Cryptography Math/CprE/InfAs 533
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1 Unit 1 January 10, Cryptography Math/CprE/InfAs 533
2 Unit 1 January 10, Instructor: Clifford Bergman, Professor of Mathematics Office: 424 Carver Hall Voice: fax: Office Hours: MWF 9 10 am cbergman@iastate.edu
3 Unit 1 January 10, WWW: T.A.: Jolie Roat 413 Carver, jdroat@iastate.edu No Required Text Suggested Texts: Cryptography, Theory and Practice, third edition, by D. Stinson, Chapman/CRC Press or Introduction to Cryptography with Coding Theory, second edition, by W. Trappe and L. Washington, Prentice-Hall
4 Unit 1 January 10, Grading 7 or 8 homework assignments approx. 1 week to complete mix of theory and implementation issues
5 Unit 1 January 10, What is Cryptography? Develop techniques for transmitting information securely Cryptography: creating ciphers Cryptanalysis: breaking ciphers Cryptology: Cryptography + Cryptanalysis Plaintext (P) Cyphertext (C) P encryption C decryption P
6 Unit 1 January 10, Some Simple Ciphers Simple Alphabetic Cipher A B C D E R E B Z W... Substitution or monoalphabetic cipher
7 Unit 1 January 10, c 2011 Clifford Bergman
8 Unit 1 January 10, c 2011 Clifford Bergman
9 Unit 1 January 10, Easily broken using statistical properties of the source language. For English, characters is enough
10 Unit 1 January 10, Block Cipher AAA AAB AAC BFT CJK XPX... This shows a cipher with a block size of 3 characters THE QUI CKB ROW NFO XJU... ubj tzf aee wrb ulm caj...
11 Unit 1 January 10, General agreement that a good block size is 16 bytes (i.e. characters) = 128 bits a 0 a 1 a 2... a b 0 b 1 b 2... b c 0 c 1 c 2... c z 0 z 1 z 2... c 127 A random 128-bit substitution would take about bytes to store!
12 Unit 1 January 10, We need a procedure that permutes the set of all 128-bit blocks and that can be described in a relatively small amount of space. I.e., we need algorithms for computing substitutions
13 Unit 1 January 10, Obviously, it is not feasible for everybody to invent their own cryptographic algorithm. Instead we wish to design cryptosystems in which the secrecy is embodied in an additional input, called the key which must be supplied to the algorithm P encryption C decryption P e-key d-key
14 Unit 1 January 10, In traditional ciphers, the decryption key is the same as (or easily deduced from) the encryption key. Such cryptosystems are called symmetric. Also called secret-key cryptosystems.
15 Unit 1 January 10, Problem: How do two parties who can not communicate securely agree on a key? The key-distribution problem
16 Unit 1 January 10, Public-Key Cryptosystems Many parties that have never met but wish to communicate securely. John Paul George Ringo Elvis Idea: Design an algorithm in such a way that the decryption key can not be easily computed from the encryption key.
17 Unit 1 January 10, Everyone s encryption key (public key) is stored in a world-readable database. But the decryption key (private key) is kept secret. Suppose George wants to send a message,p, to John. George looks up John s public key in the database, and encrypts the message: C = E J (P). Sends C to John. No one but John knows the decryption key, so only John can compute: P = D J (C).
18 Unit 1 January 10, In practice, using public-key cryptography to compute actual messages is quite slow. Instead, use PKC to agree on a randomly chosen secret key (to be used once) for some symmetric algorithm. Then the symmetric algorithm is used to communicate. Session Key
19 Unit 1 January 10, Hybrid Cryptosystem Imagine an environment with a public-key system E, D and a symmetric-key system Q. Suppose Alice wishes to initiate a conversation with Bob.
20 Unit 1 January 10, Alice looks up Bob s public key 2 Alice generates a random session-key K for Q 3 Alice sends: C = E B (A, K) to Bob 4 Bob can compute D B (C) = (A, K) 5 Now Alice can send Q K (M)
21 Unit 1 January 10, A fixed procedure such as this for exchanging messages is called a protocol How does Bob know the message really came from Alice? The Authentication Problem
22 Unit 1 January 10, Digital Signatures Alice wishes to send a message P to Bob. Bob wishes to be sure it came from Alice. Alice sends C = D A (P) to Bob. Bob can compute E A (C) since Alice s encryption key is public. D A (P) is Alice s signature on P E A (C) is Bob s verification of Alice s signature
23 Unit 1 January 10, Signing a long document this way is very expensive. Better idea: sign a hash of the document.
24 Unit 1 January 10, One-way functions A function f : X Y is called one-way if for any x X it is easy to compute f (x), but given any y Y it is computationally infeasible to find an x such that f (x) = y. The function that maps a (public-key) decryption key to its corresponding encryption key is, hopefully, one-way.
25 Unit 1 January 10, Hash Functions Takes as input a string of arbitrary length and returns a new string of some fixed, fairly short length. Message Digest, fingerprint, Message Integrity Check Original String= pre-image Output=hash
26 Unit 1 January 10, Example: Input: arbitrary sequence of bytes Output: sum (or x-or) of all bytes, ignoring overflow
27 Unit 1 January 10, One-way hash function Easy to compute the hash of a string. Given a hash, very hard to find a pre-image. Hard to find two pre-images with the same hash. ( Collision-free )
28 Unit 1 January 10, Alice wishes to sign the message P: Computes X = D A (H(P)). Sends (P, X ) For Bob to verify the signature: Computes H(P) and E A (X ) and compares
29 Unit 1 January 10, Smart Cards Credit-card size device containing a microprocessor tamper-proof circuitry Can be used to digitally sign a challenge Relatively slow. Small amount of RAM (8 kb)
30 Unit 1 January 10, Crytanalytic Attacks Objectives of an attack: Deduce the key Learn the content of some particular piece of plaintext Corrupt or alter a message
31 Unit 1 January 10, Kinds of attacks: ciphertext only Attacker intercepts some ciphertext. Knows only the general nature of the plaintext. known plaintext Attacker has access to both some plaintext and its associated ciphertext. p/c pairs
32 Unit 1 January 10, chosen plaintext Attacker is able to choose plaintext and obtain the corresponding ciphertext. chosen cyphertext Attacker is able to choose ciphertext and obtain the corresponding plaintext.
33 Unit 1 January 10, Assumption: The strength of a cryptosystem should reside entirely in the difficulty in determining the key from the above, not in the secrecy of the algorithm. Kerckhoff s principle Security by Obscurity never works...
34 Unit 1 January 10, Exhibit 1: Diebold Voting Machines c 2011 Clifford Bergman
35 Unit 1 January 10, c 2011 Clifford Bergman
36 Unit 1 January 10, Exhibit 2: AACS
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