CSC 382: Computer Security

1. CSC 382: Computer Security Applying Cryptography CSC 382: Computer Security

2. Topics • Hash Algorithms • Key Sizes • Key Generation • Information Theory • Randomness • PRNGs • Entropy Gathering • Practical Sources of Randomness • Cryptographic APIs CSC 382: Computer Security

3. 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 CSC 382: Computer Security

4. 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. CSC 382: Computer Security

5. Key Sizes: Public Key Ciphers Bit 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. CSC 382: Computer Security

6. 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. CSC 382: Computer Security

7. 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. CSC 382: Computer Security

8. Information Information: H = log2(M), where M is the number of equiprobable possibilities for the state of the system. Example: Coin flip (2 equiprobable results) H = log2(2) = 1 bit CSC 382: Computer Security

9. Information Content of English For random English letters, log2(26) @ 4.7 bits/letter For large samples of English text, 1.3 bits/letter For bzipped English text, 7.95+ bits/letter CSC 382: Computer Security

10. What is a Random Number? • Is 3 a random number? • How about 107483? • Or 3.1415927? CSC 382: Computer Security

11. 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. CSC 382: Computer Security

12. PRNGs • Determinism and Randomness • Seeding the PRNG • Linear Congruential • CSPNRGs • Blum-Blum-Shub • Tiny • Attacks on PNRGs CSC 382: Computer Security

13. 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 CSC 382: Computer Security

14. 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. CSC 382: Computer Security

15. 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. CSC 382: Computer Security

16. Linear Congruential Generator nk = (ank–1 + b) mod m m Modulus (a large prime integer) a Multiplier (integer from 2..m-1) bIncrement n0 Sequence initializer (seed) CSC 382: Computer Security

17. Linear Congruential Generator 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. CSC 382: Computer Security

18. LCG Example in Python #!/usr/bin/env python import sys def lcg(x): return a*x % 13 i = 0; li=[] a, x = map(int, sys.argv[1:3]) while(i < 10): x = lcg(x) li.append(str(x)) i += 1 print ", ".join(li) >./prng.py 5 2 11, 4, 8, 2, 11, 4, 8, 2, 11, 4 >./prng.py 6 2 0, 1, 7, 4, 12, 8, 10, 9, 3, 6 CSC 382: Computer Security

19. Linear Congruential Generator Choice of a critical Many 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 common a = 16807 is well studied full period multiplier LCGs are statistically random but predictable, giving away state with result. LCGs are not cryptographically useful. CSC 382: Computer Security

20. Secure PRNGs Cryptographically Secure PRNGs: • Statistically appear random. • Difficult to predict next member of sequence from previous members. • Difficult to extract internal state of PRNG from observing output. Similar to stream ciphers. May be re-seeded at runtime, unlike PRNGs. CSC 382: Computer Security

21. 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 CSC 382: Computer Security

22. 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. CSC 382: Computer Security

23. 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-1 Use on UNIX-based systems: (date; ps gaux) | md5 where “ps gaux” lists all information about all processes on system. CSC 382: Computer Security

24. Attacks on PNRGs Direct 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 CSC 382: Computer Security

25. 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. CSC 382: Computer Security

26. ASF PRNG Flaws • PRNG algorithm used small seed (32 bits.) • Non-cryptographic PRNG used. • Seed generated by poor source of randomness. CSC 382: Computer Security

27. Entropy Collection • Hardware Solutions • Software Solutions • Poor Entropy Collection • Entropy Estimation CSC 382: Computer Security

28. Hardware Sources Radioactive 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 CSC 382: Computer Security

29. 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. CSC 382: Computer Security

30. 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 CSC 382: Computer Security

31. 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. CSC 382: Computer Security

32. 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. CSC 382: Computer Security

33. 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. CSC 382: Computer Security

34. Cryptographic APIs • Cryptlib • OpenSSL • Crypt++ • BSAFE • Cryptix • Crypt:: CPAN modules CSC 382: Computer Security

35. Supported Ciphers 1. Range of MAC algorithms Almost all include MD5, SHA-1 2. Range of symmetric algorithms Almost all include AES, DES 3. Range of public key algorithms Almost all include RSA, Diffie-Hellman, DSA CSC 382: Computer Security

36. Cryptographic APIs Cryptlib • easy to use • free for noncommercial use OpenSSL • poorly documented • open source • popular CSC 382: Computer Security

37. Cryptographic APIs Crypto++ • C++ library • open source BSAFE • well documented • most popular commercial library • commercial SDK from RSA CSC 382: Computer Security

38. 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 CSC 382: Computer Security

39. Key Points • Keys generated must be truly random. • Algorithmic PRNG techniques: • Linear congruential generators: non-crypto. • Blum Blum Shub cryptographic PRNG. • Computer RNGs: • Hardware RNGs: thermal noise, decays. • Software RNGs: disk seeks, interrupts. • High quality open source cryptography libraries exist for most languages. CSC 382: Computer Security

40. References • Matt Bishop, Introduction to Computer Security, Addison-Wesley, 2005. • D. Eastlake, “Randomness Recommendations for Security,” RFC 1750, http://www.ietf.org/rfc/rfc1750.txt, 1994. • Ian Goldberg and David Wagner,“Randomness and the Netscape Browser,” Doctor Dobbs’ Journal, 1996. http://www.cs.berkeley.edu/~daw/papers/ddj-netscape.html • Michael Howard and David LeBlanc, Writing Secure Code, 2nd edition, Microsoft Press, 2003. • 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. • 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. • Tom Schneider, “Information Theory Primer,” http://www.lecb.ncifcrf.gov/~toms/paper/primer/, 2000. • Bruce Schneier, Applied Cryptography, 2nd edition, Wiley, 1996. • John Viega and Gary McGraw, Building Secure Software, Addison-Wesley, 2002. • John Viega and Matt Messier, Secure Programming Cookbook for C and C++, O’Reilly, 2003. • Joss Visser, “Kernel based random number generation in HP-UX 11.00,” http://www.josvisser.nl/hpux11-random/hpux11-random.html, 2003. • David Wheeler, Secure Programming for UNIX and Linux HOWTO, http://www.dwheeler.com/secure-programs/Secure-Programs-HOWTO/index.html, 2003. CSC 382: Computer Security