Analysis of Success Rate of Attacking Knapsacks from JUNA Cryptosystem by LLL Lattice Basis Reduction

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.