
Secure sending of messages over the mesh network based on bluetooth
... confidentiality of communication between the nodes of mesh networks based on smartphones. We describe the important details of Bluetooth and Bluetooth Low Energy technologies, using which you can solve some of the problems described. Next, we briefly describe elliptic curve cryptography and choose a specific curve for it. We build an Elliptic Curve Integrated Encryption Scheme based on the elliptic curves key exchange and various crypto primitives that allows exchanging protected information using symmetric encryption....

An analysis of the resistance of McEliece CS based on an AGcode to quantum Fourier sampling attack
This article tests the quantum resistance of McEliece CS based on an AGcode over any elliptic curve. Using the criteria suggested by Dinh, Moore, and Russell [3], the author proves the resistance of this CS to quantum Fourier sampling attack. Thus, Shor’s algorithm cannot identify the group structure of the code and break the CS.
1. Shor P....

On the optimal passing of distinguished points for parallelized Pollard’s rhomethod
Problems of development and realization of an efficient parallelized algorithm to solve elliptic curve discrete logarithm problem (ECDLP) based on Pollard’s rhomethod in the computational model SPMD using technology of message passing are considered. It is researched how many central processes are needed and what proportion of distinguished points ...

Development and Research of Properties of Mail Exchange Protocols Inside a Hybrid Cloud with Two ReEncryption Based on Hess Pairing
In this article we describe Hess pairing on elliptic curves and create its computational algorithm. Main purpose of this article is creation and properties overview of mailexchange protocol inside hybrid cloud with two reencryptions, based on this pairing. Also, we describe an authentification algorithm,...

Efficient algorithms for computing superelliptic curves
Represents basics algorithms of arithmetics superelliptic curves and optimal parameters superelliptic curve suitable for cryptography.
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2. ANSI X9.63 Public Key Cryptography for the Financial Services Industry: Elliptic Curve Key Agreement and Key Transport Schemes. Working Draft  Version 2.0. 1998....

Analysis of Algorithms for Computing in Jacobian of a Picard Curve
... Jacobians of Picard Curves // Public Key Cryptography — PKC 2004. 2004. P. 55—68.
4. Oyono R. Arithmetik nichthyperelliptischer Kurven des Geschlechts 3 und ihre Anwendung in der Kryptographie : PhD Diss. Univ. DuisburgEssen, 2005.
5. Handbook of Elliptic and Hyperelliptic Curve Cryptography / ed. H. Cohen, G. Frey. Chapman & Hall, 2006
6. Sutherland A. V. Fast Jacobian Arithmetic for Hyperelliptic Curves of Genus 3 //
ANTS XIII. 2019. P. 425—442.
7. Thakur S. Abelian varieties in pairingbased cryptography. 2019. aXiv:1812....

Acceleration of Computations in Jacobian Hyperelliptic Curve
... 155—172.
9. Koblitz N., Menezes A. Pairingbased Cryptography at High Security Levels // Cryptography and Coding. LNCS 3796. Springer, 2005. Р. 235—249.
10. Teruya T., Saito K., Kanayama N. et al. Constructing Symmetric Pairings over Supersingular Elliptic Curves with Embedding Degree Three // LNCS 8365. Springer, 2014. P. 97—112.
11. Granger R., Hess F. Ate Pairing on Hyperelliptic Curves // Advance in Cryptology. LNCS 4515. Springer, 2007. P. 430—447.
12. Zhang F. Twisted Ate Pairing on Hyperelliptic ...

About generations of curves of genus 2 of prank 1 over finite fields
Explicit methods of ge nerations of curves of genus 2 of prank 1 over finite fields are produced.
1. O’Connor L. H., McGuire G., Naehrig M. et al. A CM construction for curves of genus 2 with prank 1 // Journal of Number Theory (special edition on Elliptic Curve Cryptography). 2011. Vol. 131. P. 920—935.
2. Serre J. P. Sur la topologie des variete algebraiques en characteristic p // Sympos. Internac. Topologia algebraica, Mexico, 1956
3. Манин Ю. И. О матрице Хассе — Витта ...

About one algorithm of calculation of inverses in finite fields
... finite field qn F developed, where q is power of the prime number. They are received by generalisation of algorithm of Wong for a field F2n with use of the main idea for fast algorithm of calculation of inverses in the field 2 F n .
1. Handbook of elliptic and hyperelliptic curve cryptography / Scientific editors, Henry Cohen & Gerhard Frey. Chapman & Hall/CRC, 2006.
2. Handbook of finite Fields / Scientific editors, Gary L. Mullen, Daniel Panario. CRC Press, Taylor & Francis Group, 2013.
3. Itoh T., Tsujii S. A fast algorithm ...

Scalable zkSNARK
... size of the proving key depends at least linearly on the upper bound of the structure in which we work. Second, the proof requires a record of all previous steps. The article describes an algorithm for achieving a new implementation of zkSNARK using elliptic curve cryptography, field structure features, and proof integrity. In practice, this implementation is a recursive composition of the proof, while generating keys for any size of calculations carries constant memory costs. Subsequently, the entire ...