I have been thinking about a way to create publicly verifiable Bitcoin outputs whose recovery is intentionally tied to breaking a weaker cryptographic system.
The goal is to create a "quantum bounty." The output would be spendable by a valid secp256k1 private key, but the key would be generated in a public ceremony and intentionally limited to 160 bits of entropy. Recovery would additionally be facilitated by publishing an encryption of the same secret under a weaker elliptic curve system. The basic idea is that a group of independent participants runs a distributed key generation ceremony. Each participant contributes a secret share. The shares are combined into a single 160-bit scalar x. At no point is x reconstructed on any machine or revealed to any participant. >From the same distributed shares, participants jointly derive: 1. A Bitcoin public key P = xG on secp256k1. 2. An encryption of x under a separate 160-bit elliptic curve system. The transcript contains all commitments, public contributions, ciphertext contributions, and equality-of-discrete-log proofs needed to verify that both constructions are derived from the same hidden scalar. The construction does not require SNARKs or any trusted setup. It appears sufficient to use Pedersen-style commitments, ElGamal-style encryption, and Chaum-Pedersen proofs showing consistency between participant contributions across the two groups. After the transcript is finalized, participants destroy their secret shares and temporary randomness. Assuming at least one participant behaves honestly and destroys their material, the scalar x is no longer known to anyone. The final artifact consists of: * A Bitcoin public key P. * A weak-curve ciphertext C. * A complete public transcript proving that P and C were derived from the same hidden scalar. Bitcoin can then be sent to the address corresponding to P. Anyone who can recover x from the weak cryptosystem can spend the output. The effective security of the bounty is therefore determined by the weaker curve rather than by the full secp256k1 discrete logarithm problem. The intended purpose is to create a publicly auditable cryptographic canary target. One question I have not fully resolved is whether there are cleaner constructions for the recoverable encryption component than ElGamal-style encryption, while still preserving simple transcript verification and avoiding general-purpose zero-knowledge systems. -- You received this message because you are subscribed to the Google Groups "Bitcoin Development Mailing List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion visit https://groups.google.com/d/msgid/bitcoindev/CAJowKgJVwmm%3Dh6AsO4zeGTmfdK-RUQiDsMJkMRd6WZSo5FjeZg%40mail.gmail.com.
