Shor’s Algorithm
Factors integers and solves discrete logarithms in polynomial time — the exact hardness RSA, ECC, and ECDH are built on.
EndsRSAECCECDH
01 · Schemes9 cryptosystems · 2 quantum attacks
The Field
Keystone captures nine cryptosystems across the line quantum computing draws through them. Four classical schemes rest on factoring and discrete logarithms — the structure Shor’s algorithm dismantles. Five post-quantum schemes rest on lattices, hashes, and codes, where no efficient quantum attack is known.
Classical
In wide use today, and the schemes a quantum computer is built to undo.
RSApublic-keyEncryption & signaturesInteger factoringRisk · Shor's
ECCECDSASignaturesElliptic-curve discrete logRisk · Shor's
ECDHEC Diffie–HellmanKey exchangeElliptic-curve discrete logRisk · Shor's
AESFIPS 197Symmetric cipherBrute-force key searchHalved · Grover's
Post-quantum
The standardized and candidate replacements Keystone benchmarks against the classical baseline.
KyberML-KEM · FIPS 203Key encapsulationModule lattices (LWE)Resistant
DilithiumML-DSA · FIPS 204SignaturesModule lattices (SIS/LWE)Resistant
FalconFN-DSASignaturesNTRU latticesResistant
SPHINCS+SLH-DSA · FIPS 205SignaturesHash preimage resistanceResistant
Classic McElieceround-4 KEMKey encapsulationSyndrome decodingResistant
02 · Attacksbounded-error quantum polynomial time
Grover’s Algorithm
Searches unstructured space in roughly the square root of the steps, halving the effective strength of a symmetric or hash-based key.
HalvesAEShash strength