Expert technical analysis on quantum computing, post-quantum cryptography, and quantum-safe infrastructure for Ireland and the EU.
Compiled by Michael English, Co-Founder & CTO of IMPT.io
Reference Guide for Irish and EU Technology Professionals
Meta Description: Comprehensive quantum computing and post-quantum cryptography glossary by Michael English (IMPT.io). 60+ terms explained for Irish and EU tech professionals and business leaders.
Target Keywords: quantum computing glossary Ireland, post-quantum cryptography terms, quantum security definitions, PQC terminology EU, quantum computing dictionary Michael English
Account Abstraction (ERC-4337): An Ethereum standard that decouples account addresses from signing keys, enabling flexible authentication including post-quantum signature schemes. Critical for blockchain quantum migration.
Ajtai Reduction: A mathematical proof by Miklós Ajtai (1996) showing that random instances of lattice problems are as hard as worst-case instances, providing a foundation for lattice-based cryptography security proofs.
Approximate Shortest Vector Problem (ASVP): A relaxation of SVP asking for a vector within a factor γ of the shortest vector. ASVP with super-polynomial approximation factor is believed to be quantum-hard and underlies LWE security.
Asymmetric Cryptography: Cryptography using key pairs (public key + private key) where the public key can be freely shared. All current asymmetric cryptography (RSA, ECC) is quantum-vulnerable. See: Post-Quantum Cryptography.
BIKE (Bit Flipping Key Encapsulation): A code-based post-quantum KEM based on quasi-cyclic moderate-density parity-check (QC-MDPC) codes. NIST alternate candidate for standardisation.
BKZ (Block Korkine-Zolotarev): The best classical lattice basis reduction algorithm for attacking LWE-based cryptography. BKZ with block size β has complexity ≈ 2^(0.292β) — exponential, not polynomial.
Blockchain Quantum Vulnerability: All blockchain networks using ECDSA transaction signing (Bitcoin, Ethereum, most Layer-1 networks) are vulnerable to a CRQC via Shor's algorithm. Accounts with revealed public keys (after first outgoing transaction) are directly vulnerable.
BLS Signatures: Boneh-Lynn-Shacham signatures using pairing-based cryptography over elliptic curves. Used in Ethereum 2.0 validator signing. Vulnerable to Shor's algorithm via the ECDLP in the pairing groups.
CA/Browser Forum (CABF): The industry consortium of Certificate Authorities and browser vendors that sets standards for TLS certificates. CABF will publish post-quantum certificate policy timelines that determine when PQC certificates become browser-trusted.
Certificate Authority (CA): An entity that issues digital certificates binding public keys to identities. CA root keys are high-priority targets for quantum migration due to their 20+ year validity periods.
Classic McEliece: The oldest post-quantum public-key encryption scheme (1978), based on the hardness of decoding random Goppa codes. Extremely large public keys (255 KB–1.3 MB) but near-50-year security track record. NIST alternate standard.
Closest Vector Problem (CVP): A computational problem on lattices: given a lattice Λ and a target point t, find the lattice point closest to t. NP-hard in general; closely related to LWE security.
Code-Based Cryptography: Post-quantum cryptographic schemes based on the hardness of decoding random linear error-correcting codes. McEliece, BIKE, and HQC are code-based.
CNSA Suite 2.0 (Commercial National Security Algorithm Suite): NSA's updated cryptographic requirements for US National Security Systems, mandating PQC adoption by 2025–2033. Globally influential as a migration benchmark.
CORSIA: Carbon Offsetting and Reduction Scheme for International Aviation. Not quantum-related; see Carbon Credits Glossary.
CRQC (Cryptographically Relevant Quantum Computer): A quantum computer capable of executing Shor's algorithm at sufficient scale to break RSA-2048 or ECDH P-256 within hours to days. Current estimates require ~20 million physical qubits (at 0.1% gate error rate).
CRYSTALS: Cryptographic Suite for Algebraic Lattices. The umbrella name for CRYSTALS-Kyber (now ML-KEM, FIPS 203) and CRYSTALS-Dilithium (now ML-DSA, FIPS 204).
Cryptographic Agility: The architectural property of a system allowing cryptographic algorithms to be updated without fundamental redesign. Essential for post-quantum migration compliance under DORA and NIS2.
Cryptographic Inventory: A comprehensive catalogue of all asymmetric cryptographic operations in an organisation's systems. The prerequisite for any quantum-safe migration programme.
Decision LWE: The problem of distinguishing LWE samples (A, As+e) from uniformly random samples. Equivalent to Search LWE in difficulty; the foundation of IND-CPA security proofs for ML-KEM.
Dilithium: Previous name for CRYSTALS-Dilithium, now standardised as ML-DSA (Module Lattice-based Digital Signature Algorithm) under NIST FIPS 204.
DORA (Digital Operational Resilience Act): EU Regulation 2022/2554 requiring financial entities to implement robust ICT risk management including cryptographic agility and quantum risk assessment. In force from January 2025.
Discrete Logarithm Problem (DLP): The mathematical problem underlying ECC (ECDSA, ECDH): given g and g^x in a group, find x. Solvable in polynomial time by quantum computers using Shor's algorithm.
ECC (Elliptic Curve Cryptography): Public-key cryptography based on the algebraic structure of elliptic curves over finite fields. Broken by Shor's algorithm via ECDLP. Widely used as ECDSA (signatures) and ECDH (key exchange).
ECDH (Elliptic Curve Diffie-Hellman): The most common key exchange protocol for TLS. Uses ECC to establish a shared secret. Quantum-vulnerable; must be replaced with ML-KEM in post-quantum migration.
ECDLP (Elliptic Curve Discrete Logarithm Problem): The problem underlying ECC security. Solvable by Shor's algorithm on a quantum computer with approximately 2,330 logical qubits for P-256.
ECDSA (Elliptic Curve Digital Signature Algorithm): The most widely deployed digital signature algorithm (used in TLS, SSH, blockchain, code signing). Quantum-vulnerable; must be replaced with ML-DSA or FALCON.
ENISA (European Union Agency for Cybersecurity): EU agency responsible for cybersecurity guidance across the Union. Has published Post-Quantum Cryptography integration studies and recommendations aligned with NIST standards.
EuroQCI (European Quantum Communication Infrastructure): An EU initiative to deploy Quantum Key Distribution (QKD) infrastructure across all 27 member states, enabling provably secure government communications.
EU Quantum Flagship: The EU's 10-year, €1 billion quantum technology investment programme launched in 2018, covering quantum computing, communication, simulation, and sensing.
FALCON / FN-DSA: A NIST forthcoming standard (FIPS 206) for digital signatures based on NTRU lattices. Offers very compact signatures (666 bytes for FALCON-512) at the cost of complex implementation requirements.
Fault-Tolerant Quantum Computing: Quantum computation using quantum error correction to protect logical qubits from physical qubit errors. Required for running Shor's algorithm; current systems are pre-fault-tolerant (NISQ era).
FIPS (Federal Information Processing Standard): US government standards for information processing, including the NIST post-quantum cryptography standards: FIPS 203 (ML-KEM), FIPS 204 (ML-DSA), FIPS 205 (SLH-DSA).
Fiat-Shamir with Aborts: The signature paradigm used in ML-DSA. A commitment-challenge-response scheme where signing aborts and retries if the response would leak information about the secret key.
Grover's Algorithm: A quantum search algorithm by Lov Grover (1996) providing quadratic speedup over classical brute force for searching unstructured databases. Relevant to symmetric cryptography: halves effective key length (AES-128 → 64-bit security; mitigated by using AES-256).
Goppa Code: The error-correcting code underlying Classic McEliece. A structured algebraic code with efficient decoding algorithms, whose structure is hidden in the public key.
Harvest Now, Decrypt Later (HNDL): The attack strategy where an adversary records encrypted traffic today for decryption once a CRQC becomes available. Makes the quantum threat immediate for long-lived sensitive data, regardless of current CRQC timeline.
Hybrid Cryptography: Using both a classical algorithm (e.g., X25519) and a post-quantum algorithm (e.g., ML-KEM-768) simultaneously, deriving shared secrets from both. Recommended transition strategy maintaining security against both classical and quantum adversaries.
HQC (Hamming Quasi-Cyclic): A code-based post-quantum KEM alternative to Classic McEliece and BIKE with more compact key sizes than McEliece but reliable decapsulation.
HSM (Hardware Security Module): A tamper-resistant hardware device for cryptographic key management and operations. HSMs must be upgraded to PQC-capable firmware or replaced for quantum-safe CA and KMS operations.
ICHEC (Irish Centre for High-End Computing): Ireland's national HPC facility, providing Irish researchers and companies access to quantum simulators through EuroHPC partnerships.
IND-CPA Security: Indistinguishability under chosen plaintext attack. The baseline security definition for encryption schemes. ML-KEM achieves IND-CCA2 (a stronger notion), proven via the Fujisaki-Okamoto transform.
Integer Factorisation Problem (IFP): The basis of RSA security. Solvable in polynomial time by Shor's algorithm on a quantum computer.
KEM (Key Encapsulation Mechanism): A public-key primitive that generates and encapsulates a symmetric shared secret. ML-KEM (FIPS 203) is the primary post-quantum KEM. KEMs replace DH/ECDH for key exchange.
Kyber: Previous name for CRYSTALS-Kyber, now standardised as ML-KEM (FIPS 203). Often still used informally to refer to ML-KEM.
Lattice: A discrete subgroup of ℝ^n — an infinite, regularly-spaced grid of points in n-dimensional space. The mathematical foundation of ML-KEM, ML-DSA, FALCON, and NTRU.
LLL Algorithm (Lenstra-Lenstra-Lovász): The first practical lattice basis reduction algorithm (1982). Runs in polynomial time but produces only approximately short vectors. Insufficient to break modern lattice-based cryptography.
Logical Qubit: A qubit protected against errors by quantum error correction (encoding one logical qubit using many physical qubits). A CRQC requires ~4,098 logical qubits to break RSA-2048.
LWE (Learning With Errors): A fundamental hard problem in lattice cryptography introduced by Oded Regev (2005). Given (A, As+e), recovering s is provably as hard as worst-case lattice problems. Foundation of ML-KEM and ML-DSA security.
McEliece Cryptosystem: The first code-based public-key cryptosystem (1978). Based on Goppa code decoding hardness. Extremely old security foundation; impractical key sizes.
ML-DSA (Module Lattice-based Digital Signature Algorithm): NIST FIPS 204 standard (August 2024). Post-quantum digital signature algorithm based on CRYSTALS-Dilithium. The primary replacement for ECDSA and RSA signatures.
ML-KEM (Module Lattice-based Key Encapsulation Mechanism): NIST FIPS 203 standard (August 2024). Post-quantum key encapsulation mechanism based on CRYSTALS-Kyber. The primary replacement for ECDH and RSA key exchange.
MLWE (Module Learning With Errors): The specific variant of LWE used in ML-KEM and ML-DSA, operating over polynomial rings organised into module structures. Enables NTT-accelerated computation.
Mosca's Theorem: Dr. Michele Mosca's risk framework: quantum risk is current if (data lifetime) + (migration time) > (time to CRQC). Provides a practical decision framework for quantum-safe migration urgency.
MSIS (Module Short Integer Solution): The lattice problem underlying ML-DSA security. Given module matrix A, find a short non-zero vector z with Az = 0 mod q.
NCSC Ireland (National Cyber Security Centre): Ireland's government cybersecurity agency. Published Quantum Threat Advisory in 2023 recommending all public sector bodies begin PQC migration planning.
NIS2 (Network and Information Security Directive 2): EU Directive 2022/2555 requiring "state of the art" security for essential and important entities. Transposed into Irish law through NIS Regulations 2024. Mandates cryptographic agility implicitly.
NISQ (Noisy Intermediate-Scale Quantum): The current era of quantum computing: devices with 50–1000+ qubits but insufficient error correction for fault-tolerant operations. NISQ devices cannot run Shor's algorithm at useful scale.
NIST (National Institute of Standards and Technology): US standards body that ran the post-quantum cryptography competition (2016–2024) and published FIPS 203, 204, and 205 in August 2024.
NTT (Number Theoretic Transform): The finite-field analogue of the Fast Fourier Transform, enabling polynomial multiplication in O(n log n) instead of O(n²). Critical to the performance of ML-KEM and ML-DSA.
NTRU: N-th degree TRUncated polynomial ring cryptography. One of the oldest lattice-based systems (1996). The mathematical basis for FALCON/FN-DSA.
OQS (Open Quantum Safe): An open-source project providing liboqs (C library), oqs-openssl (OpenSSL integration), and language bindings (Python, Java, .NET) for post-quantum cryptographic algorithms. Available at openquantumsafe.org.
Physical Qubit: A physical two-state quantum system (superconducting circuit, trapped ion, photon, etc.) used to implement quantum computation. Subject to decoherence and gate errors. Many physical qubits encode one logical qubit via error correction.
PKI (Public Key Infrastructure): The ecosystem of certificate authorities, certificates, and policies that bind public keys to identities. PKI root keys are among the highest-priority targets for quantum-safe migration.
Post-Quantum Cryptography (PQC): Cryptographic algorithms designed to resist attacks by quantum computers, replacing quantum-vulnerable RSA and ECC. Standardised by NIST in FIPS 203, 204, and 205 (August 2024).
Polynomial Ring: An algebraic structure Rq = ℤq[x]/(x^n + 1) used in module lattice cryptography. Polynomial multiplication in this ring can be accelerated using NTT, making ML-KEM and ML-DSA fast in practice.
QKD (Quantum Key Distribution): A method for distributing cryptographic keys using quantum mechanical properties (typically photon polarisation states) to detect eavesdropping. Provides information-theoretic (rather than computational) security for key exchange. Requires dedicated fibre or free-space optical links.
QR Code (Quantum Resistant Code): Not a visual barcode — in cryptography context, algorithms proven to resist quantum computer attacks. ML-KEM, ML-DSA, SLH-DSA, and FALCON are quantum-resistant.
Quantum Advantage: The point at which a quantum computer outperforms all classical computers for a specific task. Demonstrated for narrow benchmarks (random circuit sampling); not yet demonstrated for cryptographically relevant tasks.
Quantum Coherence: The property allowing a quantum system to exist in superposition states. Decoherence — loss of quantum coherence due to environmental interaction — is the primary challenge in quantum hardware engineering.
Quantum Error Correction (QEC): Techniques for protecting quantum information from errors using redundant encoding. Requires many physical qubits per logical qubit. Below-threshold QEC (demonstrated by Google Willow) is a prerequisite for fault-tolerant quantum computing.
Quantum Key Distribution (QKD): See QKD above.
Quantum Supremacy: Now more commonly called "quantum advantage." Google's 2019 demonstration that Sycamore completed a specific sampling task in 200 seconds vs. ~10,000 years for classical computers.
Rejection Sampling: A technique in ML-DSA signing that ensures response vectors are statistically independent of the secret signing key by aborting and retrying if the response is too large. Critical for security; prevents leakage through statistical analysis.
Ring-LWE (Ring Learning With Errors): An efficient variant of LWE operating over polynomial rings, enabling NTT acceleration. The theoretical foundation underlying module lattice constructions.
RSA (Rivest-Shamir-Adleman): The most widely deployed public-key cryptosystem, based on the Integer Factorisation Problem. Broken by Shor's algorithm; must be replaced with ML-KEM (for encryption/key exchange) or ML-DSA (for signatures).
Shor's Algorithm: Peter Shor's 1994 quantum algorithm for integer factorisation and discrete logarithm computation in polynomial time. Breaks RSA, ECDSA, ECDH, DH, DSA, and all classical public-key cryptography.
Short Integer Solution (SIS): A lattice problem: given a random matrix A, find a short non-zero integer vector z with Az = 0 mod q. Hard for classical and quantum computers; underlies lattice-based signature security.
SLH-DSA (Stateless Hash-Based Digital Signature Algorithm): NIST FIPS 205 standard (August 2024). Post-quantum digital signature based on the SPHINCS+ scheme, using only hash functions for security. Conservative security; large signatures.
SPHINCS+: The algorithm standardised as SLH-DSA. A stateless hash-based signature scheme combining multiple one-time signature schemes with a hypertree structure.
Syndrome Decoding Problem: The hard problem underlying code-based cryptography (McEliece, BIKE, HQC): given a parity check matrix H and syndrome s, find a low-weight vector e with He = s mod 2.
Surface Code: The leading quantum error correction code for superconducting quantum computers. Requires ~1000 physical qubits per logical qubit at realistic (0.1%) error rates. Determines the physical qubit requirements for a CRQC.
TLS 1.3 Hybrid: A TLS 1.3 configuration using both classical (X25519) and post-quantum (ML-KEM-768) key exchange simultaneously. Standardised in IETF draft RFC. Deployed by Google Chrome (default from v124), Cloudflare, and AWS.
Topological Qubit: A proposed qubit type using topological properties of exotic quantum matter to provide intrinsic error protection. If successful at scale (Microsoft's research direction), could dramatically reduce the physical-to-logical qubit ratio needed for a CRQC.
Tyndall National Institute: Cork-based EU microelectronics and photonics research centre. Ireland's primary quantum hardware research facility, contributing to EU Quantum Flagship through photonic integration research.
Willow (Google, 2024): Google's 105-qubit superconducting quantum processor demonstrating below-threshold quantum error correction — logical error rates decreasing with increasing code distance. A critical milestone toward fault-tolerant quantum computing.
X25519: The most widely deployed classical Diffie-Hellman key exchange, using the Curve25519 elliptic curve. Quantum-vulnerable (ECDLP broken by Shor's algorithm). Often paired with ML-KEM-768 in hybrid key exchange configurations.
X25519MLKEM768: The hybrid TLS key exchange combining X25519 and ML-KEM-768. IETF-standardised in draft form; deployed by Google Chrome as default since Chrome 124 (2024).
This glossary is maintained by Michael English, Co-Founder & CTO of IMPT.io. Updated for NIST FIPS 203/204/205 finalisation (August 2024).
impt.io | Based in Clonmel, Co. Tipperary, Ireland
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