 – Boolean circuit Logic Integrated into the Single Key. It's like teaching your public key to understand complex relationship drama, except the drama is your organization's approval hierarchy.

Let's be honest. Threshold signatures are great. They're efficient. They're elegant. They allow the production of a single signature from multiple parties. But they have one critical limitation: they can only count. A 3-of-5 threshold signature says: "I don't care who exactly signs the transaction, as long as 3 of you (5) must do it". But real organizations don't work that way. Real policies look like:

To understand why we provided such examples, try expressing (A ∨ B) ∧ (C ∨ D) with a

-of-n threshold signature. Go ahead, we will wait.

You can't. That's the fundamental limitation. Threshold schemes can express cardinality but not the structure.

bitcoin

> Welcome to [BLISK](https://eprint.iacr.org/2026/088) – Boolean circuit Logic Integrated into the Single Key. It's like teaching your public key to understand complex relationship drama, except the drama is your organization's approval hierarchy.
>
> ## Limitations of Threshold Signatures
>
> Let's be honest. Threshold signatures are great. They're efficient. They're elegant. They allow the production of a single signature from multiple parties. But they have one critical limitation: they can only count. A 3-of-5 threshold signature says: "I don't care who exactly signs the transaction, as long as 3 of you (5) must do it". But real organizations don't work that way. Real policies look like:
>
> - the CEO OR the CFO must approve, AND at least one board member
> - two executives AND compliance officer AND (legal OR counsel officer)
> - Carol can send the payment if (Alice OR Bob) approves*
> - …
>
>> *Carol is a 6-year-old child of Alice and Bob, so we need to be careful about her desires. At the same time, Bob shouldn't be able to cooperate with Alice and pay for the dentist's services instead of the pink unicorn without Carol's approval.
>
> To understand why we provided such examples, try expressing (A ∨ B) ∧ (C ∨ D) with a 
-of-n threshold signature. Go ahead, we will wait.
>
> [elevator music plays]
>
> You can't. That's the fundamental limitation. Threshold schemes can express cardinality but not the structure.
>
>>  We will use a Boolean circuit with OR (∨) and AND(∧) gates as a method to express the policy. Sometimes we will use (and draw) trees instead of the circuit, but note that it's the same.
>
> [**...read more at hackmd.io**](https://hackmd.io/@olkurbatov/HJm5h0JH-l)

https://delvingbitcoin.org/t/blisk-boolean-circuit-logic-integrated-into-the-single-key/2217

Limitations of Threshold SignaturesLimitations of Threshold Signatures