Elliptic Curve DSA - Signature Verification Algorithm

Signature Verification Algorithm

For Bob to authenticate Alice's signature, he must have a copy of her public key . If he does not trust the source of, he needs to validate the key ( here indicates the identity element):

  1. Check that is not equal to and its coordinates are otherwise valid
  2. Check that lies on the curve
  3. Check that

After that, Bob follows these steps:

  1. Verify that and are integers in . If not, the signature is invalid.
  2. Calculate, where HASH is the same function used in the signature generation. Let be the leftmost bits of .
  3. Calculate .
  4. Calculate and .
  5. Calculate .
  6. The signature is valid if, invalid otherwise.

Note that using Straus's algorithm (also known as Shamir's trick) a sum of two scalar multiplications can be calculated faster than with two scalar multiplications.

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