关键词: 格, NTRU, 密钥协商协议, 可证明安全, eCK模型

Abstract: NTRU is the earliest publickey cryptosystem that reduces the difficulty of the cryptosystem to the latticehard problem. The features of NTRU are simple, and the storage space required is small. Therefore, NTRU is more simple and efficient algorithm for establishing a cryptosystem based on latticehard problems. However, there are few relevant references to design NTRUbased key agreement protocols. The existing NTRUbased key agreement protocols do not protect the keys sufficiently, which is easy to leave convenience for adversary attacks. The proof is not sufficient and incomplete. In order to solve this problem, this paper proposes two key agreement protocols based on NTRU lattice, adding temporary secret information, so that the scheme has strong forward security, and proposes a detailed security proof. The proof is based on the unforgeability of the session key under the SVP assumption on the lattice. The security proof is based on the eCK model. Compared with traditional key agreement schemes such as DH and ECDH, this NTRU scheme is based on polynomial rings, and has higher computational efficiency. Its security can be reduced to solving difficult problems on lattices, and it can resist quantum attacks.

Key words: lattice, NTRU, key agreement protocol, provable security, eCK model