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In this paper the design of programmable bit-serial Reed-Solomon encoders is considered using the traditional Berlekamp multiplier. It is suggested that there are certain advantages to be gained by deriving the generator polynomial of the code using combinational logic, or equivalently using look-up tables, rather than using an iterative LFSR based approach. The use of the recently proposed Berlekamp-like...
Linear recurring sequences over finite fields play an important role in coding theory and cryptography. It is known that subfield subcodes of linear codes yield some good codes. In this paper, we study linear recurring sequences and subfield subcodes. Let Mqm(f(x)) denote the set of all linear recurring sequences over Fqm with characteristic polynomial f(x) over Fqm. Denote the restriction of Mqm(f(x))...
Cognitive radio is an emerging technology that allows secondary communication in a frequency band originally allocated to one or more primary users (PUs). Secondary user (SU) usually operates in a low power profile to avoid interference with the PU and sudden appearance of a PU causes loss of data of the SU. Appropriate erasure correction coding (also called as anti-jamming coding) is, thus, required...
A novel pseudorandom sequence generator is presented in this paper. The genesis of this new generator is evolved from the concept of lagged Fibonacci generator by Geroge Marsagalia (1992) applied to points on elliptic curves over a finite field. It is observed that the generator has a long period. Also a successful statistical testing of the randomness attributes of the given generator, in accordance...
Overcoming the computational complexity of Dempsterpsilas rule of combination for fusing data and information continues to be an actively researched problem within Dempster-Shafer theory. Previous efforts to reduce the computational complexity have employed a variety of strategies. However, most have avoided directly evaluating the expression for combining two belief potentials because this involves...
This paper presents an extremely efficient, non-interactive protocol for verifiable secret sharing. Verifiable secret sharing (VSS) is a way of bequeathing information to a set of processors such that a quorum of processors is needed to access the information. VSS is a fundamental tool of cryptography and distributed computing. Seemingly difficult problems such as secret bidding, fair voting, leader...
We develop parallel techniques for dealing with permutation group problems. These are most effective on the class of groups with bounded non-abelian composition factors. For this class, we place in NC problems such as membership testing, finding the center and composition factors, and, of particular significance, finding pointwise-set-stabilisers. The last has applications to instances of graph-isomorphism...
We explicitly construct, for every integer n and ε ≫ 0, a family of functions (psuedo-random bit generators) fn,ε:{0,1}nε → {0,1}n with the following property: for a random seed, the pseudorandom output "looks random" to any polynomial size, constant depth, unbounded fan-in circuit. Moreover, the functions fn,ε themselves can be computed by uniform polynomial size, constant depth circuits...
We show that the permutation group membership problem can be solved in depth (logn)3 on a Monte Carlo Boolean circuit of polynomial size in the restricted case in which the group is abelian. We also show that this restricted problem is NC1-hard for NSPACE(logn).
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