Bit Coincidence Mining Algorithm

Here, we propose new algorithm for solving ECDLP named Bit Coincidence Mining Algorithm! , from which ECDLP is reduced to solving some quadratic equations system. In this algorithm, ECDLP of an elliptic curve $E$ defined over \bF_q ($q$ is prime or power of primes) reduces to solving quadratic equations system of $d-1$ variables and $d+C_0-1$ equations where $C_0$ is small natural number and $d \sim C_0 \, \log_2 q$. This equations system is too large and it can not be solved by computer. However, we can show theoritically the cost for solving this equations system by xL algorithm is subexponential under the reasonable assumption of xL algorithm

Bit Coincidence Mining Algorithm II

In 2012, Petit et al. shows that under the algebraic geometrical assumption named First Fall degree Assumption , the complexity of ECDLP over binary extension field ${\bf F}_{2^n}$ is in $O(exp(n^{2/3+o(1)}))$ where $\lim_{n \to \infty} o(1)=0$ and there are many generalizations and improvements for the complexity of ECDLP under this assumption. In 2015, the author proposes the bit coincidence mining algorithm, which states that under the heuristic assumption of the complexity of xL algorithm, the complexity of ECDLP $E/{\bf F}_q$ over arbitrary finite field including prime field, is in $O(exp(n^{1/2+o(1)}))$ where $n \sim \log_2 \#E({\bf F}_q) \sim \log_2 q$. It is the first (heuristic) algorithm for solving ECDLP over prime field in subexponential complexity. In both researches, ECDLP reduces to solving large equations system and from each assumption, the complexity for solving reduced equations system is subexponential (or polynomial) complexity. However, the obtained equations system is too large for solving in practical time and space, they are only the results for the complexity. xL algorithm, is the algorithm for solving quadratic equations system, which consists of $n$ variables and $m$ equations. Here, $n$ and $m$ are considered as parameters. Put $D=D(n,m)$ by the maximal degree of the polynomials, which appears in the computation of solving equations system by xL. Courtois et al. observe and assume the following assumption; 1) There are small integer $C_0$, such that $D(n,n+C_0)$ is usually in $O(\sqrt{n})$, and the cost for solving equations system is in $O(exp(n^{1/2+0(1)}))$. However, this observation is optimistic and it must have the following assumption 2) The equations system have small number of the solutions over algebraic closure. (In this draft we assume the number of the solutions is 0 or 1) In the previous version\u27s bit coincidence mining algorithm (in 2015), the number of the solutions of the desired equations system over algebraic closure is small and it can be probabilistically controlled to be 1 and the assumption 2) is indirectly true. For my sense, the reason that xL algorithm, which is the beautiful heuristic, is not widely used is that the general equations system over finite field does not satisfy the assumption 2) (there are many solutions over algebraic closure) and is complexity is much larger. In the previous draft, I show that the ECDLP of $E({\bf F}_q)$ reduces to solving equations system consists of $d-1$ variables and $d+C_0-1$ equations where $C_0$ is an arbitrary positive integer and $d \sim C_0 \times \log_2 q$. So, the complexity for solving ECDLP is in subexponential under the following assumption a) There are some positive integer $C_0$ independent from $n$, such that solving quadratic equations system consists of $n$ variables and $m=n+C_0$ equations (and we must assume the assumption 2)) by xL algorithm, the maximum degree of the polynomials $D=D(n,m)$, appears in this routine is in $O(\sqrt{n})$ in high probability. Here, we propose the new algorithm that ECDLP of $E({\bf F}_q)$ is essentially reducing to solving equations system consists of $d-1$ variables and $\frac{b_0}{2}d$ equations where $b_0(\ge 2)$ is an arbitrary positive integer named block size and $d \sim (b_0-1)\log_{b_0} q$. Here, we mainly treat the case block size $b_0=3$. In this case, ECDLP is essentially reducing to solving equations system consists of about $2 \log_3 q$ variables and $3 \log_3 q$ equations. So that the desired assumption 1) is always true. Moreover, the number of the solutions (over algebraic closure) of this equations system can be probabilistically controlled to be 1 and the desired assumption 2) is also true. In the former part of this manuscript, the author states the algorithm for the construction of equations system that ECDLP is reduced and in the latter part of this manuscript, the author state the ideas and devices in order for increasing the number of the equations, which means the obtained equations system is easily solved by xL algorithm

Research progress on coal mine laser methane sensor

This paper discusses the research progress of low-power technology of laser methane sensors for coal mine. On the basis of environment of coal mines, such as ultra-long-distance transmission and high stability, a series of studies have been carried out. The preliminary results have been achieved in the research of low power consumption, temperature and pressure compensation and reliability design. The technology is applied to various products in coal mines, and achieves high stability and high reliability in products such as laser methane sensor, laser methane detection alarm device, wireless laser methane detection alarm device, and optic fiber multichannel laser methane sensor. Experimental testing and analysis of the characteristics of laser methane sensors, combined with the actual application

Quantum Optical Systems for the Implementation of Quantum Information Processing

We review the field of Quantum Optical Information from elementary considerations through to quantum computation schemes. We illustrate our discussion with descriptions of experimental demonstrations of key communication and processing tasks from the last decade and also look forward to the key results likely in the next decade. We examine both discrete (single photon) type processing as well as those which employ continuous variable manipulations. The mathematical formalism is kept to the minimum needed to understand the key theoretical and experimental results

Three-dimensional laser velocimeter simultaneity detector

A three-dimensional laser Doppler velocimeter has laser optics for a first channel positioned to create a probe volume in space, and laser optics and for second and third channels, respectively, positioned to create entirely overlapping probe volumes in space. The probe volumes and overlap partially in space. The photodetector is positioned to receive light scattered by a particle present in the probe volume, while photodetectors and are positioned to receive light scattered by a particle present in the probe volume. The photodetector for the first channel is directly connected to provide a first channel analog signal to frequency measuring circuits. The first channel is therefore a primary channel for the system. Photodetectors and are respectively connected through a second channel analog signal attenuator to frequency measuring circuits and through a third channel analog signal attenuator to frequency measuring circuits. The second and third channels are secondary channels, with the second and third channels analog signal attenuators and controlled by the first channel measurement burst signal on line. The second and third channels analog signal attenuators and attenuate the second and third channels analog signals only when the measurement burst signal is false