Research On Provable Security Of Juna Cryptoscheme

The JUNA cryptoscheme is a new kind of multivariable and indeterminacy public-keycryptoscheme, which is evolved from REESSE1+. A JUNA or REESSE1+public keyis based on the multivariate permutation problem (MPP), and a correspondingplaintext is based on the anomalous subset product problem (ASPP). In the past, thereare some blanks in the format proof of the JUNA cryptoscheme. Moreover, JUNAcould be threatened by the LLL lattice basis reduction, due to An ASPP can betransformed to a special subset sum problem (SSP) through solving a discretelogarithm problem (DLP).In this paper, the author mainly does research on the security of the JUNAcryptoscheme by the method of provable security. The works in this paper includebasic studies, the cryptographic hardness assumption, the format proof and theimprovement of the cryptoscheme. First, the author puts forward the hardnessassumption which is the base of security and illustrates that the ASPP is hard relativeto the JUNA key generation algorithm. Then, the construction of the cryptoscheme iscompleted as well as the proof which indicates the scheme’s CPA-secure andCCA-secure for the probabilitic polynomial time adversary in the ramdom oraclemodel. At last, the author improves the textbook JUNA cryptoscheme by the means ofincreasing more indeterminacies. In addition, in order to explore the performance ofthe hardness assumption in the practical application,the author designs and conductsexperiments of attacking ASSP knapsacks by LLL lattice basis reduction, and thenconcludes that the JUNA cryptosystem can resist LLL lattice basis reduction.However, the paper still has certain limitations. For instances, the proof can justindicate that the cryptoscheme is with no obvious defects, due to properties of therandom oracle. The conclusions in the paper provide the factual basis for the furtherresearch on the security of JUNA.