the binary language. gate semantics over F₂ — the substrate for Boolean logic and any computation whose natural unit is a bit
| Type | Field | Size | Native ops |
|---|---|---|---|
Bit |
F₂ | 1 bit | AND (mul), XOR (add) |
Bit2 |
F₂² | 2 bits | Extension field ops |
Bit8 |
F₂⁸ | 1 byte | AES-native |
Bit32 |
F₂³² | 4 bytes | Hash-native |
Bit64 |
F₂⁶⁴ | 8 bytes | Double word |
Bit128 |
F₂¹²⁸ | 16 bytes | Security parameter |
characteristic: 2. proof system: FRI-Binius. AND is multiplication. XOR is addition. both are free. what Bt cannot do cheaply: integer arithmetic. 3 + 5 = 6 in F₂ (XOR), not 8. to perform actual addition with carry, you must build ripple-carry adders from AND/XOR gates
use cases: Blake3/SHA-256 circuits (proving legacy hashes), Keccak verification (Ethereum bridge), AES circuits, binary Merkle tree verification, binary protocol parsing
see cyb/languages for the complete language set. see cyb/multiproof for the proving architecture