D'Math University | Computing & Interdisciplinary Mathematics

MSc Cryptography & Mathematics

Mathematical security for the digital age — from elliptic curve cryptography and lattice-based post-quantum schemes to zero-knowledge proofs and blockchain security — delivered through a GCHQ and NSA-aligned curriculum.

Postgraduate 1 Year Online National Security
10
Taught Modules
£70k
Avg Graduate Salary
28+
Industry Partners
GCHQ
Aligned Curriculum

Programme Overview

What You Will Study

Cryptography is applied mathematics at its most consequential — the mathematics of secrecy, authentication, and trust. This programme covers the full spectrum from classical number-theoretic foundations to the post-quantum landscape reshaping global security.

  • Mathematical Foundations: algebraic number theory, elliptic curves, lattice theory
  • Classical Cryptography: RSA, Diffie-Hellman, AES, digital signatures
  • Post-Quantum Security: lattice-based, code-based, and hash-based schemes
  • Advanced Protocols: zero-knowledge proofs, multi-party computation, homomorphic encryption

Programme Highlights

With average graduate salaries reaching £70k and demand outstripping supply for mathematically trained cryptographers, this programme offers exceptional career prospects in government, finance, defence, and technology.

  • GCHQ-Aligned Curriculum: content designed in consultation with national security agencies
  • Post-Quantum Focus: dedicated module on NIST post-quantum standardisation algorithms
  • Industry Access: partnerships with cybersecurity firms and intelligence community
  • Clearance Pathway: guidance on UK security clearance application for eligible graduates
Course Catalogue

Click any course to view its objective and learning outcomes.

CRY 501 Number Theory & Algebra for Cryptography +

Objective

To establish the algebraic foundation for modern cryptography.

Learning Outcomes

  • Apply group, ring and field theory.
  • Use modular arithmetic and Chinese Remainder Theorem.
  • Apply quadratic reciprocity.
  • Use finite fields.
  • Implement number-theoretic algorithms.
Interactive Activity — Sieve of Eratosthenes
Watch the algorithm find all primes up to N. Composites get crossed out as their prime factors are processed.
N = 100
Interactive Activity — Euclidean Algorithm
Compute gcd(a, b) using repeated division. Bezout coefficients are also computed.
a = b =
Interactive Activity — Modular Exponentiation (RSA core)
Compute b^e mod n using fast modular exponentiation.
b = e = mod n =
CRY 502 Symmetric Key Cryptography +

Objective

To analyse and design symmetric ciphers.

Learning Outcomes

  • Apply block ciphers (AES, DES).
  • Use stream ciphers.
  • Apply modes of operation.
  • Analyse linear and differential cryptanalysis.
  • Design new symmetric primitives.
CRY 503 Public Key Cryptography +

Objective

To analyse and apply public-key cryptosystems.

Learning Outcomes

  • Apply RSA encryption and signature.
  • Use Diffie-Hellman key exchange.
  • Apply DSA and ElGamal.
  • Analyse security via computational assumptions.
  • Implement public-key protocols.
CRY 504 Elliptic Curve Cryptography +

Objective

To apply elliptic curves to efficient cryptographic protocols.

Learning Outcomes

  • Compute point operations on elliptic curves.
  • Apply ECDH and ECDSA.
  • Use pairings on elliptic curves.
  • Apply pairing-based cryptography.
  • Analyse ECC security.
CRY 505 Lattice-Based Cryptography +

Objective

To use lattice problems for post-quantum cryptography.

Learning Outcomes

  • Apply LLL and BKZ reduction.
  • Use Learning With Errors (LWE).
  • Apply NTRU encryption.
  • Use ring-LWE.
  • Analyse lattice security.
CRY 506 Cryptanalysis +

Objective

To attack cryptographic schemes to assess their security.

Learning Outcomes

  • Apply linear and differential cryptanalysis.
  • Use side-channel attacks.
  • Apply Pollard's rho and Pohlig-Hellman.
  • Use lattice-based cryptanalysis.
  • Analyse fault attacks.
CRY 507 Coding Theory +

Objective

To use error-correcting codes in cryptography and communication.

Learning Outcomes

  • Apply Hamming and Reed-Solomon codes.
  • Use cyclic and BCH codes.
  • Apply McEliece cryptosystem.
  • Use list-decoding algorithms.
  • Analyse code-based security.
CRY 508 Quantum Cryptography +

Objective

To apply quantum mechanics to cryptographic security.

Learning Outcomes

  • Apply BB84 quantum key distribution.
  • Use quantum random number generation.
  • Apply quantum digital signatures.
  • Discuss Shor's and Grover's algorithms.
  • Analyse post-quantum implications.
Interactive Activity — Vector Field & Gradient Visualizer
Pick a scalar field f(x,y). Gradient arrows point in the direction of steepest ascent. Click anywhere to drop a particle that follows the gradient.
f(x,y) =
Click on the plot to drop a particle.
Interactive Activity — Classical Cipher
Encode or decode text with the Caesar cipher (single shift) or Vigenère cipher (keyword). The output updates as you type.
Mode: Key:
Text:
CRY 509 Zero-Knowledge Proofs +

Objective

To prove statements without revealing the underlying secret.

Learning Outcomes

  • Apply Schnorr identification.
  • Use Sigma protocols.
  • Apply Fiat-Shamir transformation.
  • Use zk-SNARKs and zk-STARKs.
  • Analyse soundness and completeness.
CRY 510 Blockchain & Cryptocurrencies +

Objective

To analyse cryptographic and economic foundations of blockchains.

Learning Outcomes

  • Apply hash chains and Merkle trees.
  • Analyse Bitcoin and Ethereum protocols.
  • Apply consensus mechanisms.
  • Use smart contracts.
  • Discuss DeFi protocols.
CRY 511 Provable Security +

Objective

To formally prove security of cryptographic protocols.

Learning Outcomes

  • Apply security definitions (IND-CPA, IND-CCA).
  • Use simulation-based proofs.
  • Apply random oracle model.
  • Use universal composability.
  • Construct proofs in standard model.
CRY 512 Cryptography Research Project +

Objective

To complete an original cryptography research project.

Learning Outcomes

  • Identify a research-quality problem.
  • Apply rigorous cryptanalytic or constructive methods.
  • Implement protocols efficiently.
  • Write a research-quality dissertation.
  • Present to cryptographers and industry.

Core Modules

🔐

Public-Key Cryptography

RSA, Diffie-Hellman, ElGamal, discrete logarithm hardness, security reductions, and provable security frameworks.

🧮

Elliptic Curve Cryptography

Elliptic curve groups, ECDSA, ECDH, pairings, and elliptic curve discrete logarithm hardness.

🔢

Algebraic Number Theory for Crypto

Number fields, rings of integers, ideal class groups, and their role in cryptographic constructions.

💻

Quantum & Post-Quantum Cryptography

Shor's and Grover's algorithms, threat model, NIST PQC finalists: CRYSTALS-Kyber, CRYSTALS-Dilithium, SPHINCS+.

📐

Information Theory & Entropy

Shannon entropy, channel capacity, information-theoretic security, one-time pads, and perfect secrecy.

🌐

Zero-Knowledge Proofs

Interactive and non-interactive proofs, Schnorr protocol, zk-SNARKs, zk-STARKs, and blockchain applications.

📊

Lattice-Based Cryptography

LWE, SIS, NTRU, Ring-LWE, and the hardness of lattice problems forming the post-quantum security foundation.

🔬

Side-Channel Attacks & Defences

Timing attacks, power analysis, fault injection, and countermeasures in hardware and software implementations.

🏗️

Blockchain & Distributed Security

Consensus mechanisms, smart contract security, decentralised identity, and cryptographic guarantees of distributed systems.

🌍

Cryptographic Protocols

TLS, SSH, Signal protocol, formal verification of protocols, and security proofs in the random oracle model.

Career Outcomes

🔐

Cryptographer

Design and analyse cryptographic systems for government agencies, financial institutions, and technology companies worldwide.

🛡️

Cybersecurity Engineer

Protect digital infrastructure using cryptographic protocols, secure system design, and vulnerability analysis.

🌐

Blockchain Developer

Build cryptographically secure decentralised applications, smart contracts, and blockchain infrastructure.

🔬

Intelligence Analyst

Apply cryptographic expertise within national security agencies such as GCHQ, NSA, and allied intelligence organisations.

💻

Post-Quantum Security Researcher

Advance the development of quantum-resistant cryptographic standards at universities, standards bodies, and technology labs.

📐

Digital Trust Engineer

Design PKI, certificate authorities, and trust frameworks for enterprise, cloud, and critical national infrastructure.

Where Our Graduates Go & Top Global Universities

Oxford Cambridge ETH Zürich University of Waterloo MIT Tel Aviv University TU Eindhoven Ruhr University Bochum Stanford Royal Holloway London

Why D'Math University — Our 4-Step Approach

01

Security Proofs First

Every cryptographic primitive is understood through formal security definitions and reduction proofs — not just implementation.

02

Post-Quantum Readiness

Half the curriculum addresses post-quantum cryptography, preparing graduates for the coming transition away from classical schemes.

03

National Security Alignment

Curriculum co-developed with GCHQ-aligned advisors ensures graduates understand real operational security requirements.

04

Applied Implementation

Cryptographic protocols are implemented and attacked in lab sessions, building the practical skills that security employers demand.

Enrol in MSc Cryptography & Mathematics →

Applications open year-round — become a guardian of the digital world through mathematics.