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Weierstrass Points and Curves Over Finite Fields
For any projective embedding of a non-singular irreducible complete algebraic curve defined over a finite field, we obtain an upper bound for the number of its rational points. The constants in the…
Fermat curves over finite fields
Diagonal equations over function fields
- J. Voloch
- 1 September 1985
LetK be a function field in one variable over ℂ anda1,...,am,b non-zero elements ofK, such thatb is linearly independent froma1,...,am over ℂ. We show that forn sufficiently large, the equation…
Indifferentiable deterministic hashing to elliptic and hyperelliptic curves
- R. R. Farashahi, Pierre-Alain Fouque, I. Shparlinski, Mehdi Tibouchi, J. Voloch
- Computer Science, MathematicsMath. Comput.
- 24 April 2012
A new, simpler technique based on bounds of character sums is presented to prove the indifferentiability of similar hash function constructions based on essentially any deterministic encoding to elliptic curves or curves of higher genus, such as the algorithms by Shallue, van de Woestijne and Ulas, or the Icart-like encodings recently presented.
A formula for the Cartier operator on plane algebraic curves.
The main purpose of this paper is to establish a formula for the Cartier operator on a plane algebraic curve in terms of a differential operator in polynomials in two variables. This formula is very…
Wronskians and linear independence in fields of prime characteristic
Euclidean weights of codes from elliptic curves over rings
The authors construct certain error-correcting codes over finite rings and estimate their parameters, notably an estimate for certain exponential sums and some results on canonical lifts of elliptic curves.
The Equation ax+ by=1 in Characteristic p
- J. Voloch
- Computer Science
A central time-shared data processing system organized for character analysis and coupled to a number of remote document scanning stations each including a drum document feed to produce data identifying graphic figures for analysis by the central processing system.
Multiplicative order of Gauss periods
We obtain a lower bound on the multiplicative order of Gauss periods which generate normal bases over finite fields. This bound improves the previous bound of von zur Gathen and Shparlinski.