## Cryptology ePrint Archive: Report 2013/394

**A Public Key Cryptoscheme Using Bit-pair Shadows**

*Shenghui Su and Shuwang Lu and Xiubin Fan and Maozhi Xu*

**Abstract: **The authors give the definition and property of a bit-pair shadow, and design the three algorithms of a public key cryptoscheme that is based on a multivariate permutation problem (MPP) and an anomalous subset product problem (ASPP) to which no subexponential time solutions are found so far, and regards a bit-pair as an operation unit. Further, demonstrate that the decryption algorithm is correct, deduce the probability that a plaintext solution is nonunique is nearly zero, dissect the running times of the three algorithms, analyze the security of the new scheme against extracting a private key from a public key and recovering a related plaintext from a ciphertext by LLL lattice basis reduction, meet-in-the-middle dichotomy, and adaptive-chosen-ciphertext approach on the assumption that an integer factorization problem, a discrete logarithm problem, and a low-density subset sum problem can be solved efficiently, and prove that new scheme using random both padding and permutation is semantically secure. Meantime, give a conversion from an ASPP to an anomalous subset sum problem (ASSP). The analysis shows that the bit-pair method increases the density of a related ASSP knapsack to D > 1, and decreases the modulus length of the new scheme to lgM = 464, 544, or 640 corresponding to n = 80, 96, or 112 separately.

**Category / Keywords: **Public key cryptoscheme; Semantical security; Bit-pair shadow; Random padding Anomalous subset sum problem; Compact sequence

**Date: **received 17 Jun 2013, last revised 27 Aug 2014

**Contact author: **reesse at 126 com

**Available format(s): **PDF | BibTeX Citation

**Note: **Minor revision.

**Version: **20140827:144522 (All versions of this report)

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