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

Area of Science:

• Molecular Computing
• Nanotechnology
• Cryptography

Background:

• Public-key cryptosystems, like Rivest-Shamir-Adleman, are vulnerable to efficient prime factorization algorithms.
• Solving large-number prime factorization remains a significant computational challenge.
• Current cybersecurity relies on the difficulty of prime factorization.

Purpose of the Study:

• To design DNA origami frameworks (DOFs) for molecular computation of prime factorization.
• To demonstrate a novel method for solving computationally hard mathematical problems using DNA self-assembly.
• To explore DNA-based solutions for cryptographic challenges.

Main Methods:

• Utilized DNA origami frameworks to guide the localized assembly of double-crossover (DX) tiles.
• Engineered DX tiles with overhangs encoding prime and composite integers for computation.
• Implemented a computing, decision-making, and reporting motif system within the DOF.
• Verified factorization results using atomic force microscopy (AFM) with biotin-streptavidin labeling.

Main Results:

• Successfully demonstrated prime factorization of semiprimes 6 and 15 using the DOF model.
• Achieved visual confirmation of computational success or failure via AFM imaging.
• Showcased the sequential assembly of DNA tiles encoding mathematical operations.

Conclusions:

• DNA origami frameworks provide a viable platform for molecular computation of prime factorization.
• This strategy leverages DNA's massive parallel processing potential for complex mathematical problems.
• Opens new avenues for using molecular computing to address cryptographic and computational challenges.