Cryptography and Cryptanalysis: Lecture Notes for CS 436/636/736, Study notes of Computer Science

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Cryptography/Cryptanalysis, I

CS 436/636/

February 22, 2006

References

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Applied Cryptography, 2/e, Schneier, Wiley

• (^) Material from several chapters adapted for this set of lectures ●

RSA company web site

• (^) http://www.rsasecurity.com/
• (^) http://www.rsasecurity.com/rsalabs/ (more useful) ●

Material from the course text (Chapter 8)

Nomenclature, I

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Cryptography – encryption/decryption science

and engineering and mathematics

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Cryptanalysis – the science and engineering of

breaking encryptions

Nomenclature, II

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Plaintext – the document before it is encrypted

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Ciphertext – the document once encrypted

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encrypt/encipher: P -> M via a cryptographic

algorithm (cypher)

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decipher/decrypt: M -> P under reverse algorithm

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Idempotent algorithm: encryption and decryption

same algorithm (with same key)

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Key : what locks and unlocks a cipher

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Code : “The bird sings loudly, by the river”

Key Ideas

● (^) All secrecy must lie with the keys ● Secrecy within an algorithm is illusory (always assume your algorithm is public and has been studied, for maximum assurance, otherwise make it public!) ● Algorithms must be strong enough to prevent decryption for the useful lifetime of the secrets, given today's and anticipated future computing technology ● (^) Algorithms must be scalable enough to use as widely as needed for a given application at an acceptable cost for the level of assurance ● Cheaters and dishonesty abound between people and computers and each other, make systems work anyway

Current computing vs. future

computing

● NP hard, exponential problems with large exponents can't be solved in acceptable time limits for arbitrary inputs ● Quantum computing is fundamentally a different technology than a Turing machine ● Quantum computing makes some NP hard problems solvable easily, including in cryptographic problems (O(1) time) ● (^) Quantum encryption would replace some current methods, if Quantum computing becomes a reality ● (^) The approximate age of the Universe is 10^18 seconds, as one measure of a long period of time

Some simple ciphers, I

(Chapter 8, and Shneier)

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One-time Pad

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Transposition (EHLL_OOWLR_D <-> HELLO_

WORLD_)

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ROT13 / Caesar (rotation, special permutation)

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Simple Substitution (A<->Z,B<->Q, etc, 1-to-1,

onto mapping, a permutation), monoalphabetic

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Homophonic (e.g., A -> three symbols)

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Polygram (e.g., ABA <-> CDC)

Some simple ciphers, II

(Chapter 8, and Schneier)

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Vigenere Cipher (polyalphabetic)

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Simple XOR (Vigenere type)

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Rotors/Enigma (form of Vigenere)

• (^) Each rotor does a permutation
• (^) Input of next rotor is output of previous rotor
• (^) Enigma also did a partial rearrangement of data at input, moved the rotors at different speeds, as text flowed through

Attacking Simple Cyphers

● Entropy of data in bits, means redundancy exists (you don't need eight bits per letter to encode a poem, or your essay, not even 6 bits per letter probably) ● Frequency of letters in a language (like 'E' in English) ● Frequency of letter pairs in a language (e.g., 'HE' vs 'HY' vs 'EH' vs. 'YH') ● Knowledge in general of what plaintext contains ● (^) Index of coincidence (e.g., find key lengths) ● (^) Correlation by offset/xor (e.g., to find key lengths)

Prominence of Theoretical Math

● One-way function practical irreversibility ● (^) Factorization of large numbers difficult ● Computation of discrete logarithms difficult ● This and other computations that can or cannot be done tractably control whether or not there is sufficient assurance to key encryption algorithms ● (^) Researchers are trying to learn how to stretch what can be computed, some information is irreducible ● (^) Elusiveness of Randomness, pseudo-random sequences ● Some aspects closely related to Turing halting problem, Godel incompletness theorem, axiom vs. provability, etc

General practical strategy

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Use public-key encryption for signing documents

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Use symmetric key algorithms together with

signatures for encrypting documents

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Public-key algorithms are subject to known-

plaintext attacks, given that one key is public,

such attacks can be on-going always

One-way function

(Schneier, Section 2.3)

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Fundamental building block for public-key

cryptography

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f:x->f(x), f is the one-way function, x is the input

text

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Relatively easy to form f(x) given x

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Very hard to form x given f(x) [preimage]

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Trap-door-one-way-function, one-way-function,

but if you know a trapdoor 'y', you can compute

'x' from f(x) and y relatively easily

Message Authentication Code (MAC)

(Schneier, p. 31)

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Not Mandatory Access Control (from Comp

Sec.), nor Media Access Control (ISO OSI

model)

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Aka DAC (Data authentication code)

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Hash is both of data and a key

Security Protocol Top-Billed Dramatis Personae* (Schneier) ● Alice – the first party in a protocol ● (^) Bob – the second partyin a two or more way protocol ● Trent – The trusted arbiter for arbitrated protocols ● Mallory (female or male?) - hacker/active attacker ● (^) Eve (the person in the middle) – passive attacker ● Carol – third party in a three party or more protocol ● Dave – fourth party in a four way or more protocol