Algebraic methods in analyzing lightweight cryptographic symmetric primitives

In this work we analyze two lightweight cryptographic primitives, the hash function SPONGENT and the block cipher EPCBC, using algebraic methods. Regarding SPONGENT, we are able to improve on previously known results by finding two semi-free-start collisions for round-reduced SPONGENT-88 with 6 rounds, and prove that no semifree-start collisions exist for SPONGENT-128 with 6 rounds. For EPCBC we are able to demonstrate practical attacks for both versions, EPCBC-48 and EPCBC-96, for up to 3 rounds. For EPCBC-48 we demonstrate weaknesses and find a theoretical attack up to round 8, which is 25% of the full cipher. We obtaine similar results for EPCBC-96 up to round 5 and identified a significant class of weak keys for 6 rounds. Furthermore, we introduce a novel method of optimizing guessing strategies using Mixed Integer Linear Programming and demonstrate its application to the two primitives under investigation, which leads to our results.