Title :
Analysis of Success Rate of Attacking Knapsacks from JUNA Cryptosystem by LLL Lattice Basis Reduction
Author :
Tong Li ; Shenghui Su
Author_Institution :
Coll. of Comput. Sci., Beijing Univ. of Technol., Beijing, China
Abstract :
The JUNA cryptosystem is a new kind of multivariable public-key cryptosystem, which is evolved from REESSE1+. The security of a JUNA or REESSE1+ plaintext is based on the anomalous subset product problem (ASPP). An ASPP can be transformed to a special subset sum problem (SSP), and such a SSP is an anomalous subset sum problem (ASSP). An ASSP from REESSE1+ is of low-density, and one from JUNA is of high-density. The LLL lattice basis reduction algorithm can solve low-density SSPs in polynomial time, and also it probably solves low-density ASSPs. However, the density of a knapsack deriving from a high-density ASSP can be larger than 1, and LLL lattice reduction could hardly break such a knapsack. In this paper, on the basis of our previous work, we design and conduct experiments of attacking ASSP knapsacks by LLL lattice basis reduction, and then analyze the experimental data. Our experiments show that the success rate varies with the density and length of a knapsack, and it is almost 0 when the density is larger than 1. Hence we can conclude that the JUNA cryptosystem can resist LLL lattice basis reduction. Our experimental data in the paper provides the factual basis for our further research on the security of JUNA.
Keywords :
computational complexity; public key cryptography; set theory; JUNA cryptosystem; JUNA plaintext; JUNA security; LLL lattice basis reduction; REESSE1+ cryptosystem; REESSE1+ plaintext; SSP; anomalous subset product problem; knapsacks attack success rate; low-density ASSP; multivariable public-key cryptosystem; polynomial time; special subset sum problem; Encryption; Lattices; Public key cryptography; Vectors; Anomalous subset product problem; Anomalous subset sum problem; Density; LLL lattice basis reduction; Public key cryptosystem;
Conference_Titel :
Computational Intelligence and Security (CIS), 2013 9th International Conference on
Conference_Location :
Leshan
Print_ISBN :
978-1-4799-2548-3
DOI :
10.1109/CIS.2013.102