Elliptic Curve Signatures

As we saw in ECDSA Math, the signature generation algorithm uses a random key k, as the basis for an ephemeral private/public key pair. The value of k is not important, as long as it is random. If the same value k is used to produce two signatures on different messages (transactions), then the signing private key can be calculated by anyone. Reuse of the same value for k in a signature algorithm leads to exposure of the private key!

This is not just a theoretical possibility. We have seen this issue lead to exposure of private keys in a few different implementations of transaction-signing algorithms in bitcoin. People have had funds stolen because of inadvertent reuse of a k value. The most common reason for reuse of a k value is an improperly initialized random-number generator.

To avoid this vulnerability, the industry best practice is to not generate k with a random-number generator seeded with entropy, but instead to use a deterministic-random process seeded with the transaction data itself. This ensures that each transaction produces a different k. The industry-standard algorithm for deterministic initialization of k is defined in RFC 6979, published by the Internet Engineering Task Force.

If you are implementing an algorithm to sign transactions in bitcoin, you must use RFC 6979 or a similarly deterministic-random algorithm to ensure you generate a different k for each transaction.