# Fundamentals of Computer Security

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1 Fundamentals of Computer Security Spring 2015 Radu Sion Intro Encryption Hash Functions

2 A Message From Our Sponsors Fundamentals System/Network Security, crypto How do things work Why How to design secure stuff 2

3 What we are not How to install XXX Command line options of XXX Latest iexplorer buffer overflow bug Latest McAfee/XXX products Network administration How to break your gf/bf account 3

4 Ground Rules Dates are listed online now Zero tolerance to academic dishonesty Informal class, ask questions anytime Read your assigned readings! There may be quizzes Call me Radu Questions: office hours, or to schedule appt. Have fun! 4

5 Evaluation Homeworks (0-10%) Midterm (30-40%) Activity and pop quizzes (0-10%) Final (40-50%) Course website: check link in your 5

6 Classical Crypto Single/Symmetric Key Encryption Cryptographic Hash Functions 6

7 Meet the Cast Read: Alice (innocent) k Trent (trusted guy) does stuff too E k (M) M just listens k Bob (mostly innocent, sometimes malicious) Mallory ( mallicious, bad guy) Eve (eavesdrops, passive malicious) 7

8 An inconvenient truth Where does k come from? ( key distribution ) Can Eve distinguish between E k (M 1 ) and E k (M 2 ) if she knows M 1 and M 2? Should not be able to!!! ( semantic security ) Make sure that E k (M 1 ) E k (M 2 ) if M 1 M 2 (maybe not?) Can Mallory modify E k (M) into an E k (M mallory )? ( malleability ) etc (! lots of stuff!) Danger: things seem trivial and they are not result: super weak systems! 8

9 Caesar Cipher Example: Cæsar cipher M = { sequences of letters } K = { i i is an integer and 0 i 25 } E = { E k k K and for all letters m, E k (m) = (m + k) mod 26 } D = { D k k K and for all letters c, C = M D k (c) = (26 + c k) mod 26 } 9

10 Attacks Opponent whose goal is to break cryptosystem is the adversary Assume adversary knows algorithm used, but not key Many types of attacks: ciphertext only: adversary has only ciphertext; goal is to find plaintext, possibly key known plaintext: adversary has ciphertext, corresponding plaintext; goal is to find key chosen plaintext: adversary may supply plaintext and obtain corresponding ciphertext; goal is to find key chosen ciphertext: adversary may supply ciphertext and obtain corresponding plaintext; goal is to find key etc 10

11 How to attack? Mathematical attacks Based on analysis of underlying mathematics Statistical attacks Make assumptions about the distribution of letters, pairs of letters (digrams), triplets of letters (trigrams), etc. Called models of the language Examine ciphertext, correlate properties with the assumptions. 11

12 Statistics Compute frequency of each letter in ciphertext: G 0.1 H 0.1 K 0.1 O 0.3 R 0.2 U 0.1 Z 0.1 Apply 1-gram model of English Correlate and invert encryption 12

13 Caesar has a Problem Key is too short Can be found by exhaustive search Statistical frequencies not concealed well They look too much like regular English letters So make it longer Multiple letters in key Idea is to smooth the statistical frequencies to make cryptanalysis harder 13

14 Vigènere Cipher Like Cæsar cipher, but use a phrase Documented by Blaise de Vigenere (court of Henry III of France) in Paris, 1586 actually a variant of a cipher by a J.B. Porter Example Message THE BOY HAS THE BALL Key VIG Encipher using Cæsar cipher for each letter: key VIGVIGVIGVIGVIGV plain THEBOYHASTHEBALL cipher OPKWWECIYOPKWIRG 14

15 Holy Grail: One-Time Pad A Vigenère cipher with a random key at least as long as the message Provably unbreakable Why? Look at ciphertext DXQR. Equally likely to correspond to plaintext DOIT (key AJIY) and to plaintext DONT (key AJDY) and any other 4 letters Warning: keys must be random, or you can attack the cipher by trying to regenerate the key Approximations, such as using pseudorandom number generators to generate keys, are not random 15

16 Crypto Hash Functions Mathematical function to generate a set of k bits from a set of n bits (where k n). k is usually smaller then n Example: ASCII parity bit ASCII has 7 bits; 8th bit is parity Even parity: even number of 1 bits Odd parity: odd number of 1 bits 16

17 Sample Use Bob receives as bits. Sender is using even parity; 6 1 bits, so character was received correctly Note: could be garbled, but 2 bits would need to have been changed to preserve parity Sender is using odd parity; even number of 1 bits, so character was not received correctly 17

18 Definition Cryptographic hash h: A B: 1. For any x A, h(x) is easy to compute 2. h(x) is of fixed length for any x (compression) 3. For any y B, it is computationally infeasible to find x A such that h(x) = y. (pre-image resistance) 4. It is computationally infeasible to find any two inputs x, x A such that x x and h(x) = h(x ) (collision resistance) 5. Alternate form of 3 (stronger): Given any x A, it is computationally infeasible to find a different x A such that h(x) = h(x ). (second preimage resistance) 18

19 Collisions If x x and h(x) = h(x ), x and x are a collision Pigeonhole principle: if there are n containers for n+1 objects, then at least one container will have 2 objects in it. Application: if there are 32 files and 8 possible cryptographic checksum values, at least one value corresponds to at least 4 files 19

20 Intuition A hash is a one-way, non-invertible function of that produces unique (with high likely-hood), fixed-size outputs for different inputs. The probability of any bit flipping in the output bit-string should be always ½ for any change (even one bit) in the input ( randomness ). 20

21 Sample Cipher: MD5 Basic idea: Continuously update hash value with 512 bit blocks of message 128 bit initial value for hash Bit operations to compress Compression function: Update 128 bit hash with 512 bit block Pass 1: Based on bits in first word, select bits in second or third word Pass 2: Repeat, selecting based on last word Pass 3: xor bits in words Pass 4: y (x or ~z) 21

22 Example MD5 Digest md5_digest("the quick brown fox jumps over the lazy dog") = 9e107d9d372bb6826bd81d3542a419d6 md5_digest("the quick brown fox jumps over the lazy cog") = 1055d3e698d289f2af bd4b 22

23 Hashes to (not) use Do not use at all the following: MD5, SHA-0/1, any other obscure secret ones For use in civilian/.com setting (until 2025): SHA-256/512, SHA3 23

24 Cool Application: Keyed Hashes Message Authentication Code (MAC) MAC(msg)=H(H(key,msg,key),msg) Usage: append this to message to allow authentication 24

25 Purpose of MACs? Want to enable only a certain party to verify authenticity of data for which it has a MAC (for example). Want to prevent Mallory to alter message and simply replace MAC (cannot do it now doesn t know the secret key) 25

26 Optional for next week For +5% credit in final exam. Install openssl and decrypt any of the following ciphertexts: U2FsdGVkX18Avp0s9oaA8I2HeaLoCG1gZyRmoLWWBFZXcrm/1ZsXSjxc2XTpbPZw U2FsdGVkX18KRUFApfRXdayMo8sYd96zEAdPXyA4hzMBdWxqVigJGsLs4okBhwje U2FsdGVkX1/DUTj3FPMhUWb/hgxIchBN6LWoRbLm2L/CARN/VSAYlg== U2FsdGVkX1/+vE2czERZciAIJteLkzndHwW9QrdibZ/Z6q8= 26

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