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Some readers will note that “division” is indicated in the first line of each algorithm. In particular, in ECDSA, addition of two points (p1,p2) and (q1,q2), and the doubling of (p1,p2), are performed as follows: This is basically what is done in ECDSA, except that the operations are performed modulo some large prime number M. Indeed, one can define “addition” on the curve as finding that third point corresponding to two given points.

Elliptic curves have numerous interesting properties, such as the fact that a nonvertical line intersecting two nontangent points will always intersect a third point on the curve. In Bitcoin and most other implementations, a = 0 and b = 7, so this is simply y 2 = x 3 + 7 (see graph). An elliptic curve is an equation such as y 2 = x 3 + a x + b. The elliptic curve digital signature algorithmīlockchain is basically a publicly available ledger where participants enter data and certify their acceptance of the transaction via an elliptic curve digital signature algorithm (ECDSA). The following is based in part on an article by Eric Rykwalder, one of the founders of, a startup blockchain software firm in San Francisco. It is worth taking a brief look at the mathematics behind blockchain.

Already numerous firms, including several startup organizations, are pursuing blockchain to facilitate and streamline many types of financial transactions. In a previous Math Investor blog, we described the emerging world of blockchain, emphasizing how it might impact the financial services and investment world.