Reconstructing Public Keys from Signatures
The blog delves into reconstructing public keys from signatures in cryptographic schemes like ECDSA, RSA, Schnorr, and Dilithium. It highlights challenges, design choices, and security considerations, emphasizing the complexity and importance of robust security measures.
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The blog discusses the possibility of reconstructing public keys from signatures in various cryptographic schemes. In ECDSA, it is feasible to recover a public key from a single valid signature by solving equations. For RSA, the process is more complex, requiring two signatures and calculations involving the exponent. Schnorr signatures and Dilithium, a post-quantum scheme, also present challenges in recovering public keys due to specific design choices. SPHINCS+ and Unbalanced Oil and Vinegar schemes are explored, highlighting how public key recovery varies across different signature schemes. The blog emphasizes the importance of considering side-channel attacks and resilience in protocol design, as adversaries may exploit vulnerabilities to recover public keys. Overall, the discussion underscores the intricate nature of public key recovery in cryptographic systems and the need for robust security measures.
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4 commentsI don't follow. Surely the entire point of a public key is that it's public, and the point of signatures is to show that something belongs to you. An anonymous signature makes no sense, because signing something is putting your name on it. If you wanted to be anonymous in the sense that your public key cannot be recovered from a message, you wouldn't sign the message.
It is calculated from the signature.
I'm not sure if Bitcoin can use this trick, at least the classic transaction types explicitly included pubkey.
I suppose it's an easy enough property to add to any signature protocol via a designated verifier scheme, and just defining the public key to be a combination of the public signature key and the secret verifier key.
I also wonder whether there is any formal proof (or at least an intuitive argument for why it would be intractable) for the variant of Schnorr signatures mentioned in the article.
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