Detecting General Algebraic Manipulation Attacks

Algebraic manipulation detection codes are a class of error detecting codes which have found numerous applications in cryptography. In this paper we extend these codes to defeat general algebraic attacks we call such codes general algebraic manipulation detection (GAMD) codes. Positive results are shown for the existence of GAMDs for the families of tampering functions corresponding to point additions and affine functions over a finite field. Compared to non-malleable codes, we demonstrate both positive and negative results regarding the existence of GAMDs for arbitrary families of tampering functions.