Level 3 · Ph.D

Advanced Cryptography

Ph.D syllabus · 62 phases · +1 year

Every unit this programme teaches, in the order it is taught. Headlines only — the material itself opens once you are enrolled.

Dates, price and prerequisites

Phase 0 Foundations & tooling
Phase 1 What "advanced" means: rigor & the prereq recap
Phase 2 The toy lab & the running privacy-preserving application
Phase 3 Security definitions & the game-based method
Phase 4 Reductions & what a proof of security is
Phase 5 PRFs, PRPs & the switching lemma
Phase 6 Hybrid arguments & indistinguishability
Phase 7 The random-oracle model & its limits
Phase 8 Lattices, bases & the shortest-vector problem
Phase 9 Lattice reduction (LLL) intuition
Phase 10 LWE & Ring-LWE
Phase 11 SIS & worst-case/average-case hardness
Phase 12 Pairings on elliptic curves & bilinear maps
Phase 13 The discrete-log & factoring landscape revisited
Phase 14 The quantum threat (Shor, Grover)
Phase 15 Lattice KEMs (Kyber / ML-KEM) from toy parameters
Phase 16 Lattice signatures (Dilithium / ML-DSA) from toy parameters
Phase 17 Hash-based signatures (Lamport, Merkle, WOTS, XMSS, SPHINCS+ / SLH-DSA) from toy parameters
Phase 18 Code-based crypto & the NIST PQC migration story (toy parameters)
Phase 19 Interactive proofs & zero-knowledge (the graph-isomorphism toy)
Phase 20 Sigma protocols (Schnorr) & proofs of knowledge (toy group)
Phase 21 The Fiat–Shamir transform & non-interactive ZK (toy parameters)
Phase 22 Commitment schemes & polynomial commitments (toy parameters)
Phase 23 zk-SNARKs: R1CS, QAP, and the trusted setup (toy parameters)
Phase 24 zk-STARKs & transparent proofs (toy field 𝔽₁₇)
Phase 25 Secret sharing revisited & the MPC model (toy field 𝔽₁₁)
Phase 26 Oblivious transfer (toy group G = ⟨2⟩ ⊂ ℤ₂₃*)
Phase 27 Yao's garbled circuits (toy circuit z = (a ∧ b) ∨ c)
Phase 28 GMW & the secret-sharing approach to MPC (toy circuit z = (a ∧ b) ∨ c)
Phase 29 Malicious security & verifiable MPC (toy field 𝔽₇)
Phase 30 Private set intersection (toy group ℤ₂₃*)
Phase 31 Partially-homomorphic encryption (Paillier, toy n = 35)
Phase 32 Somewhat-/fully-homomorphic encryption (BGV/CKKS, bootstrapping)
Phase 33 Threshold signatures & distributed key generation
Phase 34 Verifiable random functions & verifiable delay functions
Phase 35 Anonymous credentials, blind signatures & mixnets
Phase 36 Blockchain & consensus cryptography
Phase 37 Advanced side-channel & fault attacks on implementations
Phase 38 Building a verified primitive: vectors, property tests, constant-time review
Phase 39 Capstone
Phase 40 Hardening, proof review & "What's Next"
Phase 41 Portal integration (slug lynx-cortex-advanced-crypto)
Phase 42 Universal composability & simulation at scale (toy group G=⟨2⟩⊂ℤ₂₃*)
Phase 43 Recursive & composable zero-knowledge: IVC and folding (toy pairing/curve)
Phase 44 Modern SNARK arithmetization: PLONKish, custom gates, lookups (toy parameters)
Phase 45 Aggregate, threshold & anonymity signatures
Phase 46 MPC-in-the-head & post-quantum ZK from symmetric primitives (toy circuit z = (a ∧ b) ∨ c)
Phase 47 Advanced FHE engineering: packing, SIMD & bootstrapping cost
Phase 48 Private information retrieval & oblivious RAM
Phase 49 Function secret sharing & lightweight private computation (toy domain X={0,1,2,3})
Phase 50 Computer-aided cryptography & machine-checked proofs
Phase 51 Concrete security, parameter selection & the research literature
Phase 52 Proposing the doctoral capstone (research method)
Phase 53 Capstone I: execute the research
Phase 54 Capstone II: verified publication & hardening
Phase 55 Frontier, ethics & close; portal integration
Phase 56 Blocks, Merkle trees & the ledger data model
Phase 57 Byzantine consensus I — proof of work & Nakamoto
Phase 58 Byzantine consensus II — proof of stake, BFT & finality
Phase 59 Transactions, UTXO vs account & double-spend
Phase 60 Smart contracts & the EVM model
Phase 61 P2P networking, scaling & the post-quantum bridge