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We introduce the notion of an arithmetic codex, or codex for short. Codices encompass several well-established notions from cryptography (various types of arithmetic secret sharing schemes, which all enjoy additive as well as multiplicative properties) and from algebraic complexity (bilinear complexity of multiplication in algebras) in a single mathematical framework. Arithmetic secret sharing schemes have important applications to secure multiparty computation and even to two-partydoi:10.1109/itw.2012.6404767 dblp:conf/itw/CascudoCX12 fatcat:kkzuoif2xbfjfgcabhmp7clu6e