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Title: The arithmetic codex
Authors: Cascudo, Ignacio
Cramer, Ronald
Xing, Chaoping
Keywords: DRNTU::Science::Mathematics
Issue Date: 2012
Source: Cascudo, I., Cramer, R., & Xing, C. (2012). The arithmetic codex. 2012 IEEE Information Theory Workshop (ITW).
Abstract: In this invited talk,1 we introduce the notion of arithmetic codex, or codex for short. It encompasses several well-established notions from cryptography (arithmetic secret sharing schemes, which enjoy additive as well as multiplicative properties) and algebraic complexity theory (bilinear complexity of multiplication) in a natural mathematical framework. Arithmetic secret sharing schemes have important applications to secure multi-party computation and even to two-party cryptography. Interestingly, several recent applications to two-party cryptography rely crucially on the existing results on “asymptotically good families” of suitable such schemes. Moreover, the construction of these schemes requires asymptotically good towers of function fields over finite fields: no elementary (probabilistic) constructions are known in these cases. Besides introducing the notion, we discuss some of the constructions, as well as some limitations.
DOI: 10.1109/ITW.2012.6404767
Rights: © 2012 IEEE.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SPMS Conference Papers


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