Codes used once.
In 1949 Claude Shannon proved that a message scrambled with a truly random key, as long as the message and never used again, cannot be broken. Not by guessing, not by any computer, ever. This is the "one-time pad". The catch is that the keys are long and must be handed over in advance.
What it could do here. Keep payment messages private with a guarantee instead of a bet.
Shannon, C. E. (1949). Communication theory of secrecy systems. Bell System Technical Journal, 28(4). doi.org/10.1002/j.1538-7305.1949.tb00928.x
Secrets cut into pieces.
Adi Shamir showed how to split a secret into many pieces so that any agreed number of them can rebuild it, while fewer pieces reveal nothing at all. Not "a little", nothing.
What it could do here. Spread the keys to your money across many guardians, so no single theft or single bad actor is enough.
Shamir, A. (1979). How to share a secret. Communications of the ACM, 22(11). doi.org/10.1145/359168.359176
A seal that shows tampering.
Mark Wegman and Larry Carter found a way to stamp a message so that anyone who changes it gets caught, using a short key shared in advance. The guarantee holds however powerful the attacker's computer is.
What it could do here. Prove a payment really came from you, without a puzzle-based signature.
Wegman, M. N., & Carter, J. L. (1981). New hash functions and their use in authentication and set equality. Journal of Computer and System Sciences, 22(3). doi.org/10.1016/0022-0000(81)90033-7
Signatures without puzzles.
Researchers have built digital signatures whose safety doesn't depend on any hard puzzle. They cost more: bigger keys, more setup, and each person who checks a signature holds a key of their own. A new 2026 paper adapts the idea for shared ledgers run by many guardians.
What it could do here. Sign payments in a way a quantum computer, or a solved puzzle, cannot forge.
Chaum, D., & Roijakkers, S. (1991). Unconditionally-secure digital signatures. Advances in Cryptology, CRYPTO '90. doi.org/10.1007/3-540-38424-3_15
Hanaoka, G., Shikata, J., Zheng, Y., & Imai, H. (2000). Unconditionally secure digital signature schemes admitting transferability. ASIACRYPT 2000. doi.org/10.1007/3-540-44448-3_11
Bagheri, K., Khodaiemehr, H., & Feng, C. (2026). SILMARILS-MV: information-theoretically secure multi-verifier signatures for permissioned blockchains. arxiv.org/abs/2610.31814