Post-quantum cryptography (PQC), sometimes referred to as quantum-proof, quantum-safe, or quantum-resistant, is the development of cryptographic algorithms (usually public-key algorithms) that are currently thought, but not proven, to be secure against a cryptanalytic attack by a quantum computer. Most widely used public-key algorithms rely on the difficulty of one of three mathematical problems: the integer factorization problem, the discrete logarithm problem, or the elliptic-curve discrete logarithm problem. All of these problems could be easily solved on a sufficiently powerful quantum computer running Shor's algorithm or possibly alternatives. As of 2026, quantum computers lack the processing power to break widely used cryptographic algorithms; however, because of the length of time required for migration to quantum-safe cryptography, cryptographers are already designing new algorithms to prepare for Y2Q or "Q-Day", the day when current algorithms will be vulnerable to quantum computing attacks. Mosca's theorem provides the risk analysis framework that helps organizations identify how quickly they need to start migrating. Their work has gained attention from academics and industry through the PQCrypto conference series hosted since 2006, several workshops on Quantum Safe Cryptography hosted by the European Telecommunications Standards Institute (ETSI), and the Institute for Quantum Computing. The rumoured existence of widespread harvest now, decrypt later programs has also been seen as a motivation for the early introduction of post-quantum algorithms, as data recorded now may still remain sensitive many years into the future. In contrast to the threat quantum computing poses to current public-key algorithms, most current symmetric cryptographic algorithms and hash functions are considered to be relatively secure against attacks by quantum computers. While the quantum Grover's algorithm does speed up attacks against symmetric ciphers, doubling the key size can effectively counteract these attacks. Thus post-quantum symmetric cryptography does not need to differ significantly from current symmetric cryptography. In 2024, the U.S. National Institute of Standards and Technology (NIST) released final versions of its first three Post-Quantum Cryptography Standards.
Preparation Digital infrastructures require robust cybersecurity. Cryptographic systems are vital to protect the confidentiality and authenticity of data. Quantum computing will be a threat to many of the classical cryptographic algorithms, which are used to achieve these protection goals but are only secure against classical computers. Data that is currently not quantum-safe, whether it is stored or transmitted, and that must remain confidential for a long time, may be compromised in the future by quantum computers ("harvest now, decrypt later" attacks). In addition, authenticity will also be jeopardised by quantum computers. The threat that quantum computing poses to cybersecurity can be countered by a timely, comprehensive and coordinated transition to post-quantum cryptography (PQC).
Algorithms Post-quantum cryptography research is mostly focused on six different approaches:
Lattice-based cryptography
This approach includes cryptographic systems such as learning with errors, ring learning with errors (ring-LWE), the ring learning with errors key exchange and the ring learning with errors signature, the older NTRU or GGH encryption schemes, and the newer NTRU signature and BLISS signatures. Some of these schemes like NTRU encryption have been studied for many years without anyone finding a feasible attack. Others like the ring-LWE algorithms have proofs that their security reduces to a worst-case problem. The Post-Quantum Cryptography Study Group sponsored by the European Commission suggested that the Stehle–Steinfeld variant of NTRU be studied for standardization rather than the NTRU algorithm. At that time, NTRU was still patented. Studies have indicated that NTRU may have more secure properties than other lattice based algorithms. Two lattice-based algorithms, ML-KEM (commonly known as Kyber) and ML-DSA (commonly known as Dilithium) were among the first post-quantum algorithms standardised by NIST.
Multivariate cryptography
This includes cryptographic systems such as the Unbalanced Oil and Vinegar signature scheme which is based on the difficulty of solving systems of multivariate equations. Various attempts to build secure multivariate equation encryption schemes have been broken, notably the Rainbow signature.
Hash-based cryptography
This includes cryptographic systems such as Lamport signatures, the Merkle signature scheme, the XMSS, the SPHINCS, the WOTS and the SPHINCS+ schemes. Hash based digital signatures were invented in the late 1970s by Ralph Merkle and have been studied ever since as an interesting alternative to number-theoretic digital signatures like RSA and DSA. Their primary drawback is that for any hash-based public key, there is a limit on the number of signatures that can be signed using the corresponding set of private keys. This fact reduced interest in these signatures until interest was revived due to the desire for cryptography that was resistant to attack by quantum computers. There appear to be no patents on the Merkle signature scheme and there exist many non-patented hash functions that could be used with these schemes. The stateful hash-based signature scheme XMSS developed by a team of researchers under the direction of Johannes Buchmann is described in RFC 8391. Note that all the above schemes are one-time or bounded-time signatures. Moni Naor and Moti Yung invented UOWHF hashing in 1989 and designed a signature based on hashing (the Naor-Yung scheme) which can be unlimited-time in use (the first such signature that does not require trapdoor properties).
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