Lattice basis reduction: improved practical algorithms and solving subset sum problems
Mathematical Programming: Series A and B
Improved algorithms for integer programming and related lattice problems
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
A knapsack-based probabilistic encryption scheme
Information Sciences: an International Journal
Solving Linear Equations Modulo Divisors: On Factoring Given Any Bits
ASIACRYPT '08 Proceedings of the 14th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Cryptanalysis of a knapsack-based probabilistic encryption scheme
Information Sciences: an International Journal
Cryptanalysis of RSA and Its Variants
Cryptanalysis of RSA and Its Variants
Quadratic compact knapsack public-key cryptosystem
Computers & Mathematics with Applications
Faster exponential time algorithms for the shortest vector problem
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Cryptanalysis of a quadratic knapsack cryptosystem
Computers & Mathematics with Applications
| Hi-index | 0.09 |
Recently, Wang and Hu have proposed a high-density quadratic compact knapsack public-key cryptosystem using the Chinese remainder theorem to disguise two secret cargo vectors. The system is claimed to be secure against certain known attacks; however, it has not been demonstrated to fulfill any provable security goals. In this work, we show that this system is not secure. Exploiting the special structure of system parameters, we first show that a candidate list for the secret modulus can be obtained by solving linear equations with small solutions. Next, we show that with this candidate list, all other secrets can be recovered in succession with lattice-based methods by solving certain modular linear equations with small solutions. As a result, recovering a private key can be done in about 11 h for the proposed system parameter n=100. We also discuss a method to thwart the proposed attack.