Prime Field ECDSA Signature Processing for Reconfigurable Embedded Systems

Algorithm 1

ECDSA signature generation.

Input:  Domain parameter 𝐷=(𝑞,𝑎,𝑏,𝐺,𝑛,ℎ), secret key 𝑑,

       message 𝑚

Output:  Signature (𝑟,𝑠)

(1)  Chose random 𝑘∈[1,𝑛−1],𝑘∈ℕ

(2)  Compute 𝑘𝐺=(𝑥₁,𝑦₁)

(3)  Compute 𝑟=𝑥₁mod𝑛. If 𝑟=0 goto step 1.

(4)  Compute 𝑒=𝐻(𝑚)

(5)  Compute 𝑠=𝑘⁻¹(𝑒+𝑑𝑟)mod𝑛. If 𝑠=0 goto step 1.

(6)  return  (𝑟,𝑠).