Elliptic Curve Cryptography: Galois Fields

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Elliptic Curves: Theory and Applications

Covers the theory and applications of elliptic curves in cryptography and number theory.

Cryptographic Primitives: Theory and Practice

Explores fundamental cryptographic primitives, security models, and the relationship between decryption security and key recovery security.

Asymmetric Cryptography: RSA, Elliptic Curves, Lattices

Explores RSA, elliptic curves, and lattice-based cryptography for secure communication.

Galois Theory Fundamentals

Explores Galois theory fundamentals, including separable elements, decomposition fields, and Galois groups, emphasizing the importance of finite degree extensions and the structure of Galois extensions.

RSA Cryptography: Computational Problems

Explores RSA cryptography computational problems, finite fields construction, and computational challenges in RSA cryptography.

Integer Factorization: Quadratic Sieve

Explores integer factorization using the quadratic sieve method and the challenges of working with algebraic number fields.

Hensel's Lemma and Field Theory

Covers the proof of Hensel's Lemma and a review of field theory, including Newton's approximation and p-adic complex numbers.

Finite Fields: Properties and Applications

Explores the properties and applications of finite fields, including isomorphism and cyclic properties.

Commutative Groups: Foundations for Cryptography

Covers commutative groups and their significance in cryptography.

Finite Degree Extensions

Covers the concept of finite degree extensions in Galois theory, focusing on separable extensions.