Bracket coefficients for polynomials are introduced. These are like specific precision floating point numbers together with error terms. Working in terms of bracket coefficients, an algorithm that computes a Grobner basis with floating point coefficients is presented, and a new criterion for determining whether a bracket coefficient is zero is proposed. Given a finite set F of polynomials with ...

The first Gröbner basis algorithm was constructed by Buchberger in 1965; thus it bears his name to this day – Buchberger’s algorithm.[9] Though Buchberger’s algorithm looks relatively simple, it can take a very large amount of time. The step that creates 0 h via a normal form calculation is computationally very difficult. This is particularly frustrating (and wasteful) if the normal form calcul...

In this paper, we consider the minimum Hamming weight for linear codes over special finite quasi-Frobenius rings. Furthermore, we obtain minimal free $R$-submodules of a finite quasi-Frobenius ring $R$  which contain a linear code and derive the relation between their minimum Hamming weights. Finally, we suggest an algorithm that computes this weight using the Grobner basis and we show that und...

In this paper, two protocols are presented for private intersection detection of moving objects’ trajectories. Assuming that the movement trajectory an object can be described by a time-dependent polynomial function, problem finding points is simplified to common roots corresponding polynomials. Thereafter, GrObner Basis used design novel secure protocol Another also designed based on distance ...

Since security and privacy problems in RFID systems have attracted much attention, numerous RFID authentication protocols have been suggested. One of the various design approaches is to use light-weight logics such as bitwise Boolean operations and addition modulo 2 between m-bits words. Because these operations can be implemented in a small chip area, that is the major requirement in RFID prot...

the concept of comprehensive grobner bases was introduced by weispfenning. montes has proposed an efficient algorithm for computing these bases. but he has not explicitly used buchberger's criteria in his algorithm. in this paper we prove that we can apply these criteria on montes algorithm. we propose a modified version of montes algorithm and evaluate its performance via some examples.