{
  "hardware": {
    "platform": "macOS-15.5-arm64-arm-64bit-Mach-O",
    "cpu": "arm",
    "python": "3.13.3"
  },
  "security_estimation": {
    "encryption": {
      "classical_beta": 112,
      "quantum_beta": 112,
      "classical_bits": 32.7,
      "quantum_bits": 29.7,
      "optimal_d": 513
    },
    "signature_forgery": {
      "classical_bits": 11.7,
      "quantum_bits": 10.6,
      "optimal_d": 257,
      "classical_beta_bkz": 40
    },
    "signature_key_recovery": {
      "classical_beta": 40,
      "quantum_beta": 40,
      "classical_bits": 11.7,
      "quantum_bits": 10.6,
      "optimal_d": 257
    },
    "methodology": "Primal uSVP attack, Core-SVP cost model (Becker et al. 2016)",
    "delta_model": "Chen-Nguyen 2011",
    "classical_cost_formula": "T = 2^(0.292 * \u03b2)",
    "quantum_cost_formula": "T = 2^(0.265 * \u03b2)"
  },
  "decryption_failure": {
    "noise_stddev_per_coeff": 362.06,
    "threshold_q_over_4": 6148.25,
    "log2_p_fail_single_coeff": -207.0,
    "log2_p_fail_total": -198.0,
    "p_fail_bound": "2^{-198.0}",
    "safe": true
  },
  "sizes_bytes": {
    "PQIE Public Key (t)": 512,
    "PQIE Secret Key (s)": 256,
    "PQIE Public Seed (a)": 32,
    "PQIE Total PK (seed+t)": 544,
    "PQIE Signature (z)": 1024,
    "PQIE Signature (c_seed)": 64,
    "PQIE Signature (total raw)": 1088,
    "PQIE Signature (JSON+b64)": 1535,
    "DID Document (pretty JSON)": 4845,
    "DID Document (compact JSON)": 4489,
    "DID String": 58,
    "Ring-LWE Hash Output (h1)": 4,
    "Ring-LWE Hash Output (h2)": 4,
    "Ed25519 Public Key": 32,
    "Ed25519 Signature": 64,
    "secp256k1 Public Key": 33,
    "ECDSA Signature": 65
  },
  "benchmarks": {
    "Ring-LWE Transform (NTT+SHA3)": {
      "mean_ms": 9.908,
      "median_ms": 9.571,
      "min_ms": 9.422,
      "max_ms": 32.475,
      "stdev_ms": 2.369,
      "n": 100
    },
    "PQIE KeyGen": {
      "mean_ms": 0.283,
      "median_ms": 0.279,
      "min_ms": 0.277,
      "max_ms": 0.417,
      "stdev_ms": 0.015,
      "n": 100
    },
    "DID Generation (single)": {
      "mean_ms": 0.015,
      "median_ms": 0.014,
      "min_ms": 0.014,
      "max_ms": 0.074,
      "stdev_ms": 0.006,
      "n": 100
    },
    "DID Document Generation": {
      "mean_ms": 12.36,
      "median_ms": 11.833,
      "min_ms": 10.747,
      "max_ms": 18.35,
      "stdev_ms": 1.741,
      "n": 100
    },
    "PQIE Sign": {
      "mean_ms": 2.486,
      "median_ms": 1.743,
      "min_ms": 0.907,
      "max_ms": 13.997,
      "stdev_ms": 2.166,
      "n": 100
    },
    "PQIE Verify": {
      "mean_ms": 0.6,
      "median_ms": 0.592,
      "min_ms": 0.587,
      "max_ms": 0.684,
      "stdev_ms": 0.02,
      "n": 100
    },
    "DID Doc Verify": {
      "mean_ms": 0.603,
      "median_ms": 0.599,
      "min_ms": 0.593,
      "max_ms": 0.661,
      "stdev_ms": 0.013,
      "n": 100
    },
    "E2E DID Create (keygen+sign+doc)": {
      "mean_ms": 12.053,
      "median_ms": 11.651,
      "min_ms": 10.753,
      "max_ms": 32.303,
      "stdev_ms": 2.363,
      "n": 100
    },
    "Ed25519 KeyGen (literature)": {
      "mean_ms": 0.03,
      "stdev_ms": 0.005,
      "note": "libsodium, x86-64"
    },
    "Ed25519 Sign (literature)": {
      "mean_ms": 0.05,
      "stdev_ms": 0.005,
      "note": "libsodium, x86-64"
    },
    "Ed25519 Verify (literature)": {
      "mean_ms": 0.12,
      "stdev_ms": 0.01,
      "note": "libsodium, x86-64"
    },
    "ECDSA-secp256k1 Sign (lit.)": {
      "mean_ms": 0.04,
      "stdev_ms": 0.005,
      "note": "libsecp256k1"
    },
    "ECDSA-secp256k1 Verify (lit.)": {
      "mean_ms": 0.08,
      "stdev_ms": 0.01,
      "note": "libsecp256k1"
    },
    "Service Token Gen": {
      "mean_ms": 0.147,
      "median_ms": 0.133,
      "min_ms": 0.13,
      "max_ms": 1.006,
      "stdev_ms": 0.088,
      "n": 100
    },
    "DID Resolution (cross-chain)": {
      "mean_ms": 1.499,
      "median_ms": 1.448,
      "min_ms": 1.4,
      "max_ms": 5.288,
      "stdev_ms": 0.386,
      "n": 100
    }
  },
  "generated_at": "2026-06-09T08:29:57.176149Z"
}