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It is known that it is possible to apply the Chinese remainder theorem and attack RSA under precise conditions.

https://tls.mbed.org/public/WSchindler-RSA_Timing_Attack.pdf

But the question is, can the Chinese remainder theorem in ECDSA be applied to the parameters in secp256k1?

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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 secp256k1 - just not that one.

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