Background: Public Key of the Cryptography | CSCI 350, Study notes of Computer Science

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CSCI 350 – Spring 2006

Slide Set 12: Public-Key Cryptography: Background

Why Encrypt?

• Communication model: Alice and Bob send

messages across a channel.

Alice Bob

M

Eve

Problem: Eavesdroppers!

Encryption

• Encryption is the process of converting text into enciphered or encoded form. The process of converting encrypted text back to the original plain text is decryption.
• The encryption/decryption process depends on a secret. The secret may be the key used in the encryption process, but could also include the details of the encryption process. Note that the secret is not the transmitted text.

The Computational Perspective

• Mathematically, encryption is done via an

invertible function e and decryption is done via its inverse d = e -1. We assume that we have programs E and D that compute e and d respectively.

• Given a message M , the encrypted version is

E(M). We can decrypt this using D(E(M)) = E-1^ (E(M)) = M.

Examples Using Ciphers

• We can write encryption functions for the

following ciphers:

• shift characters a fixed amount throught the alphabet (cyclical shift)
• apply a sequence of maps (Enigma)
• use a randomized map (one-time pad): XOR a random byte with each character.
• How good are these approaches?

Attacks

• Consider the following ways to attack the ciphers on the previous page: - brute force: try all single character shifts - statistical analysis: use letter and word frequencies - plain text attack: compare known plain text with encrypted version of that text
• One-time pad holds up against these attacks (note that we need real randomness, not C++ rand() function!). But coordination is an issue.

Problems with Shared Secrets

• Key transmission
• Key security
• Dealing with multiple parties