cryptography

the science of protecting information and proving statements about it. built on number theory, algebra, and computational complexity. four classical goals: confidentiality, integrity, authentication, non-repudiation. modern cryptography extends these to zero knowledge proofs, homomorphic encryption, and verifiable computation.

crypto/hashing

a hash function maps arbitrary input to a fixed-size digest satisfying preimage resistance, second-preimage resistance, and collision resistance. prominent families: SHA-2, BLAKE3, Poseidon/Poseidon2 (algebraic, ZK-native). cyber uses Hemera (Poseidon2 over Goldilocks field).

crypto/encryption

symmetric encryption (AES, ChaCha20) uses one shared key. asymmetric encryption (ECIES, ML-KEM, CSIDH) uses public/private key pairs. homomorphic encryption (TFHE) computes on ciphertext without decrypting. virtually all real-world systems use hybrid encryption.

crypto/signatures

a digital signature binds a message to a signer. prominent schemes: EdDSA, Schnorr (aggregatable), BLS (cross-message aggregation), SPHINCS+ and ML-DSA (post-quantum). cyber replaces signatures with STARK proofs of Hemera preimage knowledge.

crypto/commitments

bind to a value without revealing it. hash commitments, Pedersen (information-theoretic hiding), KZG (trusted setup), WHIR/FRI (transparent, post-quantum). polynomial commitments — commit to a polynomial, prove evaluations — are the foundation of modern proof systems.

crypto/key-exchange

two parties derive a shared secret over an insecure channel. ECDH (X25519) is the current standard. ML-KEM provides post-quantum security. CSIDH enables non-interactive key exchange for asynchronous systems.

crypto/zero-knowledge

prove a statement without revealing anything beyond its truth. SNARKs (Groth16, PLONK) achieve small proofs with trusted setup. STARKs require no trusted setup and are post-quantum. recursive composition, folding (Nova, HyperNova), incrementally verifiable computation, proof-carrying data, and lookup arguments (LogUp, Lasso) extend the paradigm to scalable verifiable computation.

multi-party computation

n parties jointly compute a function on private inputs. no party learns anything beyond the output. protocols: Yao's garbled circuits (2-party), SPDZ (n-party, malicious security), secret sharing (Shamir, additive). requires an honest majority assumption. see privacy trilateral

crypto/data-structures

data structures with built-in integrity: Merkle trees, NMT, MMR, Verkle trees (vector commitments), hash path accumulators, SWBF, mutator set, EdgeSet, LogUp, LtHash. erasure coding (Reed-Solomon) enables data availability sampling. see storage proofs

crypto/quantum

Shor's algorithm breaks RSA, ECDSA, ECDH. Grover halves symmetric/hash security. NIST PQC standards (2024): ML-KEM (FIPS 203), ML-DSA (FIPS 204), SLH-DSA (FIPS 205). STARKs, symmetric ciphers, and hash functions survive quantum.

cyber's stack

cyber reduces the entire stack to one field, one hash, one VM, one proof system:

field:   Goldilocks (p = 2^64 - 2^32 + 1)
hash:    Hemera (Poseidon2 over Goldilocks) — ~250 constraints
IOP:     SuperSpartan (CCS/AIR via sumcheck) — linear-time prover
PCS:     WHIR (multilinear polynomial commitment) — 290 us verification
VM:      nox (register machine over Goldilocks)

authentication via STARK preimage proofs. encryption via lattice KEM (interactive) and CSIDH (non-interactive). graph state via NMT, MMR, SWBF, EdgeSet, LogUp. domain separation with one function, six roles:

H_edge(x)        = Hemera(0x01 | x)    edge hashing
H_commit(x)      = Hemera(0x02 | x)    record commitments
H_nullifier(x)   = Hemera(0x03 | x)    SWBF index derivation
H_merkle(x)      = Hemera(0x04 | x)    NMT and MMR nodes
H_fiat_shamir(x) = Hemera(0x05 | x)    WHIR challenges
H_transcript(x)  = Hemera(0x06 | x)    proof transcript binding

see cyber/stark, cyber/proofs, BBG, cyber/identity