Exercises: Sign / Verify Messages using ECDSA and the NIST P-521 Curve

In this exercise we shall sign and verify messages using the ECDSA digital signature algorithm and the NIST P-521 curve. The NIST P-521 elliptic curve, known also as secp521r1 is 521-bit ECC curve, suitable for ECDSA digital signatures and ECDH key agreement. It uses 521-bit private keys (encoded as 65-66 bytes, 130-132 hex digits) and 1042-bit public keys (uncompressed, encoded as 130-131 bytes, 260-261 hex digits). The produced signature is 132 bytes (264 hex digits).

Sign a Message with ECDSA / P-521

Write a program to sign a message by given private key. The input consists of 2 text lines: message and private key. The message is given as text and the private key is given as hex string (130-132 hex digits). Use the ECDSA deterministic signing (following RFC 6979) and the curve NIST P-521, which also known as secp521r1. Print the output as JSON document, holding the input message + the public key of the signer (as hex string, uncompressed) + the ECDSA digital signature (as hex string).

Sample input:

Message for ECDSA-NIST-521p signing
00135799f9d1f033af26168780bf2503313acff854c44031321d7a29bba96edb3c1b93b9deea55229b1de058196ad69a79c01463e3281d9fcc82afd73aac7fdfa4af

Sample output:

{
  "msg": "Message for ECDSA-NIST-521p signing",
  "pubKey":"0078a6bb6732cb3134d2ca3912b2876fe005b20027037512cf972605f58ce5908471a1f9817c8d24290fcc943951f3113a7ee3716bd95f0b9c7326843a833ac6a0750021f08f88a6bd397525068300801521d2d97fea32f2c8b0c74dc8e231a4dd73252c4a7398e25ab20dba0a9df3df0c256617e004a9623676b9f3f9a3aa21f57c90ce",
  "signature":"00202029ab1a3326fe7d1e9ec36d7fab048e833c6c3cad37e1d5294695d28e9fd5583c23edaeecb596782a4c85bac27780623c1a9216202f3828991cbeebbeb049d9008270ea623d8d26c5ab89b621bac12c7fa8e9193e4057e16617f80cfc4279537f45169fb949deb3f9936400a130f6859aaa9c929e47c66610e59cc71a9f7ea79e81"
}

Verify Message Signature with ECDSA / P-521

Write a program to validate the ECDSA digital signature, created by the previous exercise. The input comes as JSON document, holding the message + the public key (uncompressed, hex string) + the signature. Use the P-521 elliptic curve (secp521r1). Print as output a single word: "valid' or "invalid".

Sample input (correctly signed message):

{
  "msg": "Message for ECDSA-NIST-521p signing",
  "pubKey":"0078a6bb6732cb3134d2ca3912b2876fe005b20027037512cf972605f58ce5908471a1f9817c8d24290fcc943951f3113a7ee3716bd95f0b9c7326843a833ac6a0750021f08f88a6bd397525068300801521d2d97fea32f2c8b0c74dc8e231a4dd73252c4a7398e25ab20dba0a9df3df0c256617e004a9623676b9f3f9a3aa21f57c90ce",
  "signature":"00202029ab1a3326fe7d1e9ec36d7fab048e833c6c3cad37e1d5294695d28e9fd5583c23edaeecb596782a4c85bac27780623c1a9216202f3828991cbeebbeb049d9008270ea623d8d26c5ab89b621bac12c7fa8e9193e4057e16617f80cfc4279537f45169fb949deb3f9936400a130f6859aaa9c929e47c66610e59cc71a9f7ea79e81"
}

Sample output:

valid

Sample input (tampered message):

{
  "msg": "Tampered message",
  "pubKey":"0078a6bb6732cb3134d2ca3912b2876fe005b20027037512cf972605f58ce5908471a1f9817c8d24290fcc943951f3113a7ee3716bd95f0b9c7326843a833ac6a0750021f08f88a6bd397525068300801521d2d97fea32f2c8b0c74dc8e231a4dd73252c4a7398e25ab20dba0a9df3df0c256617e004a9623676b9f3f9a3aa21f57c90ce",
  "signature":"00202029ab1a3326fe7d1e9ec36d7fab048e833c6c3cad37e1d5294695d28e9fd5583c23edaeecb596782a4c85bac27780623c1a9216202f3828991cbeebbeb049d9008270ea623d8d26c5ab89b621bac12c7fa8e9193e4057e16617f80cfc4279537f45169fb949deb3f9936400a130f6859aaa9c929e47c66610e59cc71a9f7ea79e81"
}

Sample output:

invalid