A Note on Security of Public-Key Cryptosystem Provably as Secure as Subset Sum Problem

We analyzed a typical cryptosystem and an easy extended knapsack subset sum problem is proposed. The solution is not chosen from any longer but from. Based on the problem, we construct a public key cryptosystem in which the plaintext is divided into some groups and each group has bits, so that the encryption and decryption can be very fast. The possible attacks are analyzed. Our cryptosystem not only can resist Shamir's attack but also can resist the low density attack, because of its high density. The number of the sequence is also much shorter than before with the same density.

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Equivalent key attack against a public-key cryptosystem based on subset sum problem

IET Information Security ◽

10.1049/iet-ifs.2018.0041 ◽

2018 ◽

Vol 12 (6) ◽

pp. 498-501 ◽

Cited By ~ 2

Author(s):

Jiayang Liu ◽

Jingguo Bi

Keyword(s):

Public Key ◽

Public Key Cryptosystem ◽

Subset Sum Problem ◽

Subset Sum

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Cryptanalysis on 2 Dimensional Subset-sum Public Key Cryptosystem

Proceedings of the 2nd International Conference on Interaction Sciences Information Technology, Culture and Human - ICIS '09 ◽

10.1145/1655925.1662667 ◽

2009 ◽

Author(s):

Tomohiro Shintani ◽

Ryuichi Sakai

Keyword(s):

Public Key ◽

Public Key Cryptosystem ◽

Subset Sum

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

Information ◽

10.3390/info10020075 ◽

2019 ◽

Vol 10 (2) ◽

pp. 75 ◽

Cited By ~ 1

Author(s):

Yuan Ping ◽

Baocang Wang ◽

Shengli Tian ◽

Jingxian Zhou ◽

Hui Ma

Keyword(s):

Chinese Remainder Theorem ◽

Success Probability ◽

High Density ◽

Public Key ◽

Public Key Cryptosystem ◽

The Public ◽

Attack Model ◽

Simultaneous Diophantine Approximation ◽

Subset Sum ◽

Linearization Attack

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.

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