Finite Field Arithmetic using Self-Assembly of DNA Tilings

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Finite Field Arithmetic using Self-Assembly of
DNA Tilings

• Summarized by HaYoung Jang

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DNA Tiles and Assembly
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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 Zp1, 2, , p-1.

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Finite Field Multiplication
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Basic step of computing Bx(moduloR)
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Basic step of computing Bx(moduloR)
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Input Tiles
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Example computation of 4-bit finite field
multiplication
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Example computation of 4-bit finite field
multiplication
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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

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Conclusion

• Do you know Word Game?
• This is just another illusion.