| public-key cryptography | |
|---|---|
| Name | Public-key cryptography |
| Type | Asymmetric cryptography |
| Invented | 1970s |
| Inventor | Whitfield Diffie and Martin Hellman; developments by Ronald Rivest, Adi Shamir, Leonard Adleman |
| Related | Quantum cryptography, Post-quantum cryptography |
public-key cryptography
Public-key cryptography, also called asymmetric cryptography, is a family of cryptographic algorithms that use paired public keys and private keys to enable secure communication, authentication, and digital signatures without prior shared secrets. In the context of Quantum Physics, public-key systems intersect with quantum computation and quantum information theory because advances in quantum algorithms threaten widely used schemes, while quantum technologies offer new primitives such as quantum key distribution that complement or replace classical asymmetric methods.
Public-key cryptography separates the roles of encryption and decryption into distinct keys: a publicly distributed key for encryption or signature verification and a secret key for decryption or signing. The paradigm was formalized by Whitfield Diffie and Martin Hellman in 1976 and operationalized by the RSA team of Ronald Rivest, Adi Shamir, and Leonard Adleman. Core goals include confidentiality, integrity, authenticity, and non-repudiation. Security assumptions rely on mathematical problems believed hard for classical computers, such as integer factorization and discrete logarithms; these assumptions are evaluated relative to advances in computational complexity theory and the emerging capabilities of quantum computing research programs at institutions like IBM Research, Google Quantum AI, and Microsoft Quantum.
Foundations rest on number theory and algebraic structures: the integer factorization problem underpins RSA, discrete logarithm problems underpin Diffie–Hellman key exchange and ElGamal, and elliptic curve mathematics underpins ECC (e.g., secp256k1). Lattice-based schemes derive from hard problems such as the shortest vector problem (SVP) and learning with errors (LWE), forming the basis of candidates standardized by bodies like the National Institute of Standards and Technology (NIST) for post-quantum cryptography. Hash-based signatures (e.g., XMSS), code-based systems (e.g., McEliece cryptosystem), and multivariate quadratic equation schemes are other mathematically grounded families. The security proofs often rely on reductions to worst-case hardness in number theory and lattice problems and are analyzed under adversary models including chosen-ciphertext attack (CCA) frameworks.
Public-key algorithms are integrated into protocols such as Transport Layer Security (TLS), Secure Shell (SSH), Pretty Good Privacy (PGP/OpenPGP), and X.509 certificate infrastructures. Implementations appear in libraries like OpenSSL, LibreSSL, and BoringSSL, and in hardware such as Trusted Platform Module (TPM) chips and Hardware Security Modules (HSMs) produced by companies like Thales Group and Yubico. Practical deployment requires attention to key generation, entropy sources (e.g., CSPRNGs), side-channel resistance, and certificate lifecycle management via authorities such as Internet Corporation for Assigned Names and Numbers () and standards bodies including the Internet Engineering Task Force (IETF).
Quantum algorithms fundamentally alter threat models: Peter Shor's 1994 algorithm (Shor's algorithm) can factor integers and compute discrete logarithms in polynomial time on a sufficiently large and error-corrected quantum computer, directly compromising RSA and ECC. Grover's algorithm gives a square-root speedup for unstructured search, affecting symmetric-key security parameters. These developments motivated the study of post-quantum migration strategies and the NIST standardization process for quantum-resistant algorithms. Active research programs at Google Quantum AI, IBM Research, D-Wave Systems, and academic groups track physical qubit counts, error rates, and fault-tolerance thresholds needed to execute practical quantum cryptanalysis. Transition efforts must consider interoperability, algorithm agility, and risks from "harvest now, decrypt later" attacks where adversaries store encrypted traffic until quantum capabilities mature.
Quantum-resistant (post-quantum) cryptography comprises classical algorithms believed secure against quantum adversaries; prominent families include lattice-based schemes (e.g., CRYSTALS-Kyber, CRYSTALS-Dilithium), code-based schemes (e.g., Classic McEliece), hash-based signatures (e.g., SPHINCS+), and multivariate approaches. NIST post-quantum cryptography standardization selected algorithms for standardization and ongoing evaluation. Separately, quantum primitives such as quantum key distribution (QKD), developed through protocols like BB84 and E91, rely on quantum mechanics (no-cloning theorem, quantum entanglement) to provide information-theoretic key exchange. Organizations like ID Quantique and research centers such as IQOQI implement QKD experiments and integrated networks (e.g., the SECOQC project). QKD complements but does not universally replace public-key systems, often requiring trusted nodes and specialized photonic hardware.
Public-key cryptography influences and is influenced by quantum technologies across sectors: securing cloud computing and Internet of Things (IoT) devices against future quantum threats; shaping procurement and risk management in financial institutions (e.g., SWIFT messaging); guiding standards in telecommunications (e.g., 5G and beyond); and informing research on quantum-safe consensus for blockchain systems such as Bitcoin. Quantum capabilities also enable novel cryptographic constructs like quantum digital signatures and blind quantum computing where classical public-key ideas integrate with quantum protocols. Policy and governance actors—European Union Agency for Cybersecurity (ENISA), NIST, national labs like Oak Ridge National Laboratory and Los Alamos National Laboratory—coordinate research, standardization, and migration planning to mitigate risks and harness quantum advantages.