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Why Quantum Breaks RSA

Interactive comparison: Classical cryptography vs Post-Quantum security

ENVI

Qubit Count

Drag to simulate quantum computer scaling

2,000
logical qubits
10010,000

RSA KEY VULNERABILITY (1/5 broken)

RSA-512
BROKEN
RSA-1024
SAFE
RSA-2048
SAFE
RSA-3072
SAFE
RSA-4096
SAFE
ML-KEM (all levels)
ALWAYS SAFE

No qubit threshold exists — lattice problems have no known efficient quantum solution

Classical RSA / ECC

VULNERABLE

Shor's algorithm uses quantum period-finding to factor large numbers exponentially faster than any classical algorithm. The key step is modular exponentiation in superposition, followed by the QFT. This breaks RSA, whose security relies on the difficulty of factoring.

Quantum circuit diagram with 4 qubit lines and 4 gatesHadamard, Oracle, Inverse QFT, and Measure|0⟩|0⟩|0⟩|0⟩HHHHHadamardU_fU_fU_fU_fOracleQFT†QFT†QFT†QFT†Inverse QFTMMMMMeasure

Enter a number between 2 and 999

ALGORITHM STEPS

Enter a number above to simulate Shor's algorithm

Post-Quantum (ML-KEM)

SECURE

ML-KEM (formerly CRYSTALS-Kyber), standardized in NIST FIPS 203, is based on the MLWE lattice problem. Even quantum computers with Grover's algorithm only achieve a √n speedup — not enough to break it.

Lattice visualization showing the Shortest Vector ProblemA grid of 8×8 points with the closest vector highlighted. 6 quantum search attempts shown, all missing the target — demonstrating that Grover's algorithm only provides square root speedup.closest vectorGrover: √n speedup only

WHY QUANTUM CAN'T BREAK LATTICE

Grover's Algorithm: Only √n speedup

Unlike Shor's exponential speedup for factoring, Grover's search only provides a quadratic advantage. 2^128 → 2^64 operations.

No known quantum algorithm for SVP

The Shortest Vector Problem in high-dimensional lattices has no efficient quantum algorithm — unlike integer factoring.

Noise hides the secret

LWE adds Gaussian noise to lattice computations. Even with quantum superposition, the noise prevents extracting the secret key.

GROVER'S SPEEDUP COMPARISON

Classical brute force2128 ≈ 3.40×1038
Grover's quantum search264 ≈ 1.84×1019

Still 1.8×10^19 operations — completely infeasible even for quantum computers

ML-KEM SECURITY LEVELS

  • ML-KEM-512
    SAFE
  • ML-KEM-768
    SAFE
  • ML-KEM-1024
    SAFE
ML-KEM remains secure at 2,000 qubits

No quantum algorithm can efficiently solve the lattice problem

Ref: NIST FIPS 203 (2024) · Grover (1996) · Regev (2005)

Test Your Knowledge

Question 1 of 8RSA

What mathematical problem does RSA encryption rely on for its security?

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