Elliptic curve cryptography uses the discrete logarithm problem, which involves finding a scalar x such that X = xP given group elements X and P.
Conditions: X and P are elements of the group 𝔾.; x is the unknown scalar to be recovered.; The problem is treated as computationally infeasible when only X and P are known.
Elliptic curve cryptography uses the discrete logarithm problem, which involves finding a scalar x such that X = xP given group elements X and P.
Conditions: X and P are elements of the group 𝔾.; x is the unknown scalar to be recovered.; The problem is treated as computationally infeasible when only X and P are known.
Public-key cryptography requires an asymmetric generation process: deriving the public key from the private key must be easy, but recovering the private key from the public key must be computationally hard.
Conditions: There must be an easy direction from private key to public key.; There must be a computationally hard reverse direction from public key to private key.
Public-key cryptography requires an asymmetric generation process: deriving the public key from the private key must be easy, but recovering the private key from the public key must be computationally hard.
Conditions: There must be an easy direction from private key to public key.; There must be a computationally hard reverse direction from public key to private key.