Gambling with Secrets: Part 4/8 (Private Key Cryptography)

Art Of The Problem
Feb 14, 2012
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6 Notes in this Video

Frequency Analysis Attack on Repeating Keys

FrequencyAnalysis Cryptanalysis InformationLeakage VigenereCipher

Eve the codebreaker intercepts encrypted messages and calculates letter frequencies, discovering that repeating keyword patterns create detectable statistical fingerprints despite the flatter distribution compared to simple substitution ciphers.

Information Leakage Through Repetition

InformationLeakage Repetition Cryptanalysis FrequencyDifferential

Codebreakers exploit the fundamental principle that any repetitive pattern in encryption methods creates differential frequency distributions that leak information about the underlying plaintext structure.

Keyspace Explosion: Visualizing Perfect Secrecy

KeySpace Combinatorics PerfectSecrecy Visualization

Comparing Caesar cipher’s 26 possible encryptions of Alice’s name against one-time pad’s 26 to the fifth power possibilities—nearly 12 million encryptions—visualizes how random keys create astronomical outcome spaces.

One-Time Pad: Perfect Secrecy Through Randomness

OneTimePad PerfectSecrecy RandomKey Cryptography

Alice generates a list of truly random shift values as long as her message by rolling a 26-sided die, shares this random key with Bob in advance, then uses each random shift exactly once to encrypt one message letter.

Perfect Secrecy: No Repetition and Uniform Distribution

PerfectSecrecy UniformDistribution InformationTheory Cryptography

One-time pad encryption achieves perfect secrecy through two critical properties—shifts never fall into repetitive patterns and the encrypted message exhibits perfectly uniform frequency distribution across all letters.

Vigenère Cipher: Repeating Key Encryption

VigenereCipher Encryption ClassicalCryptography SubstitutionCipher

Alice and Bob share a secret shift word that Alice converts into numbers representing alphabet positions, using these numbers as variable shift amounts to encrypt each message letter before sending it openly to Bob for decryption.