SM2 / SM3 / SM4 / SM9 / ZUC

China's ShangMi (商密) suite of national commercial-cryptography algorithms, summarized with their type, sizes, quantum status, and role. The public-key members (SM2, SM9) are classical and fall to Shor's algorithm. SM3, SM4, and ZUC are hash/symmetric primitives that are not directly broken by Shor the way SM2/SM9 are; quantum attacks show up mainly as a reduced security margin from Grover search and related quantum-collision algorithms, and the mitigation direction is larger keys, longer outputs, or higher-security-level variants.

At a glance

SM2 — elliptic-curve public key

SM2 is a 256-bit elliptic-curve cryptosystem providing public-key encryption, digital signatures, and key exchange. It is the Chinese analogue of ECDSA/ECDH and is widely deployed in TLS, PKI certificates, and electronic signatures. Its security rests on the elliptic-curve discrete logarithm problem — the same foundation as international ECC. A cryptographically relevant quantum computer running Shor's algorithm solves that problem efficiently, so SM2 is fully broken in the quantum era. Substituting SM2 for RSA gains nothing in post-quantum terms.

SM3 — cryptographic hash

SM3 produces a 256-bit digest and serves the same purposes as SHA-256: message integrity, HMAC construction, key derivation, and the hashing step inside signatures. As a hash function it is not broken by quantum computers; Grover's algorithm offers at most a quadratic speedup, reducing the effective collision/preimage margin. Against preimage attacks, 256-bit SM3 corresponds to roughly 128-bit-class security under the Grover model; but collision security cannot simply be equated with 128-bit post-quantum security, and you should distinguish preimage, second-preimage, collision, and signature-hash-binding requirements according to the specific use.

SM4 — block cipher

SM4 is a 128-bit block cipher with a 128-bit key, used for bulk symmetric encryption in TLS cipher suites, disk encryption, and VPNs — the Chinese counterpart to AES. In terms of idealized Grover search complexity, the abstract security margin of a 128-bit symmetric key can be approximately halved; long-term-confidentiality scenarios should therefore consider larger keys or higher-security-level variants. But this is a conservative security-level estimate and does not mean that a real quantum attack is already feasible. For data that must stay confidential for decades, that margin is thinner than ideal; AES-256-class strength has no 128-bit symmetric equivalent in the current SM suite, so long-lived deployments should account for this.

SM9 — identity-based cryptography

SM9 provides identity-based encryption, signatures, and key agreement, deriving keys from identity strings (such as an email address) via bilinear pairings. This removes the need for traditional certificate management. However, pairing-based cryptography is classical — its security reduces to discrete-logarithm-type problems that Shor's algorithm defeats. SM9 is therefore broken in the quantum era, like SM2.

ZUC — stream cipher

ZUC (祖冲之, named for the mathematician Zu Chongzhi) is a 128-bit stream cipher adopted by 3GPP for mobile networks, where it underpins the 128-EEA3 confidentiality and 128-EIA3 integrity algorithms in 4G LTE — renamed 128-NEA3 / 128-NIA3 in 5G NR. As a symmetric primitive it is not broken directly by Shor; under an idealized Grover model the abstract security margin of a 128-bit key can be approximated as halved (a conservative estimate, not a claim that a real attack is feasible). If you are weighing 5G long-lifecycle security, you should also consider the ZUC-256 / 256-bit direction rather than looking only at 128-bit ZUC.

Summary: who falls, who survives

• Broken by Shor (need PQC replacement): SM2, SM9 — the asymmetric/public-key algorithms.
• Weakened by Grover (increase sizes): SM3, SM4, ZUC — the hash and symmetric algorithms.

This is the identical pattern seen in the international suite, and it is why China needs post-quantum cryptography too. For the full threat model see quantum-threat.html; for the Chinese regulatory and migration context see china-overview.html.

Standards & references

• SM2 — GM/T 0003-2012; adopted in ISO/IEC 14888-3:2018.
• SM3 — GM/T 0004-2012; adopted in ISO/IEC 10118-3:2018.
• SM4 — GM/T 0002-2012; adopted in ISO/IEC 18033-3:2010/Amd 1:2021.
• SM9 — GM/T 0044-2016; signature adopted in ISO/IEC 14888-3:2018, identity-based encryption in ISO/IEC 18033-5:2015/Amd 1:2021 (SM9 mechanism), and key agreement in ISO/IEC 11770-3.
• ZUC — GM/T 0001-2012; adopted in ISO/IEC 18033-4:2011/Amd 1:2020.