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TL;DR: the signature verification process in ECDSA is very different from the one in RSA. The question's description of these signature schemes is incorrect for ECDSA, approximate for RSA. Alice who holds the private key is able to encrypt a message into a signature. That's incorrect terminology. Alice who holds the private key is able to sign a message, ...


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But the question is, can the Chinese remainder theorem in ECDSA be applied to the parameters in secp256k1? That precise attack doesn't work - we don't use the Chinese remainder theorem when computing with secp256k1 (as the group order is prime). On the other hand, there are certainly side channel attacks available against naïve implementations of ECDSA and ...


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Alice... encrypt a message into a signature. Strictly speaking, signing is different to encryption! E.g. for RSA, you use public key to encrypt a message, but to sign you use private key. What's more, verification of ECC is totally different to RSA, since they have different mathematic characteristics. One example is that for RSA you must use a good padding ...


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