Strategic Objectives
• Understand the geometric foundations of elliptic curve isogenies.
• Master the mechanics of the Supersingular Isogeny Diffie-Hellman protocol.
• Evaluate the trade-offs between key size and computational efficiency.
• Explore the latest defenses and attacks in the isogeny-based landscape.
The Core Challenge
As quantum computers threaten to shatter RSA and ECC, the cryptographic world faces an urgent need for compact, secure alternatives.
01
The Quantum Threat
02
Foundations of Elliptic Curves
03
The Nature of Isogenies
04
Supersingular Curves
05
Finite Field Arithmetic
06
The Isogeny Graph
07
The SIDH Protocol
08
Torsion Points and Subgroups
09
The J-Invariant
10
Endomorphism Rings
11
Quaternion Algebras
12
Vélu's Formulas
13
Shor’s Algorithm and Beyond
14
The SIKE Specification
15
Side-Channel Attacks
16
Active Attacks and Invalid Curves
17
Recent Breakthroughs in Cryptanalysis
18
CSIDH: A Commutative Alternative
19
Performance and Optimization
20
Comparison of PQC Candidates
21