PRF

collision-resistant

hash function

CPA-secure encryption

message authentication code

CCA-secure encryption

Cryptography v. real-life security

• If I proved “scheme S is secure under assumption A” and someone uses S in real life, in what cases can things go wrong?
• 1. Security definition does not match real-life attacking scenario
• “Provable security” only protects security on the network level; other levels could go wrong (hardware/software attacks)
• Use a weak security definition (e.g., EAV-security) in scenario where attacker is stronger than what definition covers (e.g., can observe (plaintext,ciphertext) pairs)
• 2. Assumption A is false
• 3. Implementation of S does not match algorithmic description of S
• Conceptual mistakes while implementing
• Software bugs

Public-key cryptography

• Both MAC and encryption schemes are in “symmetric” setting
• Setup: both honest parties share the same key in advance
• Assume you have some physical method to share the key (not super practical in modern setting)

​

• Public-key cryptography: remove this physical assumption
• Require (heavy?) knowledge of number theory / algebra / other areas of math (depends on how deep you want to dive into the area)

Lecture 14: Modular Arithmetic

Division

Modular arithmetic

General rules for modular arithmetic

Group Theory