The double digest problem (DDP) is a fundamental problem in bioinformatics, and it has been proven to be an NP-hard problem. As a type of promising combinational optimization method inspired by evolutionary theory, genetic algorithms have attracted much attention during the past four decades, and some genetic algorithms have been successfully applied to solve the DDP. To further enhance the ability to solve the DDP, it is of interest to couple the insights from classical genetic algorithms with the parallel capability of quantum computation. Thus, in this paper, we propose a quantum inspired genetic algorithm (QIGA) for the DDP. In our QIGA, the binary Q-bit representation is converted to mapping sequences, and on this basis, DNA fragments are reordered. The solution of the DDP is a permutation, selected by the QIGA, of all the DNA fragments. The effectiveness and efficiency of our proposal can be inferred from the simulation results for the QIGA on a classical computer. As far as we know, this is the first attempt to address the DDP using a QIGA. Compared with classical genetic algorithms for the DDP, our QIGA slightly accelerates the time require to solve the problem, and we believe that it will achieve superior performance when a quantum computer with the required scale is available. INDEX TERMS Double digest problem, quantum inspired genetic algorithm, DNA mapping.
In typical well-known cryptosystem, the hardness of classical problems plays a fundamental role in ensuring its security. While, with the booming of quantum computation, some classical hard problems tend to be vulnerable when confronted with the already-known quantum attacks, as a result, it is necessary to develop the post-quantum cryptosystem to resist the quantum attacks. With the purpose to bridge the two disciplines, it is significant to summarize known quantum algorithms and their threats toward these cryptographic intractable problems from a perspective of cryptanalysis. In this paper, we discussed the designing methodology, algorithm framework and latest progress of the mathematic hard problems on which the typical cryptosystems depend, including integer factorization problem, discrete logarithmic problem and its variants, lattice problem, dihedral hidden subgroup problems and extrapolated dihedral coset problem. It illustrated the reason why some cryptosystems such as RSA and ECC are not resistant to quantum attacks, yet some of them like lattice cryptosystems remain intact facing quantum attacks.
Background In computational biology, the physical mapping of DNA is a key problem. We know that the double digest problem (DDP) is NP-complete. Many algorithms have been proposed for solving the DDP, although it is still far from being resolved. Results We present DDmap, an open-source MATLAB package for solving the DDP, based on a newly designed genetic algorithm that combines six genetic operators in searching for optimal solutions. We test the performance of DDmap by using a typical DDP dataset, and we depict exact solutions to these DDP instances in an explicit manner. In addition, we propose an approximate method for solving some hard DDP scenarios via a scaling-rounding-adjusting process. Conclusions For typical DDP test instances, DDmap finds exact solutions within approximately 1 s. Based on our simulations on 1000 random DDP instances by using DDmap, we find that the maximum length of the combining fragments has observable effects towards genetic algorithms for solving the DDP problem. In addition, a Maple source code for illustrating DDP solutions as nested pie charts is also included.
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