This document discusses randomness and random number generation. It notes that cryptography relies on random numbers, but that generating truly random numbers is difficult. While theory assumes a perfect random source, in practice pseudorandom number generators are used. Several examples are given of systems that used weak random number generation that led to security issues. Lessons discussed include the importance of unpredictable seeds for pseudorandom number generators and using cryptographically secure functions. The document contrasts truly random and pseudorandom number generation, and provides tips for analyzing randomness in programs and web applications.

1. 1
Much Ado About Randomness.
What Is a Random Number?
Aleksandr Yampolskiy, Ph.D.
Gilt Groupe

2. Randomness
Random number generation is easy to get wrong.

3. 3
In Theory
• Cryptography is based on random
numbers:
– Secret keys must be random
– Random bits are needed for public-key
encryption, signatures, SSL, etc.
• A common assumption in theory is a
random oracle model, where all parties
have access to a perfect random
source [BR92].
• Under this assumption, many crypto
tools can be proven formally secure.

4. In Practice
• Kaminsky bug used to poison DNS caches.
• Debian OpenSSL versions <0.9.8g-9
generated weak SSL keys.
• Some Majordomo versions were
susceptible to subscribing victim to
thousands of mailing lists.
• Kerberos 4 secret keys could be guessed in
a few seconds.
• Netscape 1.1 generated SSL keys using
time and process ID as seed; easily
guessable and breakable.

5. Example #1
- unsigned char magic_cookie[LEN];
- srand(time(NULL));
- for (int i=0; i<LEN; i++) magic_cookie[i] = rand()
& 0xFF;
X Windows “magic cookie” used a weak LCG generator
and was guessable in X11R6.

6. Example #2
protected void doStart()
{
//…
_random=new java.util.Random();
_random.setSeed(_random.nextLong()^System.currentTimeMillis()
^hashCode()^Runtime.getRuntime().freeMemory());
_sessions = new MultiMap();
//...
}
Jetty 4.2.26 used java.util.Random to generate predictable
session ID which could be brute-forced.

7. 7
Example #3
• global variable seed;
• function RNG_CreateContext()
– (seconds, microseconds) = time of day;
– pid = process ID; ppid = parent process ID;
– a = mklcpr(microseconds);
– b = mklcpr(pid + seconds + (ppid << 12));
– seed = MD5(a, b);
• function mklcpr(x) // simple scrambler
– return ((0xDEECE66D * x + 0x2BBB62DC) >> 1);
• function MD5(x) // secure hash function
In 1996, two UC Berkeley students reverse exploit Netscape 1.1

8. Lessons Learnt
• Numbers, used to derive session IDs and keys,
weren’t truly random!
• Seeds must be unpredictable
– 128 bit sequences are sufficient
– All possibilities equally likely
– Best seeds are truly random
• PRG (pseudorandom number generator) must be
secure
– No detectable pattern
– Even if attacker guesses some pseudorandom bits, no
correlation to other bits.

9. 9
Two Types of Randomness
• Truly random number generator
– Radioactive decay.
– Disk timing.
– Fair coin flip.
– Randomness inherent in PC disk IO, thread scheduling, etc..
• Pseudo-random number generator (aka
computational)
– Generate a small “truly random” seed.
– Stretch into a larger pseudo-random sequence.
• Fact: In practice, we use pseudo-random number
generators.

10. 11
What is (Pseudo)-Random? (cont.)
PRG
random seed
pseudorandom string random string
look indistinguishable
to any efficient observer
Definition [Blum-Micali-Yao]:
PRG is a polytime function whose output is
indistinguishable from random by any efficient
observer
01010111001… 11010011010…
1001

11. 12
Find programs with weak PRGFind programs with weak PRG
Break-inBreak-in
Attacking Weak PRGs
Guess the initial
seed of a PRG
Guess the initial
seed of a PRG
Guess the state
of a PRG
Guess the state
of a PRG

12. Finding programs with weak PRG
• If source code is available, grep for weak API
calls.
• If only a binary is available, reverse engineer
the program or grep for weak system calls.
• For client programs, use Stompy or Ent to
analyze output’s randomness quality.
• For web-based programs, use BurpSuite or
WebScarab proxy to analyze session ID
randomness.
• Google Hacking for weak session IDs.

13. Finding programs with weak PRG
(cont.)
• High-entropy session ID generators use things like:
• java.security.SecureRandom (Java)
• System.Security.Cryptography.RNGCryptoServiceProvider (.NET)
• /dev/urandom, /dev/(s)random (if the latter, look for exhaustion attacks!)
• OpenSSL’s RAND bytes
• hardware security module.
• It’s pretty easy to quickly identify weak, low-entropy session ID
generation in the code. They use
• the time and date
• a random static string in the source code
• the output of C library rand, the output of java.util.Random
• small (32 bits or less) numbers
• a cryptographic hash (like MD5) of anything low in entropy to generate
their session IDs.

14. Know Weak API
•The weak API generally use insecure constructions such as LCG,
LSFR, Mersenne twister, etc.
•The strong API may use DES, SHA-1 based PRNG, Blum-Blum-
Shub, etc.

15. Reverse Engineering The Binaries
• Many Java programs mistakenly use
java.util.Random to generate session IDs
instead of java.security.SecureRandom
root# javap -c BadRandom | grep Random
Compiled from "BadRandom.java"
public class BadRandom extends java.lang.Object{
public BadRandom();
0: new #2; //class java/util/Random
4: invokespecial #3; //Method java/util/Random."<init>":()V
24:invokevirtual #9; //Method java/util/Random.nextInt:()I

16. Reverse Engineering the Binaries
• Similarly, C/C++ programs use rand() or random() instead
of reading from /dev/random.
• Note /dev/random blocks and /dev/urandom doesn’t
but may produce randomness of worse quality.
root# strings bad_random
__gmon_start
libc.so.6
_IO_stdin_used
srand
time
printf
…
root# nm bad_random | grep rand
U rand@@GLIBC_2.0
U srand@@GLIBC_2.0

17. 18
Analyzing the Output Without Binaries
• Compute entropy of the stream
• Count number of characters in each position
• FIPS 140-2 statistical PRNG tests
– Monobit test: Are there as many 1’s as 0’s?
– Runs test: Are the number of runs (sequences of only 0’s
or 1’s) as expected for random numbers?
– Maurer’s test: Can the sequence be compressed?
– Next-bit test: given m bits of the sequence, predict (m+1)st
bit
• Just compress the data using WinRAR

18. java.util.Random
•The java.util.Random PRG is really a linear congruential
generator (LCG) where x(n+1) = axn + b (mod m) for large
constants a, b and moduli n,m
• synchronized protected int next(int bits) { seed = (seed *
0x5DEECE66DL + 0xBL) & ((1L << 48) - 1); return (int)
(seed >>> (48 - bits)); }

19. Entropy of java.util.Random
• In practice things aren’t that bad.
• For 20,000 samples, the entropy of java.util.Random and
java.security.SecureRandom streams is almost identical.
• For both, 14.2877123795 bits of entropy.
• They also pass all FIPS 140-2 tests.
• For 200,000 samples, java.security.SecureRandom has
slightly more entropy than java.util.Random, but is it
significant?
• For java.util.Random, we get 17.6095804744 bits of entropy
• For java.security.SecureRandom, we get 17.6096204744 bits of
entropy

20. Is java.security.SecureRandom that much
worse than java.util.Random?
• Folklore says that it is. But it really depends on
OS:
• OpenSolaris (SunOS 5.11) : 67.9 slower 
• Windows XP, 64.5 times slower 
• Windows 7, 24.5 times slower 
• MAC OS X, Leopard: 25.1 times slower 

21. Hacking Java bytecode to use SecureRandom
• Java.security.SecureRandom inherits from java.util.Random
and has all its methods
• ASM bytecode manipulation framework: http://asm.ow2.org/
• Replace Random with SecureRandom in the bytecode
public class ChangeMethodCallAdapter extends
MethodAdapter {
@Override
public void visitMethodInsn(int opcode, String
owner, String name, String desc) {
System.out.println("ChangeMethodCallAdapter():
opcode=" + opcode + ",owner=" + owner +
",name=" + name + ",desc=" + desc);
if ("java/util/Random".equals(owner)) {
mv.visitMethodInsn(opcode,
"java/security/SecureRandom", name, desc);
} else {
mv.visitMethodInsn(opcode, owner, name,
desc);
}
}
gilt-ml-ayampolskiy:ClassTransformer
ayampolskiy$ javap -c API | grep Random
8: new #5; //class java/util/Random
12: invokespecial #6; //Method
java/util/Random."<init>":()V
27: invokevirtual #7; //Method
java/util/Random.nextInt:(I)I
gilt-ml-ayampolskiy:new ayampolskiy$ javap -c
API | grep Random
8: new #28; //class java/util/Random
12: invokespecial #31; //Method
java/security/SecureRandom."<init>":()V
27: invokevirtual #35; //Method
java/security/SecureRandom.nextInt:(I)I

22. Google Hacking
• Know the common session cookie names
(SESSIONID,JSESSIONID,PHPSESSID,PHPSESSIO
NID, etc.)
• Google for the cookie names: inurl:"?
sessionid=”
• Even better, try googling session IDs with non-
random sequences “66”, “128”: inurl:”?
sessionid=128”
• How about “lang:java java.util.Random
session”

23. Testing Randomness of Client
Programs
• Fourmilab’s entropy tests: http://www.fourmilab.c
• Stompy (session stomper): http://lcamtuf.coredum

24. “We could not arrest or charge this suspect because technically, no
offence was being committed as there was no legislation in place to say
that the act being committed was criminal. So, we had to let him go,” said
Sergeant Jemesa Lave of the Fiji Police Cyber Crime Unit.

25. Amazon.com experiment
• Amazon.com uses
a session-id, a 17-digit
random number- is a
persistent cookie that
expires after 7 days. It is set
the first time you reach
Amazon. Its value does not
change after you log in, nor
when you switch users.

26. Testing Randomness of Web-Based
Programs
• Several nice GUI tools to analyze session IDs
for common problems ( WebScarab,
BurpSuite, SPI Cookie Cruncher,Foundstone
CookieDigger, etc)
• Test alphabet distribution, average bits
changed, FIPS tests, etc.

27. WebScarab – Predictable Cookies
Entropy is a measure of uncertainty regarding
a discrete random variable. For many
purposes, the Shannon entropy is the only
measure needed. Shannon entropy is defined
byShannon (4.1)
has the unit bits.
Not amazon.com

28. WebScarab – amazon.com

29. Burpsuite - amazon.com

30. BurpSuite – amazon.com
Typical amazon.com
session-id 180-3029497-
6907862

31. BurpSuite – amazon.com

32. Conclusion
• Use good seeds and strong PRNGs.
• Know what the strong API for generating secure
random numbers are (SecureRandom,
/dev/random)
• Try out Stompy, Ent, WebScarab, BurpSuite.
• Happy hacking!

33. 35
Questions, Comments?