IACR News item: 30 April 2014
Ignacio Cascudo, Ronald Cramer, Chaoping Xing
ePrint Reportso far, most applications of this theory do not
require additional properties. Motivated by recent applications, we require global function fields
with the additional property that their zero class divisor groups contain at most a small number of $d$-torsion points. We capture this with the notion of torsion limit, a new asymptotic quantity for global function fields.
It seems that it is even harder to determine values of this new quantity than the Ihara constant.
Nevertheless, some non-trivial upper bounds are derived.
Apart from this new asymptotic quantity and bounds on it, we also introduce Riemann-Roch systems of equations. It turns out that this type of equation system
plays an important role in the study of several other problems in each of these areas: arithmetic secret sharing, symmetric bilinear complexity of multiplication in finite fields, frameproof codes and the theory of error correcting codes.
Finally, we show how our new asymptotic quantity, our bounds on it and Riemann-Roch systems can be used to improve results in these areas.
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