Sentence examples for index calculus from inspiring English sources

A key step of an index calculus algorithm for solving ECDLP is to solve the point decomposition problem.

To exploit the symmetry in ECDLP index calculus algorithms, we first rewrite Semaev's polynomial s m+1 with the elementary symmetric polynomials.

In this paper, we focus on Diem's version of index calculus for ECDLP over a binary field of prime extension degree n [3,7,15].

However, this is consistent with the observation already made in [7,15] that exhaustive search is more efficient than index calculus for small parameters.

We expect that the index calculus algorithms that have recently appeared in the literature will be subject to further theoretical improvements and practical optimizations in a close future.

In Section 2, we recall previous index calculus algorithms for ECDLP, in particular FPPR method attack on binary elliptic curves and previous work exploiting the symmetry of Semaev's polynomials when the extension degree is composite.

Both debris index and calculus index are the means of six debris (calculus) scores assessed on six tooth surfaces: 0 = No debris (calculus); 1 = Debris (calculus) on less than 1/3 of the tooth surface; 2 = Debris (calculus) covering between 1/3 and 2/3; 3 = Debris (calculus) covering more than 2/3.

Both plaque index and calculus index are the means of 6 plaque (calculus) scores assessed on 6 tooth surfaces.

Debris Index and Calculus Index which comprise the OHI-S therefore, could have not been reliably re-tested.

The dental examination included the degree of mouth cleaning and periodontal disease (referred Debris Index and Calculus Index for judgment), condition of the temporomandibular joint (using the Japan Association of School Dentists index), number and condition of remaining teeth, and the condition of any dental prostheses.

The calculus index simplified (CI-S) and debris index simplified (DI-S) value may range from 0 to 3, the OHI-S value which is the sum of CI-S and DI-S range from 0 to 6. Oral hygiene index score of 0 1.2 means good oral hygiene; 1.3-3.0 means fair oral hygiene and 3.0-6.0 3.0-6.0oor oral hygiene.