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

Algorithm 1

Procedure ParallelAdder (𝑇₀,𝑛,𝑝,𝑞,𝑟).

(1) For 𝑗=0 to 𝑛−1

 (1a) 𝑇₁=+(𝑇₀,𝑥^1𝑝+𝑗) and 𝑇₂=−(𝑇₀,𝑥^1𝑝+𝑗)

 (1b) 𝑇₃=+(𝑇₁,𝑥^1𝑞+𝑗) and 𝑇₄=−(𝑇₁,𝑥^1𝑞+𝑗)

 (1c) 𝑇₅=+(𝑇₂,𝑥^1𝑞+𝑗) and 𝑇₆=−(𝑇₂,𝑥^1𝑞+𝑗)

 (1d) 𝑇₇=∪(𝑇₄,𝑇₅) and 𝑇₈=∪(𝑇₃,𝑇₆)

 (1e) Append (𝑇₇,𝑥^1𝑟+𝑗) and Append (𝑇₈,𝑥^0𝑟+𝑗)

 (1f) 𝑇₀=∪(𝑇₇,𝑇₈)

 EndFor

EndProcedure