Known AttacksKnown Attacks

Summary

Kyber has undergone extensive cryptanalysis since its publication in 2017. As of July 2026, no attack is known that breaks the recommended parameters in practical time. However, attacks exist that reduce the cost, and there are open research lines.

Classical Attacks

Lattice Attacks (BKZ + SVP)

The best known attack against LWE is to solve the underlying lattice problem using the BKZ (Block Korkine-Zolotarev) algorithm with an SVP (Shortest Vector Problem) oracle.

Estimated cost for ML-KEM-768:
  - BKZ with block β ≈ 500
  - Estimated time: > 2²⁰⁷ operations
  - Memory: several TB

Complexity grows exponentially with block size. For Kyber, parameters are chosen so that the required block exceeds any foreseeable practical capacity.

Decision Attacks

An attacker may try to distinguish LWE instances from random ones using statistical techniques. These attacks do not recover the key but can break semantic security.

For Kyber, parameters are chosen so that the distinguisher's advantage is insignificant (< 2⁻¹⁴⁰).

Algebraic Attacks

Some works have explored algebraic attacks exploiting the ring structure (for example, using Gröbner bases). For Module-LWE with Kyber's parameters, no significant cost reduction has been found.

Quantum Attacks

Grover's Attack on the Secret

Grover can search for the secret s in space O(2^(n/2)). For Kyber:

Grover offers a quadratic speedup, but it remains intractable for Kyber's dimensions.

Shor's Algorithm

Shor does not solve LWE. Shor solves the discrete logarithm problem and factoring by exploiting the hidden abelian group structure. LWE over lattices does not have that structure — it is a lattice approximation problem, not a group one.

Regev's Algorithm (quantum)

Regev (2023) proposed a new quantum algorithm that solves LWE in time 2^(n/2) under certain conditions, comparable to the classical BKZ attack but with memory advantages. So far, it has not been shown to outperform classical attacks for Kyber's parameters.

Fourier Attacks

Quantum attacks based on the Fourier transform over lattices (such as Kuperberg's algorithm for isogenies) have no known efficient analog for standard LWE or Module-LWE.

Side-Channel Attacks

Timing

The Kyber reference implementation is constant-time. However, incorrect implementations can leak:

• The secret s through variations in non-constant NTT multiplication
• The value m during decompression if not implemented carefully

Mitigation: use the verified reference implementation or audited libraries (liboqs, AWS-LC, BoringSSL).

Power Consumption / EM

Power analysis attacks (DPA/SPA) can recover s if the device has no countermeasures. Kyber is particularly vulnerable in embedded devices without shielding.

Mitigation: exponent blinding, randomization of NTT operations, signal decoupling.

Fault Attacks

Inducing errors in NTT computation during decapsulation can cause the incorrect result to leak information about s.

Mitigation: redundant verification, error detection in NTT.

Hybrid Attacks

The NSA recommends X25519Kyber768 precisely because no one trusts Kyber alone 100%. An attack that breaks Kyber but not X25519 would still be stopped by the classical layer, and vice versa.

Open Research Lines

Conclusion

Kyber is secure against all known attacks as of July 2026. Its greatest risk is not cryptanalytic but implementation and protocol: a poor implementation or a poorly designed protocol can break security even though the underlying algorithm is sound.

This is no different from classical cryptography. The novelty is that, being newer, it has less cumulative auditing than AES or SHA-3.

References

• Albrecht, M. et al. (2022). "Estimate all the LWE, NTRU schemes!" — Attack cost estimates.
• Regev, O. (2023). "An Efficient Quantum Algorithm for LWE?" — Preprint, open debate.
• Bernstein, D. J. & Lange, T. (2020). "Post-quantum cryptography: handling the fallout."
• Xagawa, K. (2022). "Side-channel attacks on lattice-based KEMs." CHES 2022.