1. Digital Signatures Campbell R. Harvey Duke University, NBER and
November 23, 2016
Digital Signatures
Campbell R. Harvey
Duke University, NBER and
Investment Strategy Advisor, Man Group, plc

2. Two Keys Private and public keys
Private key is sometimes known as the “signing key”. It is secret.
Public key is mathematically linked to the private key
With the private key (which could be a random number), it is easy to generate a public key
With the public key, it is nearly impossible to generate the private key
Public key is available for anyone to see
Public key sometimes called the “verification key”
Campbell R. Harvey 2016

3. Generating a signature
We start with a message, M.
I generate a key pair, SK (private or signing key) and VK (public or verification key)
Message M and SK pass through a digital signature algorithm (DSA) to generate the digital signature or signed message SM. M
DSA SM SK
(private key)
Campbell R. Harvey 2016

4. Generating a signature
Verification
Mathematically determine that I signed the message with my private key, SK, without knowing SK.
Three ingredients: Message (M), digital signature (SM), verification or private key (VK) M SM
DSA
Valid? (Yes/No) VK
(public key)
Campbell R. Harvey 2016

5. Generating a signature
Notice
Proves that the person with the private key (that generated the public key) signed the message.
Interestingly, digital signature is different from a usual signature in that it depends on the message, i.e. the signature is different for each different message
In practice, we do not sign the message, we sign a cryptographic hash of the message. This means that the size of the input is the same no matter how long the message is.
Campbell R. Harvey 2016

6. References The Math Behind Bitcoin
Elliptic Curve Digital Signature Algorithm (Bitcoin)
What does the curve used in Bitcoin, secp256k1, look like?
Elliptic Curve Digital Signature Algorithm (Wikipedia)
Elliptic Curve Cryptography (UCSB)
Elliptic Curve Cryptography and Digital Rights Management (Purdue)
Zero to ECC in 30 minutes (Entrust)
The Elliptic Curve Cryptosystem
Campbell R. Harvey 2016