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Gregor Pogačnik
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ecc101.md
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## Eliptic Curve Cryptography 101 ## Eliptic Curve Cryptography 101
An elliptic curve is defined by formula: An elliptic curve is defined by formula:
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a and b are parameters that define the curve and are carefully tuned. a and b are parameters that define the curve and are carefully tuned.
Secp256k1 curve used by Bitcoin (and others) has the formula Secp256k1 curve (defined through Standards for Efficient Cryptography) used by Bitcoin (and others) has the formula
![equation](http://www.sciweavers.org/tex2img.php?eq=y%5E2%3Dx%5E3%2B7&bc=Black&fc=White&im=jpg&fs=12&ff=arev&edit=) (a = 0, b = 7) and looks like this: ![equation](http://www.sciweavers.org/tex2img.php?eq=y%5E2%3Dx%5E3%2B7&bc=Black&fc=White&im=jpg&fs=12&ff=arev&edit=) (a = 0, b = 7) and looks like this:
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Basically random integer x can be a private key, while P = x*G is the public key. And knowing P or G doesn't help in any way to find out x. This is the eliptic curve discrete logarithm problem that is believed to be computationaly hard. Basically random integer x can be a private key, while P = x*G is the public key. And knowing P or G doesn't help in any way to find out x. This is the eliptic curve discrete logarithm problem that is believed to be computationaly hard.
Private key is usually a 256 bit long integer. It appears that P would have 512 bits (256 bits for x and 256 bits for y coordinate), but it actually suffices to use just one coordinate (due to the nature of eliptic curves) and one additional bit. So the representation of P is just 257 bits long.
[Previous - main page](./README.md) [Previous - main page](./README.md)
[Next - Schnorr Signature Scheme](./schnorr.md) [Next - Schnorr Signature Scheme](./schnorr.md)

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schnorr.md
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It was invented by german mathematician Claus-Peter Schnorr. Unfortunately he patented the scheme in 1988 (it expired in February 2008). So during the creation of Bitcoin it was "free", unfortunately the space lacked good libraries. Therefore ECDSA scheme was used. It was invented by german mathematician Claus-Peter Schnorr. Unfortunately he patented the scheme in 1988 (it expired in February 2008). So during the creation of Bitcoin it was "free", unfortunately the space lacked good libraries. Therefore ECDSA scheme was used.
### Operation
[Previous - ECC](./ecc101.md) [Previous - ECC](./ecc101.md)
[Next - DLC](./dlc.md) [Next - DLC](./dlc.md)