Signatures indepth

Apart from hash based Signatures(lamport signature scheme) there are other cool signatures. Hash based signatures are not used in bitcoin.

Disadvantages of lamport signatures

1. One time use
2. They are kind of huge (8kilobytes for a signature and keys are 16 kilobytes)

Ellptic curve signatures

Curves of the form y^2= x^3+ax+b Bitcoin curve's is y^2= x^3+7