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

CC BY-SA 4.0
2023-07-22T20:53:59.277Z
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.
Pieter Wuille
CC BY-SA 4.0
2023-07-22T16:32:13.540Z
2023-07-22T19:06:08.310Z
2023-07-22T19:06:08.310Z
Pieter Wuille
<p>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)</p>

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

(Asked by: username_0 on 2023-07-22)

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)

**Tags:** math


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## 1 answers

### Answer by username_1 on 2023-07-22. Score: 3

> 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.

> **Comments:**
> **username_1**: 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.  

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