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Introduction to cryptography - INFO-F-405 - 4. Public Crypto - Coggle…
Introduction to cryptography - INFO-F-405 - 4. Public Crypto
🌐
Fundamentals
🔑
Asymmetric Keys
Uses a public key for encryption and a private key for decryption.
🔒
Applications
Confidentiality (encryption/decryption)
Authenticity (digital signatures)
⚠️
Threats
Man-in-the-middle attacks without proper verification.
🏛️
Public Key Infrastructure (PKI)
Binding Keys to Identities
Certificates issued by trusted CAs.
Trust Models
Hierarchical (CA-based)
Web of trust (e.g., PGP)
📜
Certificate Structure
Contains public key, owner identity, CA’s digital signature.
🧮
Key Algorithms
🔢
Factorization Problem
RSA encryption.
📉
Discrete Logarithm Problem
Diffie-Hellman, ElGamal.
📈
Elliptic Curve Cryptography (ECC)
Secure with smaller keys.
⚡
Hybrid Encryption
Combines
asymmetric
and
symmetric
encryption.
Steps
:
Encrypt symmetric key with receiver’s public key.
Use symmetric key to encrypt the message.
Receiver decrypts symmetric key, then the message.
📖
Mathematical Foundations
Groups and Modular Arithmetic
Essential for RSA, DLP methods.
GCD and Bezout’s Identity
Verifies relative primacy in RSA.
Fermat’s & Euler’s Theorems
Underpin modular exponentiation.
🔐
RSA
Key Generation
:
Choose two primes \( p \) and \( q \), compute \( n = pq \)
Encryption/Decryption
:
\( c = m^e \mod n \), \( m = c^d \mod n \)
⚠️
Vulnerabilities
:
Cyclic, message factorization, short message attacks.
🔄
Diffie-Hellman
Generates shared secret over insecure channels.
Ephemeral Diffie-Hellman
:
Temporary keys for enhanced security.
✍️
ElGamal
Encryption
:
Uses unique ephemeral keys.
Signatures
:
Reusing ephemeral keys risks exposure.
✨
Elliptic Curve Cryptography (ECC)
Weierstrass Equation
: \( y^2 = x^3 + ax + b \)
Point Operations
:
Point addition and doubling.
Efficiency
:
Smaller key sizes for equivalent security.
✅
Recommendations
Hybrid Encryption
: Best for efficiency and security.
Avoid Textbook Implementations
:
Use padded RSA (OAEP) or PSS for security.
ECC for Resource-Constrained Systems
:
Smaller keys suitable for mobile devices.