Prime factorization via localized tile assembly in a DNA origami framework.

Abstract

Modern cybersecurity built on public-key cryptosystems like Rivest-Shamir-Adleman is compromised upon finding solutions to the prime factorization. Nevertheless, solving the prime factorization problem, given a large <i>N</i>, remains computationally challenging. Here, we design DNA origami frameworks (DOFs) to direct localized assembly of double-crossover (DX) tiles for solving prime factorization with a model consisting of the computing, decision-making, and reporting motifs. The model implementation is based on the sequential assembly of different DX tiles in the DOF cavity that carries overhangs encoding the prime and composite integers. The primes are multiplied and then verified with the composite, and the result is visualized under atomic force microscopy via the presence (success) or absence (failure) of biotin-streptavidin labels on the reporting DX tile. The factorization of semiprimes 6 and 15 is realized with this DOF-based demonstration. Given the potential of massively parallel processing ability of DNA, this strategy opens an avenue to solve complex mathematical puzzles like prime factoring with molecular computing.