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Security

141RSA Mathematical Foundation: Primes and Modular Arithmetic
142RSA Key Generation: Selecting Primes and Computing Parameters
143RSA Encryption and Decryption Operations
144RSA Key Sizes and Security Strength
145RSA Padding Schemes: PKCS#1 v1.5
146OAEP: Optimal Asymmetric Encryption Padding
147RSA Signature Generation and Verification
148PSS: Probabilistic Signature Scheme
149Common RSA Implementation Vulnerabilities
150RSA Performance and Hybrid Cryptosystems
151RSA vs Other Asymmetric Algorithms
152RSA Cryptanalysis: Factoring and Future Threats
153Diffie-Hellman Key Exchange Fundamentals
154Discrete Logarithm Problem and Security Foundation
155Diffie-Hellman Parameter Selection and Groups
156Man-in-the-Middle Attacks on Diffie-Hellman
157Ephemeral Diffie-Hellman and Forward Secrecy
158Elliptic Curve Diffie-Hellman (ECDH)
159Small Subgroup and Invalid Curve Attacks
160Authenticated Key Exchange Protocols
161Introduction to Elliptic Curves
162Elliptic Curve Point Operations
163ECC vs RSA: Security and Performance
164ECDSA (Elliptic Curve Digital Signature Algorithm)
165ECDH (Elliptic Curve Diffie-Hellman)
166Standard Elliptic Curves (NIST, secp256k1)
167Curve25519 and EdDSA
168ECC Implementation Vulnerabilities
169Choosing Secure Elliptic Curves
170ECC in Practice: TLS and Beyond
171X.509 Certificate Structure and Format
172Certificate Fields: Subject and Issuer Distinguished Names
173Public Key Information and Algorithm Identifiers
174Certificate Extensions: Basic Constraints and Key Usage
175Subject Alternative Names and Wildcard Certificates
176Certificate Signing Requests (CSR)
177Certificate Chains and Hierarchies
178Self-Signed Certificates vs CA-Issued Certificates
179Certificate Encoding: PEM, DER, PKCS#12, and Formats
180Certificate Lifecycle: Issuance to Expiration
181Certificate Chain Validation Process
182Trust Anchors and Root Certificate Stores
183Path Building and Discovery
184Certificate Policy and Practice Statements
185Name Constraints and Certificate Extensions
186Certificate Pinning Techniques
187Common Certificate Validation Failures
188Time Validation and Clock Attacks
189Certificate Transparency Logs Verification
190Certificate Revocation Fundamentals
191Certificate Revocation Lists (CRLs)
192Online Certificate Status Protocol (OCSP)
193OCSP Stapling and Must-Staple
194Certificate Transparency Logs
195Certificate Transparency Verification
196Revocation Checking Failures and Soft-Fail
197Modern Revocation Alternatives

Security

141RSA Mathematical Foundation: Primes and Modular Arithmetic
142RSA Key Generation: Selecting Primes and Computing Parameters
143RSA Encryption and Decryption Operations
144RSA Key Sizes and Security Strength
145RSA Padding Schemes: PKCS#1 v1.5
146OAEP: Optimal Asymmetric Encryption Padding
147RSA Signature Generation and Verification
148PSS: Probabilistic Signature Scheme
149Common RSA Implementation Vulnerabilities
150RSA Performance and Hybrid Cryptosystems
151RSA vs Other Asymmetric Algorithms
152RSA Cryptanalysis: Factoring and Future Threats
153Diffie-Hellman Key Exchange Fundamentals
154Discrete Logarithm Problem and Security Foundation
155Diffie-Hellman Parameter Selection and Groups
156Man-in-the-Middle Attacks on Diffie-Hellman
157Ephemeral Diffie-Hellman and Forward Secrecy
158Elliptic Curve Diffie-Hellman (ECDH)
159Small Subgroup and Invalid Curve Attacks
160Authenticated Key Exchange Protocols
161Introduction to Elliptic Curves
162Elliptic Curve Point Operations
163ECC vs RSA: Security and Performance
164ECDSA (Elliptic Curve Digital Signature Algorithm)
165ECDH (Elliptic Curve Diffie-Hellman)
166Standard Elliptic Curves (NIST, secp256k1)
167Curve25519 and EdDSA
168ECC Implementation Vulnerabilities
169Choosing Secure Elliptic Curves
170ECC in Practice: TLS and Beyond
171X.509 Certificate Structure and Format
172Certificate Fields: Subject and Issuer Distinguished Names
173Public Key Information and Algorithm Identifiers
174Certificate Extensions: Basic Constraints and Key Usage
175Subject Alternative Names and Wildcard Certificates
176Certificate Signing Requests (CSR)
177Certificate Chains and Hierarchies
178Self-Signed Certificates vs CA-Issued Certificates
179Certificate Encoding: PEM, DER, PKCS#12, and Formats
180Certificate Lifecycle: Issuance to Expiration
181Certificate Chain Validation Process
182Trust Anchors and Root Certificate Stores
183Path Building and Discovery
184Certificate Policy and Practice Statements
185Name Constraints and Certificate Extensions
186Certificate Pinning Techniques
187Common Certificate Validation Failures
188Time Validation and Clock Attacks
189Certificate Transparency Logs Verification
190Certificate Revocation Fundamentals
191Certificate Revocation Lists (CRLs)
192Online Certificate Status Protocol (OCSP)
193OCSP Stapling and Must-Staple
194Certificate Transparency Logs
195Certificate Transparency Verification
196Revocation Checking Failures and Soft-Fail
197Modern Revocation Alternatives

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Lesson 159 of 3,052·4. Asymmetric Cryptography and PKIPro lesson

Small Subgroup and Invalid Curve Attacks

Exploiting weak parameters or malicious public keys to recover private keys or compromise key exchange.

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