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What happens to bitcoin if math is found that makes reversing multiplication, modular math, etc, easy to reverse in a few steps? What if DH exhanges can be decoded almost as fast as they can happen? Would bitcoin pay to keep this out of public? (In real money, of course)

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What happens to bitcoin if math is found that makes reversing multiplication, modular math, etc, easy to reverse in a few steps?

All of these are already easy.

Reversing elliptic curve point multiplication, is however considered hard. This is the cryptographic hardness assumption that underlies Bitcoin's signature algorithms, ECDSA and Schnorr. If that changes, new cryptography will need to be adopted. If these breakthroughs happen quickly and unexpectedly before migrations can happen, Bitcoin users may be affected.

What if DH exhanges can be decoded almost as fast as they can happen?

Bitcoin doesn't currently use Diffie-Hellman anywhere in the protocol, though BIP324 proposes it for transport encryption. This would be very easy to upgrade, and low impact if broken.

Would bitcoin pay to keep this out of public? (In real money, of course)

Bitcoin is a currency, not an entity that can choose to pay anything, in whatever currency. Hypothetically, some bitcoin users may be incentivized to prevent cryptographic breaks that would affect the system becoming public, but I cannot speak for them.

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  • In your previous answer, are you saying that finding the factors of the product of multiplication is already easy (fast)? This i did not know. Are you saying that it is easy to find the random number used in a modulus operation only using the remainder of the operation? (Not using tables, of course). This i did not know either. That being the case, some of my efforts have been wasted.
    – user143624
    Commented Jul 22, 2023 at 20:39
  • The reverse of multiplication is division, which is easy, yes, even in a modulo setting (look up modular inverse). Factoring is not easy in general, but this is not relevant for any of the cryptographic protocols used in Bitcoin. Commented Jul 22, 2023 at 20:53

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