A Hardware-Accelerated ECDLP with High-Performance Modular Multiplication

Algorithm 1

Square and multiply modular exponentiation [24].

Input: 𝑧∈𝔽_𝑞, 𝑒[𝑡∶0]

Output: 𝑧^𝑒 mod 𝑞

 𝑟←1

 for 𝑖=𝑡→0 do

  𝑟←𝑟⋅𝑟 mod 𝑞

  if 𝑒[𝑖]=1 then

   𝑟←𝑟⋅𝑧 mod 𝑞

 return 𝑟