Exact equivalence
Show that two worlds induce exactly the same observable distribution.
L0≡L1
First clean example: OTP / Shamir
IERG4150
Introduction to Cryptography
An undergraduate introduction to modern cryptography centered on precise security definitions, adversarial thinking, constructions, attacks, proofs, and applications.
Define security · break bad constructions · prove good ones · understand what the primitives enable.
- InstructorSherman S. M. Chow
- LecturesMon 4:30–6:15 PM · Science Centre L3
Wed 4:30–5:15 PM · Mong Man Wai Bldg 703 - TextbookThe Joy of Cryptography
IERG4150 · FALL 2026
A RECURRING CRYPTOGRAPHIC WORKFLOW
Define → Attack → Construct → Prove → Apply
A security claim is meaningful only relative to a threat model and explicit assumptions.
Course map
From perfect secrecy to modern public-key cryptography.
Click a stage to filter the lecture atlas. The two application threads underneath show where the primitives are heading.
Secure communicationOTP → PRG/ratchet → CPA → CCA → MAC → DH + signatures → AKE
Private data & computationSecret sharing → PSI/SSE → ElGamal homomorphism → encrypted tally → FHE teaser
Lecture atlas
The semester at a glance.
Each card contains a one-sentence big idea, cumulative recall, independent skills, and the main conceptual connection.
No lecture cards match that search/filter.
Proof toolkit
Five moves recur across the course.
The surface syntax changes; the proof architecture often does not.
Replace a primitive
Factor out a building block and swap its real world for its ideal world using a known security guarantee.
real primitive≈ideal primitive
PRG/PRF-based constructions
Identical until bad
If two executions differ only after a rare event, the distinguishing gap is at most the probability of that event.
sameuntilbad
Birthday collisions, repeated nonces
Variable hybrid
Change one interaction at a time, then sum polynomially many negligible gaps.
H0≈ … ≈Hq
PRF / MAC / one-time → many-time
Reduction / contrapositive
Turn an attack on the construction into an attack on the assumed-secure primitive.
break construction⇒break assumption
Merkle–Damgård, ElGamal/DDH
When facing a new proof: What is the target pair of worlds? What is the first local change? Which previously proved fact justifies it?
Applications map
Basic primitives lead somewhere.
The application layer is deliberately tied back to mechanisms already taught, rather than becoming a disconnected advanced-crypto tour.
Thread A
Secure communication
- OTPperfect one-time secrecy
- PRGstream cipher · symmetric ratchet · forward secrecy
- CPA / modessecure repeated encryption · practical block processing
- CCA + MACresist active ciphertext manipulation
- DH + signaturesauthenticated key exchange
Thread B
Private data & computation
- Secret sharingdistributed trust · secure aggregation intuition
- PRFprivate set intersection · contact discovery
- SSEsearch over encrypted data · explicit leakage tradeoffs
- HashMerkle hash trees · authenticated data structures
- ElGamalhomomorphic aggregation · encrypted tally / e-voting
- FHE teaserfrom one supported operation to arbitrary computation
CORE fully examinable
APPLICATION examinable at stated conceptual/mechanism level
ENRICHMENT useful intuition; technical details not examined
REFERENCE supporting detail kept in the full notes
Fall 2026
Teaching sequence.
The exact calendar, assignment releases, and examination arrangements are announced through the official course channels; this table shows the intended intellectual sequence.
| Unit | Topic | Primary reading |
|---|---|---|
| 0–1 | Overview, security goals, One-Time Pad | One-Time Pad & the Provable Security Mindset ↗ |
| 2 | Provable Security | Rudiments of Provable Security ↗ |
| 3 | Secret Sharing | Secret Sharing ↗ |
| 4 | Basing Cryptography on Intractable Computation | Modern Computational Cryptography ↗ |
| 5–6 | Pseudorandom Generators; Pseudorandom Functions & Block Ciphers | PRG ↗ · PRF ↗ |
| 7–9 | CPA Security; Modes of Operation; CCA Security | CPA & modes ↗ · CCA ↗ |
| Special | Applications of PRG and PRF | Applied Cryptography preview ↗ |
| 10–11 | Message Authentication Codes; Hash Functions | MAC / Encrypt-then-MAC ↗ · Collision-Resistant Hash Functions ↗ |
| 13 | RSA & Digital Signatures | RSA ↗ · Digital Signatures ↗ |
| 14–15 | Diffie–Hellman Key Agreement; Public-Key Encryption | Key Exchange ↗ · Public-Key Encryption ↗ |
Course information
Fall 2026.
Class
Mon 4:30–6:15 PM · Science Centre L3
Wed 4:30–5:15 PM · Mong Man Wai Bldg 703
Tutorial Submit preference by Sep 14
Teaching team
Instructor
Sherman S. M. Chow ↗
Teaching Assistant
Ying-yu Pan · SHB726 · py022 [at] ie
Assessment
3 written assignments 40%
Mid-term 20%
Final exam 40%
Refer to official course announcements for current details.
Resources
Blackboard ↗
The Joy of Cryptography ↗
ENGG5383 Applied Cryptography ↗
Who takes IERG4150?
Current class
IE · CS · Math · MIE · IDA · Exchange
Previous cohorts
Students have also joined from MSc(IE) ↗.