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Title:
NTRU in Quaternion Algebras of Bounded Discriminant
Authors: Cong Ling, Andrew Mendelsohn
Abstract:The NTRU assumption provides one of the most prominent problems on which to base post-quantum cryptography. Because of the efficiency and security of NTRU-style schemes, structured variants have been proposed, using modules. In this work, we create a structured form of NTRU using lattices obtained from orders in cyclic division algebras of index 2, that is, from quaternion algebras. We present a public-key encryption scheme, and show that its public keys are statistically close to uniform. We then prove IND-CPA security of a variant of our scheme when the discriminant of the quaternion algebra is not too large, assuming the hardness of Learning with Errors in cyclic division algebras.
ePrint: https://eprint.iacr.org/2023/1471
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