1. Finite Field Arithmetic using Self-Assembly of DNA Tilings
Summarized by HaYoung Jang

2. DNA Tiles and Assembly

3. Finite Field Arithmetic
Finite field: a field with a finite number of elements.
GF(pn): each prime p and each natural number n, there exists a unique finite field of pn elements.
The elements of this field can be represented as polynomials in x, of degree less than n and having coefficients from Zp={1, 2, …, p-1}.

4. Finite Field Multiplication

5. Basic step of computing B*x(moduloR)

6. Basic step of computing B*x(moduloR)

7. Input Tiles

8. Example computation of 4-bit finite field multiplication

9. Example computation of 4-bit finite field multiplication

10. Implementation Issues
Constructing the input DNA strands
Converting the input ssDNA to tiles
Constructing the computation tiles & output tiles
Executing the computation
Reading the result

11. Conclusion
Do you know “Word Game”?
This is just another illusion.