The Torsion-Limit for Algebraic Function Fields and Its Application to Arithmetic Secret Sharing

Explore the groundbreaking research on the torsion-limit for algebraic function fields and its application to arithmetic secret sharing in this 20-minute talk from Crypto 2011. Delve into the work of Ronald Cramer, Chaoping Xing, and Ignacio Cascudo as they present their findings on intron-codes, asymptotics of arithmetic secret sharing schemes, and efficient error correction. Examine the main results, including the solvability of RR systems and upper bounds for r-torsion limit when r is prime. Gain insights into arithmetic secret sharing schemes derived from algebraic geometric codes and their potential applications in cryptography.

Intro
n-Codes
Asymptotics of Arithmetic Secret Sharing Schemes
Applications
Efficient error correction
Main results
Arithmetic SSS from Algebraic Geometric Codes
Solvability of RR systems
General result
Upper bounds for r-torsion limit, r prime
Conclusions