Encryption Key Strength Estimator
Estimates the effective security strength of encryption keys based on algorithm type, key length, and resistance to known attacks. Uses NIST SP 800-57 guidelines and current cryptanalytic estimates.
Formulas Used
Symmetric (AES, ChaCha20):
Security bits = Key length (k). Full key-space exhaustion requires 2k operations.
Quantum (Grover): Effective bits = k / 2
RSA / Diffie-Hellman:
Security governed by GNFS complexity: L[n, 1/3, 1.923] = e(1.923 + o(1))(ln n)1/3(ln ln n)2/3
NIST SP 800-57 Table 2 mapping: 2048-bit RSA ≈ 112-bit symmetric strength.
Quantum (Shor): Polynomial time → 0 effective bits.
Elliptic Curve Cryptography (ECC):
Security bits = k / 2 (Pollard-rho attack on ECDLP: O(√(2k)) = O(2k/2))
Quantum (Shor for ECDLP): Polynomial time → 0 effective bits.
Hash Functions:
Collision resistance: n/2 bits (birthday attack: O(2n/2))
Preimage resistance: n bits
Quantum collision (BHT): n/3 bits — O(2n/3)
Quantum preimage (Grover): n/2 bits
Time-to-Break Model:
Baseline (2024): ~260 operations/year at nation-state budget ($1B compute cluster).
Moore's Law adjustment: +0.5 bits/year effective gain.
Remaining security margin = Effective bits − (60 + 0.5 × years ahead)
Assumptions & References
- Keys are assumed to be truly random (full entropy). Weak key generation reduces effective strength significantly.
- Security strength values follow NIST SP 800-57 Part 1 Rev 5 (2020) recommendations.
- RSA/DH security mapping uses NIST Table 2: 1024-bit ≈ 80-bit, 2048-bit ≈ 112-bit, 3072-bit ≈ 128-bit, 7680-bit ≈ 192-bit, 15360-bit ≈ 256-bit.
- ECC Pollard-rho complexity: O(√n) group operations where n is the curve order ≈ 2k.
- Quantum threat model uses Grover's algorithm (symmetric/hash) and Shor's algorithm (RSA/ECC) per NIST IR 8105.
- The BHT quantum collision algorithm (Brassard, Høyer, Tapp 1997) gives O(2n/3) for hash collisions.
- Moore's Law doubling assumed every ~2 years (0.5 bits/year effective compute gain); this is conservative given recent slowdowns.
- Nation-state compute baseline (~260 ops/year) based on estimates from academic literature and NSA guidance.
- NIST recommends a minimum of 112-bit security through 2030 and 128-bit beyond.
- Post-quantum safe algorithms (CRYSTALS-Kyber, CRYSTALS-Dilithium) are not modeled here; see NIST PQC standards (FIPS 203/204/205).
- References: NIST SP 800-57 Rev 5; NIST IR 8105; Lenstra & Verheul (2001); BSI TR-02102; ECRYPT-CSA D5.4.