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The mathematics behind blockchain


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






It is worth taking a brief look at the mathematics behind blockchain. The following is based in part on an article by Eric Rykwalder, one of the founders of Chain.com, a startup blockchain software firm in San Francisco.

The elliptic curve digital signature algorithm

Blockchain 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). An elliptic curve is an equation such as y² = x3 + a x + b. In Bitcoin and most other implementations, a = 0 and b = 7, so this is simply y² = x3 + 7 (see graph). 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. Indeed, one can define “addition” on the curve as finding that third point corresponding to two given points. This is basically what is done in ECDSA, except that the operations are performed modulo some large prime number M.

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Read more:
http://www.financial-math.org/blog/2016/10/the-mathematics-behind-blockchain/

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