Digital Signatures Campbell R. Harvey Duke University, NBER and

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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

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

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

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

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

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