorphisms of the affine plane: its structure as an amalgamated free product and as an infinite-dimensional algebraic variety. We introduce a new conjecture, and…
A cryptographic algorithm is proposed based on fully quantum mechanical keys and ciphers. Encryption and decryption are carried out via an appropriate measurement process on entangled states as governed by a quantum mechanical, asymmetrical…
A filtration of a representation whose successive quotients are isomorphic to Demazure modules is called an excellent filtration. In this paper we study graded multiplicities in excellent filtrations of fusion products for the current…
In this paper we introduce a multistep generalization of the guess-and-determine or hybrid strategy for solving a system of multivariate polynomial equations over a finite field. In particular, we propose performing the exhaustive…
In this paper homomorphic cryptosystems are designed for the first time over any finite group. Applying Barrington's construction we produce for any boolean circuit of the logarithmic depth its encrypted simulation of a polynomial size over…
Formal multiple zeta values allow to study multiple zeta values by algebraic methods in a way that the open question about their transcendence is circumvented. In this note we show that Hoffman's basis conjecture for formal multiple zeta…
The work offers a new approach to the formation of functions which are used in cryptography and cryptanalysis. It will use alternative forms of representation of Boolean functions, that is, those which are different from the classical form,…
So far, the pseudo cross-variogram is primarily used as a tool for the structural analysis of multivariate random fields. Mainly applying recent theoretical results on the pseudo cross-variogram, we use it as a cornerstone in the…
We propose a new approach in cryptanalysis based on an evolution of the concept of \textit{Combinatorial Equivalence}. The aim is to rewrite a cryptosystem under a combinatorially equivalent form in order to make appear new properties that…
Post-Quantum Cryptography (PQC) attempts to find cryptographic protocols resistant to attacks using Shor polynomial time algorithm for numerical field problems or Grover search algorithm. A mostly overlooked but valuable line of solutions…
This article describes a post-quantum multirecipient symmetric cryptosystem whose security is based on the hardness of the LWE problem. In this scheme a single sender encrypts multiple messages for multiple recipients generating a single…
A conjugate code pair is defined as a pair of linear codes either of which contains the dual of the other. A conjugate code pair represents the essential structure of the corresponding Calderbank-Shor-Steane (CSS) quantum error-correcting…
A cluster algebra is a commutative algebra whose structure is decided by a skew-symmetrizable matrix or a quiver. When a skew-symmetrizable matrix is invariant under an action of a finite group and this action is admissible, the folded…
This paper presents a new technique for disturbing the algebraic structure of linear codes in code-based cryptography. This is a new attempt to exploit Gabidulin codes in the McEliece setting and almost all the previous cryptosystems of…
Current asymmetric cryptography is based on the principle that while classical computers can efficiently multiply large integers, the inverse operation, factorization, is significantly more complex. For sufficiently large integers, this…
We apply quantum homomorphic encryption (QHE) schemes suitable for circuits with a polynomial number of $T/T^{\dagger}$-gates to Grover's algorithm, performing a simulation in Qiskit of a Grover circuit that contains 3 qubits. The…