CSE 127: Introduction to Security
Public-Key Cryptography
UCSD Winter 2022
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Slides adapted from
► Key Exchange
► Public Key Encryption ► Digital Signatures
Asymmetric cryptography/public-key cryptography
Main insight: Separate keys for different operations.
Keys come in pairs, and are related to each other by the specific
► Public key: used to encrypt or verify signatures ► Private key: used to decrypt and sign
Public-key encryption
► Encryption: (public key, plaintext) → ciphertext Encpk(m) = c
► Decryption: (secret key, ciphertext) → plaintext Decsk(c) = m
Properties:
► Encryption and decryption are inverse operations:
Public-key encryption
► Encryption: (public key, plaintext) → ciphertext Encpk(m) = c
► Decryption: (secret key, ciphertext) → plaintext Decsk(c) = m
Properties:
► Encryption and decryption are inverse operations:
Decsk (Encpk (m)) = m
Secrecy: ciphertext reveals nothing about plaintext ► Computationally hard to decrypt without secret key
► The point:
► Anybody with your public key can send you a secret message! Solves key distribution problem.
Modular Arithmetic Review
Division: Let n,d,q,r be integers.
n = qd + r
0≤r