Fast Parallel Molecular Algorithms for DNA-Based Computation: Solving the Elliptic Curve Discrete Logarithm Problem over 𝐺𝐹(2^𝑛)

Algorithm 2

Procedure ParallelComparator 𝑇₁.

(1) If (𝑇₀,𝑝,𝑞,𝑗,𝑘,𝑇₁,𝑇₂) then

 (1a) For (𝑞−𝑝>𝑘−𝑗) to 𝑚=1

  (1a1) 𝑞−𝑝−(𝑘−𝑗)

  (1a2) 𝑇₃=+(𝑇₀,𝑥^{1𝑝+𝑚−1})

 EndFor

EndIf

(2) For 𝑇₁=∪(𝑇₁,𝑇₃) to 𝑚=𝑞−(𝑘−𝑗)−𝑝

 (2a) 𝑞−𝑝

 (2b) 𝑇₃=+(𝑇₀,𝑥^1𝑝+𝑚)

 (2c) 𝑇₄=−(𝑇₃,𝑥^{1𝑗+𝑚−(𝑞−𝑝−𝑘+𝑗)})

 (2d) 𝑇₅=−(𝑇₀,𝑥^1𝑝+𝑚)

 (2e) 𝑇₆=+(𝑇₅,𝑥^{1𝑗+𝑚−(𝑞−𝑝−𝑘+𝑗)}) and 𝑇₁=∪(𝑇₁,𝑇₄) and

   𝑇₂=∪(𝑇₂,𝑇₃,𝑇₆)

EndFor

EndProcedure