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....
On the optimal passing of distinguished points for parallelized Pollard’s rho-method
Problems of development and realization of an efficient parallelized algorithm to solve elliptic curve discrete logarithm problem (ECDLP) based on Pollard’s rho-method 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 Re-Encryption 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 mail-exchange protocol inside hybrid cloud with two re-encryptions, based on this pairing. Also, we describe an authentification algorithm,...
An analysis of the resistance of McEliece CS based on an AG-code to quantum Fourier sampling attack
This article tests the quantum resistance of McEliece CS based on an AG-code 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....
Acceleration of Computations in Jacobian Hyperelliptic Curve
... 155—172.
9. Koblitz N., Menezes A. Pairing-based 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 ...
Efficient algorithms for computing superelliptic curves
Represents basics algorithms of arithmetics superelliptic curves and optimal parameters superelliptic curve suitable for cryptography.
1.Koblitz N. Elliptic curve cryptosystems // Mathematics of Computation. 1987. № 48 (177). P. 203–209.
2. ANSI X9.63 Public Key Cryptography for the Financial Services Industry: El-liptic Curve Key Agreement and Key Transport Schemes. Working Draft - Ver-sion 2.0. 1998....