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If the discrete logarithm problem is broken (either through a mathematical breakthrough or a quantum computer) what are the implications for the history of Monero transactions?

Will past anonymity be broken?

With Tornado Cash (ZKP-based) for example, breaking the discrete logarithm problem will allow to forge proofs and drain the existing fund pools, but anonymity will not be broken.

Also, as an interesting aside, re-implementing Tornado Cash using the FRI protocol (ex. zk-STARK) will be immune to discrete logarithm breaks.

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