[Resource Topic] 2023/1901: Middle-Products of Skew Polynomials and Learning with Errors

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Middle-Products of Skew Polynomials and Learning with Errors

Authors: Cong Ling, Andrew Mendelsohn


We extend the middle product to skew polynomials, which we use to define a skew middle-product Learning with Errors (LWE) variant. We also define a skew polynomial LWE problem, which we connect to Cyclic LWE (CLWE), a variant of LWE in cyclic division algebras. We then reduce a family of skew polynomial LWE problems to skew middle-product LWE, for a family which includes the structures found in CLWE. Finally, we give an encryption scheme and demonstrate its IND-CPA security, assuming the hardness of skew middle-product LWE.

ePrint: https://eprint.iacr.org/2023/1901

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