CSC 382: Computer SecuritySlide #1 CSC 382: Computer Security Applying Cryptography

CSC 382: Computer Security Slide #1

CSC 382: Computer Security

Applying Cryptography


Topics

1. Hash Algorithms

2. Key Sizes

3. Key Generation

4. Information Theory

5. Randomness

6. PRNGs

7. Entropy Gathering

8. Practical Sources of Randomness

9. Cryptographic APIs


State of Hash Functions

Avoid the following widely-used hash algorithms:– MD5, SHA-1

We don’t have a theory of how to design hashes.– No hash algorithm has been secure for 10 years.– Too optimistic in the past: MD5 and SHA-1 would

have been secure with twice as many rounds.

What can we do?– Design protocols (digital signatures, SSL, etc.) so that

they can switch hash functions easily.– Use SHA-256 for now.– Look at new hashes: FORK-256, DHA-256, VSH


Key Sizes: Symmetric Ciphers

Advanced Encryption Standard– AES supports 128-, 192-, and 256-bit keys.– 128-bit keys should be good enough for all time

provided no attack better than brute force discovered.

Bit size means different things for symmetric and public key ciphers.


Key Sizes: Public Key CiphersBit size measures different characteristics for different public key algorithms.

Public key cipher security dependent on advances in number theory and computing approaches like quantum computing.

Recommended size is 2048-bits for RSA, DSA, and Diffie-Hellman.

ECC uses much smaller keys.


Key Generation

Goal: generate difficult to guess keys

Given set of K potential keys, choose one randomly.– Equivalent to selecting a random number between 0 and

K–1 inclusive.

Difficulty: generating random numbers– Computer generated numbers are pseudo-random, that is,

generated by an algorithm.


Information

The amount of information in a message is the minimal number of bits needed to encode all possible meanings.

Example: day of the week– Encode in <3 bits– 000 Sunday to 110 Saturday, with 111 unused– ASCII strings “Sunday” through “Saturday”

use more bits, but don’t encode more information.


Information

Information:

H = log2(M),where M is the number of equiprobablepossibilities for the state of the system.

Example: Coin flip (2 equiprobable results)

H = log2(2)

= 1 bit


Information Content of English

For random English letters,

log2(26) bits/letter

For large samples of English text,

1.3 bits/letter

For bzipped English text,

7.95+ bits/letter


What is a Random Number?

1. Is 3 a random number?

2. How about 107483?

3. Or 3.1415927?


What is Randomness?

A byte stream is random if– H is approximately 8 bits/byte

How can we get a random byte stream?– Compression is a good randomizing function.– Cryptography is a good randomizing function.

Statistical tests for randomness– 0s occur about as often as 1s.– Pairs of 0s occur about half as often as single 0s

and as often as pairs of 1s.


PRNGs

1. Determinism and Randomness

2. Seeding the PRNG

3. Linear Congruential

4. CSPNRGs

5. Blum-Blum-Shub

6. Tiny

7. Attacks on PNRGs


Determinism

Computers are deterministic.

– They can’t produce random numbers.

– “Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin.” – John vonNeumann


Pseudo-random Numbers

Pseudo-random numbers appear to be random to certain statistical tests.– Tests can be derived from compression.– If you can compress sequence, it’s not random.

Software generated pseudo-random sequences are periodic and predictable.


Seeds

Input used to generate initial PR number.

Should be computationally infeasible to predict– Generate seed from random, not PR, data.

– Large seed: 32 bits too small; only 232 combinations.

Sequence still repeats, but starts from different point for each different seed.– Identical sequences produced for identical seeds.

– Period needs to be large for security.


Linear Congruential Generator

nk = (ank–1 + b) mod m

m Modulus (a large prime integer)a Multiplier (integer from 2..m-1)b Increment

n0 Sequence initializer (seed)



Why must m be prime?– Prevents sequence from becoming all zeros.

Why must m be large?– Maximum period is m.

What’s important about a and b?– Constants a and b determine if LCG will have a

full period (m) or repeat sooner.


LCG Example in Python#!/usr/bin/env pythonimport sysdef lcg(x): return a*x % 13i = 0; li=[]a, x = map(int, sys.argv[1:3])while(i < 10): x = lcg(x) li.append(str(x)) i += 1print ", ".join(li)

>./prng.py 5 211, 4, 8, 2, 11, 4, 8, 2, 11, 4>./prng.py 6 20, 1, 7, 4, 12, 8, 10, 9, 3, 6



Choice of a criticalMany choices of a produce a full period.

• Sequence is permutation of integers 1..m-1• Ex: 2, 6, 7, 11 for m=13

For production LCGs, m=232-1 commona = 16807 is well studied full period multiplier

LCGs are statistically randombut predictable, giving away state with result.

LCGs are not cryptographically useful.


Secure PRNGs

Cryptographically Secure PRNGs:1. Statistically appear random.2. Difficult to predict next member of sequence

from previous members.3. Difficult to extract internal state of PRNG from

observing output.

Similar to stream ciphers.May be re-seeded at runtime, unlike PRNGs.


Blum Blum Shub

xn+1 = xn2 mod M

Blum Number M– Product of two large primes, p and q– p mod 4 = 3, q mod 4 = 3

Seed– Choose random integer x, relatively prime to M.

– x0 = x2 mod M


Blum Blum Shub

Random Output:– LSB of xn+1

– Can safely use log2M bits.

Provably secure– Distinguishing output bits from random bits is

as difficult as factoring M for large M.

Slow– Requires arbitrary precision software math libs.


Strong Mixing Functions

Strong mixing function: function of 2 or more inputs with each bit of output depending on some nonlinear function of all input bits.

Examples: AES, DES, MD5, SHA-1Use on UNIX-based systems:

(date; ps gaux) | md5

where “ps gaux” lists all information about all processes on system.


Attacks on PNRGsDirect Cryptanalytic

– Distinguish between PRNG output and random output with better than 50% accuracy.

Input-Based– Use knowledge of PRNG input to predict output.– Insert input into PRNG to control output.

State Compromise Extension– Extend previously successful attack that has recovered

internal state to recover either or both:• past unknown PRNG outputs• future PRNG outputs after additional inputs given to

PRNG


ASF On-line Gambling

Re-seed PRNG before each shuffle– always start with ordered deck.

Shuffling– Fair: 52! 2226 combinations– 32-bit seed: 232 combinations– ms seed: 86,400,000 combinations– synchronize time: 200,000 combinations

Predict deck based on 5 known cards.


ASF PRNG Flaws

1. PRNG algorithm used small seed (32 bits.)

2. Non-cryptographic PRNG used.

3. Seed generated by poor source of randomness.


Entropy Collection

1. Hardware Solutions

2. Software Solutions

3. Poor Entropy Collection

4. Entropy Estimation


Hardware SourcesRadioactive Decay

– Hotbits: 256 bits/s– http://www.fourmilab.ch/hotbits/

Thermal Noise– Comscire QNG Model J1000KU, 1 Mbit/s– Pentium III RNG

LavaRnd– SGI used LavaLite; LavaRnd uses lenscapped digicam– http://www.lavarnd.org/– up to 200 kbits/s


Software Sources

Less Secure, More Convenient– Software sufficiently complex to be almost

impossible to predict.

User Input: Push, don’t Pull– Record time stamp when keystroke or mouse

event occurs.– Don’t poll most recent user input every .1s

• Far fewer possible timestamps.


Software Sources: /dev/random

Idea: use multiple random software sources.– Store randomness in pool for user requests.– Use hash functions (i.e., strong mixing functions) to

distill data from multiple sources.

/dev/random can use random sources such as– CPU load– disk seeks– kernel interrupts– keystrokes– network packet arrival times– /dev/audio sans microphone


Software Sources: /dev/random

/dev/random– each bit is truly random.– blocks unless enough random bits are available.

/dev/urandom– supplies requested number of bits immediately.– reuses current state of pool—lower quality

randomness.– cryptographically secure RNG.


When to use /dev/{u}random?

Use true entropy for– Generating long-term cryptographic keys.– Seeding cryptographically secure RNGs.– But true randomness is in low supply so

Use cryptographically secure RNGs– For everything else.


Poor Entropy: Netscape 1.1

SSL encryption– generates random 40- or 128-bit session key

– Netscape 1.1 seeded PRNG with

• time of day

• PID and PPID

– All visible to attacker on same machine.

Remote attack broke keys in 30 seconds– guessed limited randomness in PID/PPID.

– packet sniffing can determine time of day.


Cryptographic APIs

1. Cryptlib

2. OpenSSL

3. Crypt++

4. BSAFE

5. Cryptix

6. Crypt:: CPAN modules


Supported Ciphers

1. Range of MAC algorithmsAlmost all include MD5, SHA-1

2. Range of symmetric algorithmsAlmost all include AES, DES

3. Range of public key algorithmsAlmost all include RSA, Diffie-Hellman, DSA


Cryptographic APIs

Cryptlib– easy to use– free for noncommercial use

OpenSSL– poorly documented– open source– popular


Cryptographic APIs

Crypto++– C++ library– open source

BSAFE– well documented– most popular commercial library– commercial SDK from RSA


Cryptographic APIs

Cryptix– open source Java library

Python Cryptographic Toolkit– open source crypt, hash, rand modules– http://www.amk.ca/python/code/crypto

Crypt:: CPAN modules for perl– well documented– many different libraries


Key Points

1. Keys generated must be truly random.2. Algorithmic PRNG techniques:

– Linear congruential generators: non-crypto.– Blum Blum Shub cryptographic PRNG.

3. Computer RNGs:– Hardware RNGs: thermal noise, decays.– Software RNGs: disk seeks, interrupts.

4. High quality open source cryptography libraries exist for most languages.


References1. Matt Bishop, Introduction to Computer Security, Addison-Wesley, 2005.2. D. Eastlake, “Randomness Recommendations for Security,” RFC 1750,

http://www.ietf.org/rfc/rfc1750.txt, 1994.3. Ian Goldberg and David Wagner, “Randomness and the Netscape Browser,” Doctor

Dobbs’ Journal, 1996. http://www.cs.berkeley.edu/~daw/papers/ddj-netscape.html4. Michael Howard and David LeBlanc, Writing Secure Code, 2nd edition, Microsoft Press,

2003.5. Alfred J. Menezes, Paul C. van Oorschot and Scott A. Vanstone, Handbook of Applied

Cryptography, http://www.cacr.math.uwaterloo.ca/hac/, CRC Press, 1996.6. S. K. Park, K. W. Miller, “Random number generators: good ones are hard to find,”

Communications of the ACM, Volume 31 Issue 10 , October 1988.7. Tom Schneider, “Information Theory Primer,”

http://www.lecb.ncifcrf.gov/~toms/paper/primer/, 2000.8. Bruce Schneier, Applied Cryptography, 2nd edition, Wiley, 1996.9. John Viega and Gary McGraw, Building Secure Software, Addison-Wesley, 2002.10. John Viega and Matt Messier, Secure Programming Cookbook for C and C++, O’Reilly,

2003.11. Joss Visser, “Kernel based random number generation in HP-UX 11.00,”

http://www.josvisser.nl/hpux11-random/hpux11-random.html, 2003.12. David Wheeler, Secure Programming for UNIX and Linux HOWTO,

http://www.dwheeler.com/secure-programs/Secure-Programs-HOWTO/index.html, 2003.

http://www.cacr.math.uwaterloo.ca/hac/authors/ajm.html

http://www.dwheeler.com/secure-programs/Secure-Programs-HOWTO/index.html

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CSC 382: Computer SecuritySlide #1 CSC 382: Computer Security Applying Cryptography