Construction of k-ary Pseudorandom Elliptic Curve Sequences

We present a method for constructing k-ary sequences over elliptic curves. Using the multiplicative character of order k of finite fields, we construct a family of k-ary pseudorandom elliptic curve sequences. The pseudorandom measures, such as the well-distribution measure, the correlation measure of order e, and the linear complexity are estimated by using certain character sums. Such sequences share the same order of magnitude on the well-distribution measure, the correlation measure of order e as the ＇truly＇ random sequences. The method indicates that it is possible to construct ＇good＇ pseudorandom sequences over elliptic curves widely used in public key cryptography.

A novel absolute displacement detecting magnetic sensor

A novel magnetic grating based on calibration was proposed.Two tracks,look-up track and index track,were used to realize absolute output.Magnets of look-up track were magnetized according to N-S-N-S,and magnetic field was sensed by 6 linear Hall sensors.Three signals whose phase shift is 120° were obtained through difference,and the offset of magnetic head in a signal period could be obtained by look-up table;Magnets of index track were magnetized according to pseudorandom binary sequence.Hall sensors were used to get the absolute offset of the signal period to which the magnetic head is belonged.The magnetic grating was calibrated using a higher resolution optical grating:output of optical grating and signals from magnetic grating were sampled at the same time and transmitted to computer,the relation between them could be got and stored in MCU for looking-up.The displacement was got according to Hall signals while in working state.A magnetic grating prototype was made,and it could realize absolute detecting in 2048 mm and the resolution could achieve to 0.001 mm.Its structure is simple,cost is very low and it is suitable for mass production.

On the Linear Complexity of New Generalized Cyclotomic Binary Sequences of Order Two and Period pqr

Periodic sequences over finite fields, constructed by classical cyclotomic classes and generalized cyclotomic classes, have good pseudorandom properties. The linear complexity of a period sequence plays a fundamental role in the randomness of sequences. Let p, q, and r be distinct odd primes with gcd（p-1, q-1 ）=gcd（p- 1, r-1）=gcd（q-1, r-1）=2. In this paper, a new class of generalized cyclotomic sequence with respect to pqr over GF（2） is constructed by finding a special characteristic set. In addition, we determine its linear complexity using cyclotomic theory. Our results show that these sequences have high linear complexity, which means they can resist linear attacks.

On the Largest Linear Span of Binary Sequences with Period p^2 from Interleaved Construction

Let S be a family of binary sequences constructed from interleaved construction. The linear spans of binary sequences in S are studied in this paper. In order to achieve the largest linear span, a criterion is presented for the base sequences with periodp, where p is a prime and 2 is a primitive root modulop2. It is shown that any sequence in S has the largest linear span under the criterion. Moreover, such base sequences can be chosen easily.

5D Hyper-Chaotic System with Multiple Types of Equilibrium Points

A chaotic system with various equilibrium types has rich dynamic behaviors.Its state can switch flexibly among different families of attractors,which is beneficial to the practical applications.So it has been widely concerned in recent years.In this paper,a new 5D hyper-chaotic system is proposed.The important characteristic of the system is that it may have multiple types of equilibrium points by changing system parameters,namely,linear equilibrium point,no equilibrium point,non-hyperbolic unstable equilibrium point and stable hyperbolictype equilibrium point.Furthermore,there are hyper-chaotic phenomena and multi-stability about the coexistence of multiple chaotic attractors and the coexistence of hyper-chaotic attractors and chaotic attractors in the system.In addition,the system,complexity is analyzed.It is found that the complexity is close to 1 in the hyper-chaotic state and a pseudo-random sequence generated by the system passes all the statistical tests.Finally,an analog circuit of the system is designed and simulated.

A robust and simple two-mode digital calibration technique for pipelined ADC

This paper presents a two-mode digital calibration technique for pipelined analog-to-digital converters （ADC）.The proposed calibration eliminates the errors of residual difference voltage induced by capacitor mismatch of pseudorandom（PN） sequence injection capacitors at the ADC initialization,while applies digital background calibration to continuously compensate the interstage gain errors in ADC normal operation.The presented technique not only reduces the complexity of analog circuit by eliminating the implementation of PN sequence with accurate amplitude in analog domain,but also improves the performance of digital background calibration by minimizing the sensitivity of calibration accuracy to sub-ADC errors.The use of opamps with low DC gains in normal operation makes the proposed design more compatible with future nanometer CMOS technology.The prototype of a 12-bit 40-MS/s pipelined ADC with the two-mode digital calibration is implemented in 0.18-μm CMOS process.Adopting a simple telescopic opamp with a DC gain of 58-dB in the first stage,the measured SFDR and SNDR within the first Nyquist zone reach 80-dB and 66-dB,respectively.With the calibration,the maximum integral nonlinearity （INL） of the ADC reduces from 4.75-LSB to 0.65-LSB,while the ADC core consumes 82-mW at 3.3-V power supply.