Classifier Instance:

Anchor text: Pollard's rho
Target Entity: Pollard\u0027s_rho_algorithm_for_logarithms
Preceding Context: Since all the fastest known algorithms that allow to solve the ECDLP (baby-step giant-step,
Succeeding Context: , etc.), need O(\sqrt{n}) steps, it follows that the size of the underlying field shall be roughly twice the security parameter. For example, for 128-bit security one needs a curve over \mathbb{F}_q , where q \approx 2^{256} . This can be contrasted with finite-field cryptography (e.g., DSA) which requires 3072-bit public keys and 256-bit private keys, and integer factorization cryptography (e.g., ) which requires 3072-bit public and private keys.
Paragraph Title: Key sizes
Source Page: Elliptic curve cryptography

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