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Information 2019, 10(2), 75; https://doi.org/10.3390/info10020075

PKCHD: Towards a Probabilistic Knapsack Public-Key Cryptosystem with High Density

1
School of Information Engineering, Xuchang University, Xuchang 461000, China
2
Information Technology Research Base of Civil Aviation Administration of China, Civil Aviation University of China, Tianjin 300300, China
3
Key Laboratory of Computer Networks and Information Security, Ministry of Education, Xidian University, Xi’an 710071, China
*
Authors to whom correspondence should be addressed.
Received: 22 January 2019 / Revised: 14 February 2019 / Accepted: 19 February 2019 / Published: 21 February 2019
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Abstract

By introducing an easy knapsack-type problem, a probabilistic knapsack-type public key cryptosystem (PKCHD) is proposed. It uses a Chinese remainder theorem to disguise the easy knapsack sequence. Thence, to recover the trapdoor information, the implicit attacker has to solve at least two hard number-theoretic problems, namely integer factorization and simultaneous Diophantine approximation problems. In PKCHD, the encryption function is nonlinear about the message vector. Under the re-linearization attack model, PKCHD obtains a high density and is secure against the low-density subset sum attacks, and the success probability for an attacker to recover the message vector with a single call to a lattice oracle is negligible. The infeasibilities of other attacks on the proposed PKCHD are also investigated. Meanwhile, it can use the hardest knapsack vector as the public key if its density evaluates the hardness of a knapsack instance. Furthermore, PKCHD only performs quadratic bit operations which confirms the efficiency of encrypting a message and deciphering a given cipher-text. View Full-Text
Keywords: public key cryptography; knapsack problem; low-density attack; lattice reduction public key cryptography; knapsack problem; low-density attack; lattice reduction
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Ping, Y.; Wang, B.; Tian, S.; Zhou, J.; Ma, H. PKCHD: Towards a Probabilistic Knapsack Public-Key Cryptosystem with High Density. Information 2019, 10, 75.

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