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Level 3 · Ph.D

Ph.D Advanced Cryptography

Cryptography · Live · v0

Doctoral cryptography — security proofs, advanced protocols, and an original verified contribution to the field.

Path type

Cryptography

Requirements

MSc Advanced Cryptography

Enrollment

€19.95

Deadline

Next cohort starts 2027-09-06 (AY 2027/28)

Length

+1 year · 56 phases

Language

English · Español

Content freshness

Curriculum updated 2026-08-22 · content rev 678703ca

Cortex Credits (CC)

280 CC · 364 CC across all tiers of this programme
What are Cortex Credits?

Syllabus

View the phase syllabus

0. Foundations & tooling
1. What "advanced" means: rigor & the prereq recap
2. The toy lab & the running privacy-preserving application
3. Security definitions & the game-based method
4. Reductions & what a proof of security is
5. PRFs, PRPs & the switching lemma
6. Hybrid arguments & indistinguishability
7. The random-oracle model & its limits
8. Lattices, bases & the shortest-vector problem
9. Lattice reduction (LLL) intuition
10. LWE & Ring-LWE
11. SIS & worst-case/average-case hardness
12. Pairings on elliptic curves & bilinear maps
13. The discrete-log & factoring landscape revisited
14. The quantum threat (Shor, Grover)
15. Lattice KEMs (Kyber / ML-KEM) from toy parameters
16. Lattice signatures (Dilithium / ML-DSA) from toy parameters
17. Hash-based signatures (Lamport, Merkle, WOTS, XMSS, SPHINCS+ / SLH-DSA) from toy parameters
18. Code-based crypto & the NIST PQC migration story (toy parameters)
19. Interactive proofs & zero-knowledge (the graph-isomorphism toy)
20. Sigma protocols (Schnorr) & proofs of knowledge (toy group)
21. The Fiat–Shamir transform & non-interactive ZK (toy parameters)
22. Commitment schemes & polynomial commitments (toy parameters)
23. zk-SNARKs: R1CS, QAP, and the trusted setup (toy parameters)
24. zk-STARKs & transparent proofs (toy field $\mathbb{F}_{17}$)
25. Secret sharing revisited & the MPC model (toy field $\mathbb{F}_{11}$)
26. Oblivious transfer (toy group $G = \langle 2\rangle \subset \mathbb{Z}_{23}^*$)
27. Yao's garbled circuits (toy circuit $z = (a \wedge b) \vee c$)
28. GMW & the secret-sharing approach to MPC (toy circuit $z = (a \wedge b) \vee c$)
29. Malicious security & verifiable MPC (toy field $\mathbb{F}_7$)
30. Private set intersection (toy group $\mathbb{Z}_{23}^{*}$)
31. Partially-homomorphic encryption (Paillier, toy $n = 35$)
32. Somewhat-/fully-homomorphic encryption (BGV/CKKS, bootstrapping)
33. Threshold signatures & distributed key generation
34. Verifiable random functions & verifiable delay functions
35. Anonymous credentials, blind signatures & mixnets
36. Blockchain & consensus cryptography
37. Advanced side-channel & fault attacks on implementations
38. Building a verified primitive: vectors, property tests, constant-time review
39. Capstone
40. Hardening, proof review & "What's Next"
41. Portal integration (slug Advanced Cryptography)
42. Universal composability & simulation at scale (toy group $G=\langle 2\rangle\subset\mathbb{Z}_{23}^*$)
43. Recursive & composable zero-knowledge: IVC and folding (toy pairing/curve)
44. Modern SNARK arithmetization: PLONKish, custom gates, lookups (toy parameters)
45. Aggregate, threshold & anonymity signatures
46. MPC-in-the-head & post-quantum ZK from symmetric primitives (toy circuit $z = (a \wedge b) \vee c$)
47. Advanced FHE engineering: packing, SIMD & bootstrapping cost
48. Private information retrieval & oblivious RAM
49. Function secret sharing & lightweight private computation (toy domain $X={0,1,2,3}$)
50. Computer-aided cryptography & machine-checked proofs
51. Concrete security, parameter selection & the research literature
52. Proposing the doctoral capstone (research method)
53. Capstone I: execute the research
54. Capstone II: verified publication & hardening
55. Frontier, ethics & close; portal integration
56. Blocks, Merkle trees & the ledger data model
57. Byzantine consensus I — proof of work & Nakamoto
58. Byzantine consensus II — proof of stake, BFT & finality
59. Transactions, UTXO vs account & double-spend
60. Smart contracts & the EVM model
61. P2P networking, scaling & the post-quantum bridge

Syllabus →

Enrolment prerequisites

• A verified account and admissions-committee approval.
• Completion of MSc Advanced Cryptography.