# 3. Signatures | Summary and Q&A

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July 12, 2019
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MIT OpenCourseWare
3. Signatures

## TL;DR

Elliptic Curve Signatures (ECDSA) are a secure and efficient method in cryptography, allowing easy verification and non-reproducibility. They are based on elliptic curves and use points and scalars to perform operations.

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### Q: How are elliptic curve signatures generated?

Elliptic curve signatures are generated by multiplying the private key with the generator point on the curve.

### Q: What are the advantages of elliptic curve signatures?

Elliptic curve signatures are smaller, faster, and more secure compared to other signature schemes like RSA. They also allow for key exchange and encryption.

### Q: Can elliptic curve signatures be forged?

Elliptic curve signatures cannot be easily forged as they rely on the discrete logarithm problem, which is computationally difficult to solve.

### Q: How are elliptic curve signatures verified?

To verify an elliptic curve signature, you need the public key, the signature, and the original message. By performing certain operations, you can verify the authenticity of the signature.

## Summary & Key Takeaways

• Elliptic Curve Signatures utilize points on a curve and scalars to perform operations and ensure security.

• Private keys are multiplied by a generator point to generate public keys.

• Signatures are created by multiplying a random scalar with the generator point and performing operations on the result.

• Verification involves checking the computed signature against the public key and the original message.