Abstract:
1st Talk: In this talk, we provide an overview of modern cryptography, beginning with the core concepts of symmetric and public-key systems. In this talk, we explain how classical algorithms like RSA and Diffie-Hellman are built on one-way functions and computationally hard problems like integer factorization and discrete logarithms. The talk then introduces the threat from quantum computers, which can break these systems, establishing the urgent need for Post-Quantum Cryptography (PQC) and listing the major families of quantum-resistant algorithms being developed today.

2nd Talk: In this talk, we introduce Multivariate Public Key Cryptography (MPKC), a family of post-quantum algorithms secure against quantum computer attacks. The security of MPKC is based on the proven NP-completeness of the MQ-Problem—the difficulty of solving systems of multivariate quadratic equations over a finite field.
We will explore the core "trapdoor" mechanism that allows a private key holder to solve an otherwise intractable public problem efficiently. We then demonstrate how this principle is applied to construct both public-key encryption and digital signature schemes, with a specific focus on the fast and efficient Unbalanced Oil & Vinegar (UOV) signature system. The talk concludes by summarizing the key advantages of MPKC, such as high-speed operations, and its primary practical challenge: large public key sizes.

Abstract:
This talk is a quick review of the main ideas behind the notion of quantum computation. We discuss challenges towards manufacturing a quantum computer and review the state of the art. This talk is not technical and should be accessible to non-experts.

Abstract:
Hash-based signature schemes are digital-signature families grounded in the security of cryptographic hash functions. They rely on minimal assumptions and are believed to resist known quantum attacks. They are commonly categorized into three groups: one-time signatures (OTS), few-time signatures, and many-time signatures.
NIST has standardized the stateful LMS and XMSS and, more recently, the stateless SPHINCS+. In this talk, I will review Lamport OTS (LOTS) and Winternitz OTS (WOTS) as core one-time signature schemes, explain the central role of Merkle trees in building multi-message schemes from OTS, and, finally, review XMSS and SPHINCS+ as two major standardized designs. In particular, I focus on SPHINCS+, which is built from WOTS+ (a variant of WOTS), FORS (a ew-time signature scheme), and a hypertree of Merkle trees.

Abstract:
Isogeny-based cryptography is a subfield of Post-Quantum Cryptography (PQC) that builds secure primitives (key exchange, signatures) from the hard mathematical problem of finding an isogeny path between two supersingular elliptic curves. This problem is conjectured to be hard for quantum computers, ensuring quantum resistance. This talk provides an introduction to the concepts of elliptic curves and isogenies, followed by a review of the field's primary cryptographic algorithms.

Abstract:
1st Talk: In this talk, I will first introduce algebraic lattices, their properties, and some hard problems related to them including shortest (independent) vector problem, learning with errors, and short integer solution. I will then show how these algebraic tools form basis of lattice-based cryptography resistant against quantum computers.

2nd Talk: I will introduce codes and the hard problems related to them including information set decoding and code equivalence problems. I will also introduce one code-based cryptographic schemes resistant against scalable quantum computers.