Prime Field ECDSA Signature Processing for Reconfigurable Embedded Systems

Algorithm 2

ECDSA signature verification.

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

      public key 𝑄, message 𝑚, signature (𝑟,𝑠).

Output:  Acceptance or Rejection of the signature

(1)  if ¬(𝑟,𝑠∈[1,𝑛−1]∩ℕ)  then

(2)   return “reject”

(3)  end  if

(4)  Compute 𝑒=𝐻(𝑚)

(5)  Compute 𝑤=𝑠⁻¹mod𝑛.

(6)  Compute 𝑢₁=𝑒𝑤mod𝑛 and 𝑢₂=𝑟𝑤mod𝑛.

(7)  Compute 𝑋=(𝑥_𝑋,𝑦_𝑋)=𝑢₁𝐺+𝑢₂𝑄.

(8)  if 𝑋=∞  then

(9)   return “reject”

(10)  end  if

(11)  Compute 𝑣=𝑥_𝑋mod𝑛.

(12)  if 𝑣=𝑟  then

(13)   return “accept”

(14)  else

(15)   return “reject”

(16)  end if