Message authentication code (MAC) guarantees the authenticity of messages and is one of the most important primitives in cryptography. We study related-key attacks with which the adversary is able to choose function f and observe the behavior of the MAC under the modified authenticated key f (k), and consider unforgeability of MAC under (selectively) chosen message attack with f (k). We focus on MAC schemes from the Learning parity with noise (LPN) and the Learning with errors (LWE) problem by

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... iltz et al. in EUROCRYPT 2011. We first prove that the MAC schemes from LPN/ LWE can resist key-shift attacks and enlarge the key-shift function set to support a subclass of affine functions.