soft3/mudra/specs/seal.md

mudra crypto entity crypto
π 0.0% 405 words · 3 min

seal — encrypt for a recipient

seal a message so only the intended recipient can open it. lattice-based key encapsulation (Module-RLWE). interactive — the receiver publishes a public key, the sender seals a shared secret under it. NIST standardized as ML-KEM (FIPS 203, 2024). post-quantum secure.

interface

keygen() → (SecretKey, PublicKey)
encap(pk: &PublicKey) → (Ciphertext, SharedSecret)
decap(sk: &SecretKey, ct: &Ciphertext) → Result<SharedSecret, DecapError>

algebra

Module-RLWE over Goldilocks field. same field as hemera, nox, zheng — native arithmetic, no conversion.

Ring R = Z_p[x] / (x^64 + 1)       cyclotomic polynomial, degree 64
Module dimension: 4×4 over R
Field: p = 2^64 - 2^32 + 1         Goldilocks

protocol

keygen():
  s ← small_distribution(R^4)       secret key: short vector
  A ← uniform(R^{4×4})              public matrix
  e ← error_distribution(R^4)       noise
  b = A·s + e                       public key: noisy product
  return (sk=s, pk=(A, b))

encap(pk=(A, b)):
  r ← small_distribution(R^4)       ephemeral randomness
  e' ← error_distribution(R^4)
  e'' ← error_distribution(R)
  c1 = A^T · r + e'
  c2 = b^T · r + e'' + encode(shared_secret)
  return ((c1, c2), shared_secret)

decap(sk=s, ct=(c1, c2)):
  shared_secret = decode(c2 - s^T · c1)
  return shared_secret

security assumption: given A and b = A·s + e, recovering s is computationally hard. the error term masks the secret.

parameter sets

set classical security public key ciphertext shared secret
ML-KEM-512 128 bit 800 B 768 B 32 B
ML-KEM-768 192 bit 1184 B 1088 B 32 B
ML-KEM-1024 256 bit 1568 B 1568 B 32 B

comparison with stealth

property seal stealth
interaction interactive (receiver key first) non-interactive (NIKE)
quantum security post-quantum (Module-LWE, proven reduction) conjectured PQ (isogeny)
public key size 800-1568 B 64-256 B
performance fast ~5x slower
standardization NIST FIPS 203 (2024) research

seal handles interactive key exchange. stealth handles non-interactive scenarios (stealth addresses, anonymous channels).

usage in cyber

  • private neuron-to-neuron data: receiver publishes lattice public key as a particle, sender encrypts cyberlink metadata
  • encrypted spell parameters
  • private particle delivery

dependencies

  • nebu: Goldilocks field arithmetic, NTT for polynomial multiplication in R
  • hemera: hash for key derivation (shared secret → symmetric key)

Graph