IEICE TRANSACTIONS on Fundamentals
Using Cab Curves in the Function Field Sieve
Summary :
In Adleman's Function Field Sieve algorithm solving the discrete logarithm problem in a finite field, it is assumed that a random bivariate polynomial in the certain class is absolutely irreducible with high probability. In this letter we point out that if we use Cab type random polynomials then we always get absolutely irreducible polynomials. We can also simplify the calculation of a product of many rational functions on a curve that belongs to the field of definition by the use of a Cab curve.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E82-A No.3 pp.551-552
- Publication Date
- 1999/03/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- LETTER
- Category
- Image Theory
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Ryutaroh MATSUMOTO, "Using Cab Curves in the Function Field Sieve" in IEICE TRANSACTIONS on Fundamentals,
vol. E82-A, no. 3, pp. 551-552, March 1999, doi: .
Abstract: In Adleman's Function Field Sieve algorithm solving the discrete logarithm problem in a finite field, it is assumed that a random bivariate polynomial in the certain class is absolutely irreducible with high probability. In this letter we point out that if we use Cab type random polynomials then we always get absolutely irreducible polynomials. We can also simplify the calculation of a product of many rational functions on a curve that belongs to the field of definition by the use of a Cab curve.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e82-a_3_551/_p
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author={Ryutaroh MATSUMOTO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Using Cab Curves in the Function Field Sieve},
year={1999},
volume={E82-A},
number={3},
pages={551-552},
abstract={In Adleman's Function Field Sieve algorithm solving the discrete logarithm problem in a finite field, it is assumed that a random bivariate polynomial in the certain class is absolutely irreducible with high probability. In this letter we point out that if we use Cab type random polynomials then we always get absolutely irreducible polynomials. We can also simplify the calculation of a product of many rational functions on a curve that belongs to the field of definition by the use of a Cab curve.},
keywords={},
doi={},
ISSN={},
month={March},}
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TY - JOUR
TI - Using Cab Curves in the Function Field Sieve
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 551
EP - 552
AU - Ryutaroh MATSUMOTO
PY - 1999
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E82-A
IS - 3
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - March 1999
AB - In Adleman's Function Field Sieve algorithm solving the discrete logarithm problem in a finite field, it is assumed that a random bivariate polynomial in the certain class is absolutely irreducible with high probability. In this letter we point out that if we use Cab type random polynomials then we always get absolutely irreducible polynomials. We can also simplify the calculation of a product of many rational functions on a curve that belongs to the field of definition by the use of a Cab curve.
ER -
English
