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Date: Fri, 24 Jun 2011 04:02:05 +0400
From: Solar Designer <solar@...nwall.com>
To: oss-security@...ts.openwall.com
Subject: Re: CVE request: crypt_blowfish 8-bit character mishandling

Hi,

I analyzed the impact of the crypt_blowfish bug more thoroughly.

Initially, I thought that only lengths n*4-1 and very large lengths were
at risk of easy collisions.  And, for small lengths, I estimated that
roughly 3 out of 16 passwords containing one 8-bit character were at risk.

After more thorough analysis, it turns out that other odd lengths are
also at risk, and that "very large" starts at length 20.  Thus, I have
to revise my "3 of 16" estimate.  The new estimate for risky passwords
with one 8-bit character is 30% for lengths up to 20 inclusive.  Like
before, this assumes uniform distribution of lengths and positions for
the 8-bit character, which is obviously not the case in practice, yet it
works as an estimate.

Lengths that are _not_ at risk: 1, 2, 4, 6, 8, 10, 12, 14, 16, 18.
The rest are at risk (meaning that 8-bit chars in _some_ positions
result in 1 to 3 preceding chars being ignored).

I also analyzed the number of collisions seen on Russian words in koi8-r
and utf-8 encodings.  I used Russian wordlists found in the Openwall
collection:

http://download.openwall.net/pub/wordlists/languages/Russian/koi8-r/

After zcat'ing the wordlists together and removing comment lines, I got
97946 different lines.  Of those, a quick grep for [ -~] suggests that
1805 contain some regular ASCII characters, and a review of those shows
that they are indeed genuine Russian wordlist entries - geographical
names that contain more than one word (and thus contain spaces),
composite words with dashes, etc.  Anyhow, 1805 out of 97946 is not
many.  The rest are apparently 8-bit only.

I also converted the resulting file to utf-8 using:

iconv -f koi8-r -t utf-8

Then I ran a trivial program crypt()'ing every line, with the buggy
version of crypt_blowfish (below 1.1) and using the same salt.

This resulted in 70890 (72%) and 97213 (99%) unique hashes for koi8-r
and utf-8, respectively.

For koi8-r, 22 hashes are seen over 100 times each, with the top one
being seen 190 times.  For utf-8, the top hash (most common) is seen 4
times, then 84 hashes are seen 3 times each.

Thus, obviously the bug does cause collisions.  There are not as many of
those as some people might expect for nearly purely 8-bit inputs.
Yet the very common hashes for koi8-r are worrisome.  Even though if one
were to run the entire koi8-r wordlist against a bunch of hashes they'd
only achieve a 30% speedup due to the bug, if they focus on words
producing 22 top hashes - so they only try 22 words - they'd crack
around 3% of passwords based on randomly picked words from that list
(assuming uniform distribution of random word numbers).  For utf-8, this
risk is much lower: trying top 85 passwords (0.087% of candidates)
effectively tests 256 of them (0.26%).

The relative speedup may be worse for more complicated passwords.  Their
guessing entropy may be reduced to being not that much higher than that
of the simple wordlist passwords above.  A mitigating factor is that
those passwords contain at least some non-8-bit characters (digits,
spaces, punctuation), which would not overwrite any preceding characters
(but may be getting overwritten themselves, unfortunately).

I've attached two files - a list of affected {length, position}s with
their corresponding overwritten character positions, and the program
used to generate this list.  (Yes, this message is just below the size
threshold for this mailing list.)

Alexander

length 3, 8-bit @ 2 overwrites @ 1
length 3, 8-bit @ 3 overwrites @ 1 2
length 5, 8-bit @ 2 overwrites @ 1
length 5, 8-bit @ 4 overwrites @ 3
length 7, 8-bit @ 2 overwrites @ 1
length 7, 8-bit @ 3 overwrites @ 1 2
length 7, 8-bit @ 4 overwrites @ 1 2 3
length 7, 8-bit @ 6 overwrites @ 5
length 7, 8-bit @ 7 overwrites @ 5 6
length 9, 8-bit @ 2 overwrites @ 1
length 9, 8-bit @ 4 overwrites @ 3
length 9, 8-bit @ 6 overwrites @ 5
length 9, 8-bit @ 8 overwrites @ 7
length 11, 8-bit @ 2 overwrites @ 1
length 11, 8-bit @ 3 overwrites @ 1 2
length 11, 8-bit @ 4 overwrites @ 1 2 3
length 11, 8-bit @ 6 overwrites @ 5
length 11, 8-bit @ 7 overwrites @ 5 6
length 11, 8-bit @ 8 overwrites @ 5 6 7
length 11, 8-bit @ 10 overwrites @ 9
length 11, 8-bit @ 11 overwrites @ 9 10
length 13, 8-bit @ 2 overwrites @ 1
length 13, 8-bit @ 4 overwrites @ 3
length 13, 8-bit @ 6 overwrites @ 5
length 13, 8-bit @ 8 overwrites @ 7
length 13, 8-bit @ 10 overwrites @ 9
length 13, 8-bit @ 12 overwrites @ 11
length 15, 8-bit @ 2 overwrites @ 1
length 15, 8-bit @ 3 overwrites @ 1 2
length 15, 8-bit @ 4 overwrites @ 1 2 3
length 15, 8-bit @ 6 overwrites @ 5
length 15, 8-bit @ 7 overwrites @ 5 6
length 15, 8-bit @ 8 overwrites @ 5 6 7
length 15, 8-bit @ 10 overwrites @ 9
length 15, 8-bit @ 11 overwrites @ 9 10
length 15, 8-bit @ 12 overwrites @ 9 10 11
length 15, 8-bit @ 14 overwrites @ 13
length 15, 8-bit @ 15 overwrites @ 13 14
length 17, 8-bit @ 2 overwrites @ 1
length 17, 8-bit @ 4 overwrites @ 3
length 17, 8-bit @ 6 overwrites @ 5
length 17, 8-bit @ 8 overwrites @ 7
length 17, 8-bit @ 10 overwrites @ 9
length 17, 8-bit @ 12 overwrites @ 11
length 17, 8-bit @ 14 overwrites @ 13
length 17, 8-bit @ 16 overwrites @ 15
length 19, 8-bit @ 2 overwrites @ 1
length 19, 8-bit @ 3 overwrites @ 1 2
length 19, 8-bit @ 4 overwrites @ 1 2 3
length 19, 8-bit @ 6 overwrites @ 5
length 19, 8-bit @ 7 overwrites @ 5 6
length 19, 8-bit @ 8 overwrites @ 5 6 7
length 19, 8-bit @ 10 overwrites @ 9
length 19, 8-bit @ 11 overwrites @ 9 10
length 19, 8-bit @ 12 overwrites @ 9 10 11
length 19, 8-bit @ 14 overwrites @ 13
length 19, 8-bit @ 15 overwrites @ 13 14
length 19, 8-bit @ 16 overwrites @ 13 14 15
length 19, 8-bit @ 18 overwrites @ 17
length 19, 8-bit @ 19 overwrites @ 17 18

Bad / total {length, position}s: 60 / 190 = 0.32

length 20, 8-bit @ 14 overwrites @ 13
length 20, 8-bit @ 18 overwrites @ 17
length 21, 8-bit @ 2 overwrites @ 1
length 21, 8-bit @ 4 overwrites @ 3
length 21, 8-bit @ 6 overwrites @ 5
length 21, 8-bit @ 8 overwrites @ 7
length 21, 8-bit @ 10 overwrites @ 9
length 21, 8-bit @ 12 overwrites @ 11
length 21, 8-bit @ 14 overwrites @ 13
length 21, 8-bit @ 16 overwrites @ 15
length 21, 8-bit @ 18 overwrites @ 17
length 21, 8-bit @ 20 overwrites @ 19
length 22, 8-bit @ 8 overwrites @ 7
length 22, 8-bit @ 12 overwrites @ 11
length 22, 8-bit @ 16 overwrites @ 15
length 22, 8-bit @ 20 overwrites @ 19
length 23, 8-bit @ 2 overwrites @ 1
length 23, 8-bit @ 3 overwrites @ 1 2
length 23, 8-bit @ 4 overwrites @ 1 2 3
length 23, 8-bit @ 6 overwrites @ 5
length 23, 8-bit @ 7 overwrites @ 5 6
length 23, 8-bit @ 8 overwrites @ 5 6 7
length 23, 8-bit @ 10 overwrites @ 9
length 23, 8-bit @ 11 overwrites @ 9 10
length 23, 8-bit @ 12 overwrites @ 9 10 11
length 23, 8-bit @ 14 overwrites @ 13
length 23, 8-bit @ 15 overwrites @ 13 14
length 23, 8-bit @ 16 overwrites @ 13 14 15
length 23, 8-bit @ 18 overwrites @ 17
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length 70, 8-bit @ 32 overwrites @ 29 30 31
length 70, 8-bit @ 34 overwrites @ 33
length 70, 8-bit @ 35 overwrites @ 33 34
length 70, 8-bit @ 36 overwrites @ 33 34 35
length 70, 8-bit @ 38 overwrites @ 37
length 70, 8-bit @ 39 overwrites @ 37 38
length 70, 8-bit @ 40 overwrites @ 37 38 39
length 70, 8-bit @ 42 overwrites @ 41
length 70, 8-bit @ 43 overwrites @ 41 42
length 70, 8-bit @ 44 overwrites @ 41 42 43
length 70, 8-bit @ 46 overwrites @ 45
length 70, 8-bit @ 47 overwrites @ 45 46
length 70, 8-bit @ 48 overwrites @ 45 46 47
length 70, 8-bit @ 50 overwrites @ 49
length 70, 8-bit @ 51 overwrites @ 49 50
length 70, 8-bit @ 52 overwrites @ 49 50 51
length 70, 8-bit @ 54 overwrites @ 53
length 70, 8-bit @ 55 overwrites @ 53 54
length 70, 8-bit @ 56 overwrites @ 53 54 55
length 70, 8-bit @ 58 overwrites @ 57
length 70, 8-bit @ 59 overwrites @ 57 58
length 70, 8-bit @ 60 overwrites @ 57 58 59
length 70, 8-bit @ 62 overwrites @ 61
length 70, 8-bit @ 63 overwrites @ 61 62
length 70, 8-bit @ 64 overwrites @ 61 62 63
length 70, 8-bit @ 66 overwrites @ 65
length 70, 8-bit @ 67 overwrites @ 65 66
length 70, 8-bit @ 68 overwrites @ 65 66 67
length 70, 8-bit @ 70 overwrites @ 69
length 71, 8-bit @ 2 overwrites @ 1
length 71, 8-bit @ 3 overwrites @ 1 2
length 71, 8-bit @ 4 overwrites @ 1 2 3
length 71, 8-bit @ 6 overwrites @ 5
length 71, 8-bit @ 7 overwrites @ 5 6
length 71, 8-bit @ 8 overwrites @ 5 6 7
length 71, 8-bit @ 10 overwrites @ 9
length 71, 8-bit @ 11 overwrites @ 9 10
length 71, 8-bit @ 12 overwrites @ 9 10 11
length 71, 8-bit @ 14 overwrites @ 13
length 71, 8-bit @ 15 overwrites @ 13 14
length 71, 8-bit @ 16 overwrites @ 13 14 15
length 71, 8-bit @ 18 overwrites @ 17
length 71, 8-bit @ 19 overwrites @ 17 18
length 71, 8-bit @ 20 overwrites @ 17 18 19
length 71, 8-bit @ 22 overwrites @ 21
length 71, 8-bit @ 23 overwrites @ 21 22
length 71, 8-bit @ 24 overwrites @ 21 22 23
length 71, 8-bit @ 26 overwrites @ 25
length 71, 8-bit @ 27 overwrites @ 25 26
length 71, 8-bit @ 28 overwrites @ 25 26 27
length 71, 8-bit @ 30 overwrites @ 29
length 71, 8-bit @ 31 overwrites @ 29 30
length 71, 8-bit @ 32 overwrites @ 29 30 31
length 71, 8-bit @ 34 overwrites @ 33
length 71, 8-bit @ 35 overwrites @ 33 34
length 71, 8-bit @ 36 overwrites @ 33 34 35
length 71, 8-bit @ 38 overwrites @ 37
length 71, 8-bit @ 39 overwrites @ 37 38
length 71, 8-bit @ 40 overwrites @ 37 38 39
length 71, 8-bit @ 42 overwrites @ 41
length 71, 8-bit @ 43 overwrites @ 41 42
length 71, 8-bit @ 44 overwrites @ 41 42 43
length 71, 8-bit @ 46 overwrites @ 45
length 71, 8-bit @ 47 overwrites @ 45 46
length 71, 8-bit @ 48 overwrites @ 45 46 47
length 71, 8-bit @ 50 overwrites @ 49
length 71, 8-bit @ 51 overwrites @ 49 50
length 71, 8-bit @ 52 overwrites @ 49 50 51
length 71, 8-bit @ 54 overwrites @ 53
length 71, 8-bit @ 55 overwrites @ 53 54
length 71, 8-bit @ 56 overwrites @ 53 54 55
length 71, 8-bit @ 58 overwrites @ 57
length 71, 8-bit @ 59 overwrites @ 57 58
length 71, 8-bit @ 60 overwrites @ 57 58 59
length 71, 8-bit @ 62 overwrites @ 61
length 71, 8-bit @ 63 overwrites @ 61 62
length 71, 8-bit @ 64 overwrites @ 61 62 63
length 71, 8-bit @ 66 overwrites @ 65
length 71, 8-bit @ 67 overwrites @ 65 66
length 71, 8-bit @ 68 overwrites @ 65 66 67
length 71, 8-bit @ 70 overwrites @ 69
length 71, 8-bit @ 71 overwrites @ 69 70
length 72, 8-bit @ 2 overwrites @ 1
length 72, 8-bit @ 3 overwrites @ 1 2
length 72, 8-bit @ 4 overwrites @ 1 2 3
length 72, 8-bit @ 6 overwrites @ 5
length 72, 8-bit @ 7 overwrites @ 5 6
length 72, 8-bit @ 8 overwrites @ 5 6 7
length 72, 8-bit @ 10 overwrites @ 9
length 72, 8-bit @ 11 overwrites @ 9 10
length 72, 8-bit @ 12 overwrites @ 9 10 11
length 72, 8-bit @ 14 overwrites @ 13
length 72, 8-bit @ 15 overwrites @ 13 14
length 72, 8-bit @ 16 overwrites @ 13 14 15
length 72, 8-bit @ 18 overwrites @ 17
length 72, 8-bit @ 19 overwrites @ 17 18
length 72, 8-bit @ 20 overwrites @ 17 18 19
length 72, 8-bit @ 22 overwrites @ 21
length 72, 8-bit @ 23 overwrites @ 21 22
length 72, 8-bit @ 24 overwrites @ 21 22 23
length 72, 8-bit @ 26 overwrites @ 25
length 72, 8-bit @ 27 overwrites @ 25 26
length 72, 8-bit @ 28 overwrites @ 25 26 27
length 72, 8-bit @ 30 overwrites @ 29
length 72, 8-bit @ 31 overwrites @ 29 30
length 72, 8-bit @ 32 overwrites @ 29 30 31
length 72, 8-bit @ 34 overwrites @ 33
length 72, 8-bit @ 35 overwrites @ 33 34
length 72, 8-bit @ 36 overwrites @ 33 34 35
length 72, 8-bit @ 38 overwrites @ 37
length 72, 8-bit @ 39 overwrites @ 37 38
length 72, 8-bit @ 40 overwrites @ 37 38 39
length 72, 8-bit @ 42 overwrites @ 41
length 72, 8-bit @ 43 overwrites @ 41 42
length 72, 8-bit @ 44 overwrites @ 41 42 43
length 72, 8-bit @ 46 overwrites @ 45
length 72, 8-bit @ 47 overwrites @ 45 46
length 72, 8-bit @ 48 overwrites @ 45 46 47
length 72, 8-bit @ 50 overwrites @ 49
length 72, 8-bit @ 51 overwrites @ 49 50
length 72, 8-bit @ 52 overwrites @ 49 50 51
length 72, 8-bit @ 54 overwrites @ 53
length 72, 8-bit @ 55 overwrites @ 53 54
length 72, 8-bit @ 56 overwrites @ 53 54 55
length 72, 8-bit @ 58 overwrites @ 57
length 72, 8-bit @ 59 overwrites @ 57 58
length 72, 8-bit @ 60 overwrites @ 57 58 59
length 72, 8-bit @ 62 overwrites @ 61
length 72, 8-bit @ 63 overwrites @ 61 62
length 72, 8-bit @ 64 overwrites @ 61 62 63
length 72, 8-bit @ 66 overwrites @ 65
length 72, 8-bit @ 67 overwrites @ 65 66
length 72, 8-bit @ 68 overwrites @ 65 66 67
length 72, 8-bit @ 70 overwrites @ 69
length 72, 8-bit @ 71 overwrites @ 69 70
length 72, 8-bit @ 72 overwrites @ 69 70 71

Bad / total {length, position}s: 1617 / 2628 = 0.62


#define _XOPEN_SOURCE
#include <unistd.h>
#include <stdio.h>
#include <string.h>

#define MAX 72

int main(void)
{
	const char *setting = "$2a$04$abcdefghijklmnopqrstuu";
	char pw[MAX + 1], saved[61], *hash;
	unsigned int i, j, n;
	unsigned int total, bad;

	total = bad = 0;
	for (n = 0; n < MAX; n++) {
		pw[n] = 'a';
		pw[n + 1] = 0;

		for (i = 0; i <= n; i++) {
			int reported = 0;

			pw[i] = 0xa3;
			memcpy(saved, crypt(pw, setting), sizeof(saved));

			for (j = (i < 3) ? 0 : (i - 3); j < i; j++) {
				pw[j] = 'b';
				hash = crypt(pw, setting);
				pw[j] = 'a';

				if (memcmp(hash, saved, sizeof(saved)))
					continue;

				if (!reported)
					printf(
"length %u, 8-bit @ %u overwrites @", n + 1, i + 1);
				printf(" %u", j + 1);
				reported = 1;
			}

			pw[i] = 'a';

			total++;
			if (reported) {
				putchar('\n');
				bad++;
			}
		}

		if (n != (19 - 1) && n != (MAX - 1))
			continue;

		printf("\nBad / total {length, position}s: %u / %u = %.2f\n\n",
		    bad, total, (double)bad / total);
	}

	return 0;
}

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