BITRU: Binary Version of the NTRU Public Key Cryptosystem via Binary Algebra

Abstract

New terms such as closest vector problem (CVP) and the shortest vector problem (SVP), which have been illustrated as NP-hard problem, emerged, leading to a new hope for designing public key cryptosystem based on certain lattice hardness. A new cryptosystem called NTRU is proven computationally efficient and it can be implemented with low cost. With these characteristics, NTRU possesses advantage over others system that rely on number-theoretical problem in a finite field (e.g. integer factorization problem or discrete logarithm problem). These advantages make NTRU a good choice for many applications. After the adaptation of NTRU, many attempts to generalize its algebraic structure have appeared. In this study, a new variant of the NTRU public key cryptosystem called BITRU is proposed. BITRU is based on a new algebraic structure used as an alternative to NTRU-mathematical structure called binary algebra. This commutative and associative. Establishing two public keys in the proposed system has distinguished it from NTRU and those similar to NTRU cryptosystems. This new structure helps to increase the security and complexity of BITRU. The clauses of BITRU, which include key generation, encryption, decryption, and decryption failure, are explained in details. Its suitability of the proposed system is proven and its security is demonstrated by comparing it with NTRU.