¹State Key Lab of Software Development Environment, Beihang University, Beijing, China
²North China University of Water Conservancy and Electric Power, Zhengzhou, China

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Abstract—The asymmetric cryptosystem plays an important role in the cryptology nowadays. It is widely used in the fields of data encryption, digital watermarking, digital signature, secure network protocol, etc. However, with the improvement of computing capability, longer and longer the key length is required to ensure the security of interaction information. To shorten the key length and improve the encryption efficiency, by defining the two-dimension discrete logarithm problem (DLP), a new public-key cryptosystem is proposed. This new cryptosystem generalizes the public-key cryptosystem from one dimension to two dimensions. The core algorithms of the proposed cryptosystem are also designed, including the fast algorithm, computing the inverse matrix modulo p and finding the period. To verify the correctness and rationality of the new cryptosystem, two examples are carried out. Meanwhile, the efficiency and security are analyzed in detail. Experimental results and theoretical analyses show that the new cryptosystem possesses the advantages of the outstanding robustness, short key length, high security and encrypting many data once.

Index Terms—Asymmetric cryptosystem, discrete logarithm problem (DLP), two dimensions, RSA, ECC (elliptic curve cryptosystem).

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Cite: Xiaoqiang Zhang, Guiliang Zhu, Weiping Wang, Mengmeng Wang, Shilong Ma, "New Public-Key Cryptosystem Based on Two- Dimension DLP," Journal of Computers vol. 7, no. 1, pp. 169-178, 2012.