Posted by conduition
Jun 5, 2026/23:46 UTC
Exploring the potential interactions between quantum adversaries and cryptographic systems, an intriguing method is proposed that leverages inherent capabilities of such adversaries to authenticate their prowess without necessitating Zero-Knowledge (ZK) protocols. Specifically, a scenario is described where a quantum adversary could be challenged to compute the discrete logarithm of a point on a cryptographic curve. This computation involves a scalar ( k ) and a preimage ( x ), with verification following the equation ( K = k*G = HashToCurve(x) ). This approach simplifies the interaction by eliminating the need for complex ZK machinery commonly used in these contexts.
However, the proposal also acknowledges the risk of collision attacks where a classical prover might find a collision across all ( (x, k) ) pairs, particularly on a 160-bit curve. To mitigate this, it is suggested to fix ( x ) as a constant within the proof system, thereby reducing the feasibility of such attacks. This entire process would occur off-chain, thus avoiding complications involving Bitcoin Improvement Proposals (BIPs) or Unspent Transaction Outputs (UTXOs).
In situations where a quantum adversary demands compensation for providing such cryptographic proofs, Zero-Knowledge Contingent Payments (ZKCPs) are recommended as a viable solution. The discussion reflects skepticism regarding the practicality of such demands from quantum adversaries, suggesting instead that a self-interested quantum computer (QC) might prefer to wait until it can directly compromise cryptographic keys, such as those based on the secp256k1 algorithm, to misappropriate digital assets covertly.
TLDR
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