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"""Receipts, revocations, levels, spot-check sampling and reviewer error bounds.
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Non-normative; see spec/08-fidelity.md.
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"""
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import base64
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import binascii
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import hashlib
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import math
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from fractions import Fraction
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from math import comb
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from . import crypto, jcs, mldsa, vrf
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from .model import LEVELS
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from .text import record_id, sha256_hex
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SIGNED_FORMATS = ("scienting-receipt/1", "scienting-revocation/1", "scienting-policy/1", "scienting-qa-report/1")
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def record_hash(rec):
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"""SHA-256 of the canonical JSON of a signed record without its `id` and `signature`."""
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return sha256_hex(jcs.dumpb({k: v for k, v in rec.items() if k not in ("id", "signature")}))
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def signing_payload(rec):
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return jcs.dumpb({"format": rec["format"], "hash": record_hash(rec)})
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def seal(rec, secret, key_id):
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"""Fill in a record's root (for receipts), ID and Ed25519 signature."""
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rec = dict(rec)
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if rec["format"] == "scienting-receipt/1":
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rec["root"] = crypto.merkle_root(crypto.receipt_items(rec))
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rec.pop("id", None)
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rec.pop("signature", None)
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sig = crypto.ed25519_sign(secret, signing_payload(rec))
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rec["id"] = record_id(record_hash(rec))
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rec["signature"] = {"scheme": "ed25519", "key": key_id, "value": base64.b64encode(sig).decode("ascii")}
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return rec
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def _b64(s):
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"""Strict Base64 decoding; None for anything that is not Base64."""
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try:
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return base64.b64decode(s, validate=True)
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except (binascii.Error, ValueError, TypeError):
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return None
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def verify_signature(rec, roster):
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"""Whether the record's signature verifies under the roster key it names, for the schemes the tools implement
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(`ed25519` and `ml-dsa-65`); any other scheme does not verify. Never raises."""
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sig = rec.get("signature") or {}
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if not isinstance(sig, dict):
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return False
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key = roster.get(sig.get("key"))
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if not key or sig.get("scheme") != key.get("scheme"):
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return False
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pub, value = _b64(key.get("public", "")), _b64(sig.get("value", ""))
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if pub is None or value is None:
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return False
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try:
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if sig["scheme"] == "ed25519":
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return len(pub) == 32 and len(value) == 64 and crypto.ed25519_verify(pub, signing_payload(rec), value)
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if sig["scheme"] == "ml-dsa-65":
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return mldsa.verify(pub, signing_payload(rec), value)
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except (ValueError, TypeError):
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return False
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return False
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def seal_mldsa(rec, sk, key_id):
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"""Fill in a record's root (for receipts), ID and ML-DSA-65 signature, deterministically."""
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rec = dict(rec)
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if rec["format"] == "scienting-receipt/1":
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rec["root"] = crypto.merkle_root(crypto.receipt_items(rec))
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rec.pop("id", None)
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rec.pop("signature", None)
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sig = mldsa.sign(sk, signing_payload(rec))
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rec["id"] = record_id(record_hash(rec))
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rec["signature"] = {"scheme": "ml-dsa-65", "key": key_id, "value": base64.b64encode(sig).decode("ascii")}
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return rec
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def key_valid_at(key, at):
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return key["registered_at"] <= at and (key.get("revoked_at") is None or at < key["revoked_at"])
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# --- spot-checks --------------------------------------------------------------
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def seed_payload(receipt):
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return jcs.dumpb({"format": "scienting-spot-check/1", "receipt": record_hash(receipt)})
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def make_seed(receipt, checker_secret):
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"""The seed: the checker's VRF proof (RFC 9381, ECVRF-EDWARDS25519-SHA512-TAI) for the receipt's payload."""
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return vrf.prove(checker_secret, seed_payload(receipt))
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def sample_size(n, rate="0.05", minimum=10):
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return min(n, max(minimum, math.ceil(Fraction(rate) * n)))
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def sample(receipt, seed, rate="0.05", minimum=10):
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"""The sample a seed selects: ranked by SHA-256 of the proof's VRF output followed by the node ID."""
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beta = vrf.proof_to_hash(seed)
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if beta is None:
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raise ValueError("the seed is not a VRF proof")
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ids = [nid for nid, _ in receipt["nodes"]]
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m = sample_size(len(ids), rate, minimum)
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ranked = sorted(ids, key=lambda nid: (hashlib.sha256(beta + nid.encode("utf-8")).hexdigest(), nid))
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return sorted(ranked[:m])
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def upper_bound(k, n, confidence="0.95"):
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"""One-sided Clopper-Pearson upper bound on an error rate, as a float."""
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if n <= 0:
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raise ValueError("n must be positive")
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if k >= n:
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return 1.0
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alpha = 1.0 - float(Fraction(confidence))
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def cdf(p):
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if p <= 0:
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return 1.0
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if p >= 1:
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return 0.0
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lp, lq = math.log(p), math.log1p(-p)
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total = 0.0
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for i in range(k + 1):
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total += math.exp(math.lgamma(n + 1) - math.lgamma(i + 1) - math.lgamma(n - i + 1) + i * lp
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+ (n - i) * lq)
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return total
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lo, hi = 0.0, 1.0
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for _ in range(200):
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mid = (lo + hi) / 2
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if cdf(mid) > alpha:
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lo = mid
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else:
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hi = mid
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return hi
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def bound_string(k, n, confidence="0.95"):
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"""The bound as the spec reports it: six decimal places, rounded up, computed exactly.
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The reported value is the least multiple of 10^-6 at which the probability of at most k errors in n is
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at most 1 - c, found by bisection with integer arithmetic, so no floating point enters the result.
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"""
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if n <= 0:
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raise ValueError("n must be positive")
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if k >= n:
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return "1.000000"
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alpha = 1 - Fraction(confidence)
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scale = 10**6
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def tail_at_most(m):
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# P[X <= k] at p = m / scale, compared with alpha, both scaled by scale**n and alpha's denominator.
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total = sum(comb(n, i) * m**i * (scale - m)**(n - i) for i in range(k + 1))
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return total * alpha.denominator <= alpha.numerator * scale**n
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lo, hi = 0, scale # the tail at 0 is 1 (above alpha); at 1 it is 0 (k < n)
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while hi - lo > 1:
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mid = (lo + hi) // 2
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if tail_at_most(mid):
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hi = mid
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else:
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lo = mid
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return "%d.%06d" % (hi // scale, hi % scale)
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# --- levels -------------------------------------------------------------------
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def revoked(receipt, revocations):
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for r in revocations:
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if r.get("receipt") == receipt["id"]:
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return True
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if r.get("signer") == receipt["by"] and r.get("period"):
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p = r["period"]
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if p["from"] <= receipt["at"] <= p["to"]:
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return True
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return False
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def valid_revocations(revocations, receipts_by_id, roster):
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"""The revocations signed by the receipt's signer, the signer they name, or a key the roster makes an owner."""
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owners = {k for k, v in roster.items() if v.get("role") == "owner"}
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out = []
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for r in revocations:
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if not verify_signature(r, roster):
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continue
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signer = r["signature"]["key"]
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allowed = set(owners)
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if r.get("receipt") in receipts_by_id:
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allowed.add(receipts_by_id[r["receipt"]]["by"])
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if r.get("signer"):
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allowed.add(r["signer"])
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if signer in allowed:
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out.append(r)
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return out
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def _base_status(rec, roster, valid_revs):
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"""`invalid`, `revoked` or `valid` for one receipt, before spot-checks are considered (spec/08 §8.6)."""
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try:
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if rec.get("root") != crypto.merkle_root(crypto.receipt_items(rec)):
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return "invalid"
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if rec["id"] != record_id(record_hash(rec)) or not verify_signature(rec, roster):
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return "invalid"
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key = roster.get(rec["by"])
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if not key or not key_valid_at(key, rec["at"]) or rec["signature"]["key"] != rec["by"]:
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return "invalid"
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except (KeyError, TypeError, ValueError):
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return "invalid"
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return "revoked" if revoked(rec, valid_revs) else "valid"
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def statuses(records, roster):
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"""The status of every receipt in `records` (spec/08 §8.6), computed once.
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A receipt is suspended when a valid spot-check of it found an error, and a spot-check's own validity may
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depend on its own spot-check, so statuses are settled from the end of each chain of spot-checks; a chain
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that loops back on itself settles nothing, and its receipts are invalid.
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"""
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receipts = [x for x in records if x.get("format") == "scienting-receipt/1"]
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revs = [x for x in records if x.get("format") == "scienting-revocation/1"]
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by_id = {x["id"]: x for x in receipts}
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valid_revs = valid_revocations(revs, by_id, roster)
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base = {rec["id"]: _base_status(rec, roster, valid_revs) for rec in receipts}
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checkers = {}
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for q in receipts:
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qa = q.get("qa")
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if isinstance(qa, dict) and qa.get("errors") and base.get(q["id"]) == "valid" and qa.get("of") in by_id:
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checkers.setdefault(qa["of"], []).append(q["id"])
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final = {rid: s for rid, s in base.items() if s != "valid" or rid not in checkers}
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pending = set(base) - set(final)
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progress = True
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while pending and progress:
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progress = False
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for rid in sorted(pending):
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qs = checkers[rid]
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if all(q in final for q in qs):
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final[rid] = "suspended" if any(final[q] == "valid" for q in qs) else "valid"
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pending.discard(rid)
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progress = True
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for rid in pending:
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final[rid] = "invalid"
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return final
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def receipt_status(rec, records, roster):
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"""`valid`, `revoked`, `suspended`, or `invalid` for one receipt among `records`."""
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return statuses(records, roster).get(rec.get("id"), "invalid")
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def effective_levels(nodes, values, records, roster):
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"""Every leaf's level: its recorded level, raised by valid receipts that list it at its current hash.
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A spot-check's `qa:` receipt does not raise the nodes it found in error (spec/08 §8.2).
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"""
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level = {n["id"]: n.get("fidelity") for n in nodes if "fidelity" in n}
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status = statuses(records, roster)
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for rec in records:
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if rec["format"] != "scienting-receipt/1":
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continue
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if status.get(rec["id"]) != "valid":
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continue
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wrong = {e["node"] for e in (rec.get("qa") or {}).get("errors", [])}
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for nid, h in rec.get("nodes", []):
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if nid in level and nid not in wrong and values[nid]["node_hash"] == h:
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if LEVELS.index(rec["level"]) > LEVELS.index(level[nid]):
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level[nid] = rec["level"]
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return level
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def distribution(levels):
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counts = {lv: 0 for lv in LEVELS}
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for lv in levels.values():
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counts[lv] += 1
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lowest = next((lv for lv in LEVELS if counts[lv]), None)
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return {"lowest": lowest, "counts": counts}
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