The C&O department has 36 faculty members and 60 graduate students. We are intensely research oriented and hold a strong international reputation in each of our six major areas:
- Algebraic combinatorics
- Combinatorial optimization
- Continuous optimization
- Cryptography
- Graph theory
- Quantum computing
Read more about the department's research to learn of our contributions to the world of mathematics!
News
Laura Pierson wins Governor General's Gold Medal
The Governor General’s Gold Medal is one of the highest student honours awarded by the University of Waterloo.
Sepehr Hajebi wins Graduate Research Excellence Award, Mathematics Doctoral Prize, and finalist designation for Governor General's Gold Medal
The Mathematics Doctoral Prizes are given annually to recognize the achievement of graduating doctoral students in the Faculty of Mathematics. The Graduate Research Excellence Awards are given to students who authored or co-authored an outstanding research paper.
Three C&O faculty win Outstanding Performance Awards
The awards are given each year to faculty members across the University of Waterloo who demonstrate excellence in teaching and research.
Events
Algebraic and enumerative combinatorics seminar - Mahrud Sayrafi-Constructing exceptional collections for toric varieties
| Speaker: | Mahrud Sayrafi |
| Affiliation: | McMaster University |
| Location: | MC 5417 |
Abstract: Exceptional collections are a powerful tool for understanding the derived category of coherent sheaves on algebraic varieties, with applications in commutative algebra, birational geometry, and mirror symmetry. While the existence of exceptional collections is known for classical varieties such as Grassmannians and flag varieties, constructing explicit collections for toric varieties presents challenges in combinatorial algebraic geometry. In this talk I will describe a computational approach to constructing full strong exceptional collections consisting of complexes of line bundles for toric varieties. No background in derived categories is assumed.
There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:30pm.
Crypto Reading Group - Elnaz Hessami Pilehrood-Shadowfax: Hybrid Security and Deniability for AKEMs
Abstract:As cryptographic protocols transition to post-quantum security, most adopt hybrid solutions combining classical and post-quantum assumptions. This shift often sacrifices efficiency, compactness, or even security. One such property is deniability, which enables users to plausibly deny authorship of potentially incriminating messages. While classical protocols like X3DH key agreement (used in Signal and WhatsApp) provide deniability, post-quantum protocols like PQXDH and Apple’s iMessage with PQ3 do not. This work addresses this gap by investigating how to efficiently preserve deniability in post-quantum protocols. Specifically, we propose two hybrid schemes for authenticated key encapsulation mechanisms (AKEMs). The first is a black-box construction that preserves deniability when both constituent AKEMs are deniable. The second is Shadowfax, a non-black-box AKEM that achieves hybrid security, integrating a classical non-interactive key exchange, a post-quantum key encapsulation mechanism, and a post-quantum ring signature. Shadowfax satisfies deniability in both dishonest and honest receiver settings, relying on statistical security in the former and on a single pre- or post-quantum assumption in the latter. Finally, we provide several portable implementations of Shadowfax. When instantiated with standardised components (ML–KEM and Falcon), Shadowfax yields ciphertexts of 1 728 bytes and public keys of 2 036 bytes, with encapsulation and decapsulation costs of 1.8M and 0.7M cycles on an Apple M1 Pro. |
Crypto Reading Group - Maggie Simmons-Formally Verified Correctness Bounds for Lattice-Based Cryptography
Abstract: Decryption errors play a crucial role in the security of KEMs based on
Fujisaki-Okamoto because the concrete security guarantees provided by
this transformation directly depend on the probability of such an event
being bounded by a small real number. In this paper we present an
approach to formally verify the claims of statistical probabilistic
bounds for incorrect decryption in lattice-based KEM constructions. Our
main motivating example is the PKE encryption scheme underlying ML-KEM.
We formalize the statistical event that is used in the literature to
heuristically approximate ML-KEM decryption errors and confirm that the
upper bounds given in the literature for this event are correct. We
consider FrodoKEM as an additional example, to demonstrate the wider
applicability of the approach and the verification of a correctness
bound without heuristic approximations. We also discuss other
(non-approximate) approaches to bounding the probability of ML-KEM
decryption.
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