lkml.org 
[lkml]   [2013]   [Sep]   [22]   [last100]   RSS Feed
Views: [wrap][no wrap]   [headers]  [forward] 
 
Messages in this thread
Patch in this message
/
From
Subject[PATCH, RFC 12/12] random: adjust the generator polynomials in the mixing function slightly
Date
Our mixing functions were analyzed by Lacharme, Roeck, Strubel, and
Videau in their paper, "The Linux Pseudorandom Number Generator
Revisited" (see: http://eprint.iacr.org/2012/251.pdf).

They suggested a slight change to improve our mixing functions
slightly. I also adjusted the comments to better explain what is
going on, and to document why the polynomials were changed.

Signed-off-by: "Theodore Ts'o" <tytso@mit.edu>
---
drivers/char/random.c | 104 ++++++++++++++++++++++++--------------------------
1 file changed, 50 insertions(+), 54 deletions(-)

diff --git a/drivers/char/random.c b/drivers/char/random.c
index 86879d1..5726ff6 100644
--- a/drivers/char/random.c
+++ b/drivers/char/random.c
@@ -321,23 +321,62 @@ static const int trickle_thresh = (INPUT_POOL_WORDS * 28) << ENTROPY_SHIFT;
static DEFINE_PER_CPU(int, trickle_count);

/*
- * A pool of size .poolwords is stirred with a primitive polynomial
- * of degree .poolwords over GF(2). The taps for various sizes are
- * defined below. They are chosen to be evenly spaced (minimum RMS
- * distance from evenly spaced; the numbers in the comments are a
- * scaled squared error sum) except for the last tap, which is 1 to
- * get the twisting happening as fast as possible.
+ * Originally, we used a primitive polynomial of degree .poolwords
+ * over GF(2). The taps for various sizes are defined below. They
+ * were chosen to be evenly spaced except for the last tap, which is 1
+ * to get the twisting happening as fast as possible.
+ *
+ * For the purposes of better mixing, we use the CRC-32 polynomial as
+ * well to make a (modified) twisted Generalized Feedback Shift
+ * Reigster
+ *
+ * (See M. Matsumoto & Y. Kurita, 1992. Twisted GFSR generators. ACM
+ * Transactions on Modeling and Computer Simulation 2(3):179-194.
+ * Also see M. Matsumoto & Y. Kurita, 1994. Twisted GFSR generators
+ * II. ACM Transactions on Mdeling and Computer Simulation 4:254-266)
+ *
+ * Thanks to Colin Plumb for suggesting this.
+ *
+ * The mixing operation is much less sensitive than the output hash,
+ * where we use SHA-1. All that we want of mixing operation is that
+ * it be a good non-cryptographic hash; i.e. it not produce collisions
+ * when fed "random" data of the sort we expect to see. As long as
+ * the pool state differs for different inputs, we have preserved the
+ * input entropy and done a good job. The fact that an intelligent
+ * attacker can construct inputs that will produce controlled
+ * alterations to the pool's state is not important because we don't
+ * consider such inputs to contribute any randomness. The only
+ * property we need with respect to them is that the attacker can't
+ * increase his/her knowledge of the pool's state. Since all
+ * additions are reversible (knowing the final state and the input,
+ * you can reconstruct the initial state), if an attacker has any
+ * uncertainty about the initial state, he/she can only shuffle that
+ * uncertainty about, but never cause any collisions (which would
+ * decrease the uncertainty).
+ *
+ * Our mixing functions were analyzed by Lacharme, Roeck, Strubel, and
+ * Videau in their paper, "The Linux Pseudorandom Number Generator
+ * Revisited" (see: http://eprint.iacr.org/2012/251.pdf). In their
+ * paper, they point out that we are not using a true Twisted GFSR,
+ * since Matsumoto & Kurita used a trinomial feedback polynomial (that
+ * is, with only three taps, instead of the six that we are using).
+ * As a result, the resulting polynomial is neither primitive nor
+ * irreducible, and hence does not have a maximal period over
+ * GF(2**32). They suggest a slight change to the generator
+ * polynomial which improves the resulting TGFSR polynomial to be
+ * irreducible, which we have made here.
*/
-
static struct poolinfo {
int poolbitshift, poolwords, poolbytes, poolbits, poolfracbits;
#define S(x) ilog2(x)+5, (x), (x)*4, (x)*32, (x) << (ENTROPY_SHIFT+5)
int tap1, tap2, tap3, tap4, tap5;
} poolinfo_table[] = {
- /* x^128 + x^103 + x^76 + x^51 +x^25 + x + 1 -- 105 */
- { S(128), 103, 76, 51, 25, 1 },
- /* x^32 + x^26 + x^20 + x^14 + x^7 + x + 1 -- 15 */
- { S(32), 26, 20, 14, 7, 1 },
+ /* was: x^128 + x^103 + x^76 + x^51 +x^25 + x + 1 */
+ /* x^128 + x^104 + x^76 + x^51 +x^25 + x + 1 */
+ { S(128), 104, 76, 51, 25, 1 },
+ /* was: x^32 + x^26 + x^20 + x^14 + x^7 + x + 1 */
+ /* x^32 + x^26 + x^19 + x^14 + x^7 + x + 1 */
+ { S(32), 26, 19, 14, 7, 1 },
#if 0
/* x^2048 + x^1638 + x^1231 + x^819 + x^411 + x + 1 -- 115 */
{ S(2048), 1638, 1231, 819, 411, 1 },
@@ -368,49 +407,6 @@ static struct poolinfo {
};

/*
- * For the purposes of better mixing, we use the CRC-32 polynomial as
- * well to make a twisted Generalized Feedback Shift Reigster
- *
- * (See M. Matsumoto & Y. Kurita, 1992. Twisted GFSR generators. ACM
- * Transactions on Modeling and Computer Simulation 2(3):179-194.
- * Also see M. Matsumoto & Y. Kurita, 1994. Twisted GFSR generators
- * II. ACM Transactions on Mdeling and Computer Simulation 4:254-266)
- *
- * Thanks to Colin Plumb for suggesting this.
- *
- * We have not analyzed the resultant polynomial to prove it primitive;
- * in fact it almost certainly isn't. Nonetheless, the irreducible factors
- * of a random large-degree polynomial over GF(2) are more than large enough
- * that periodicity is not a concern.
- *
- * The input hash is much less sensitive than the output hash. All
- * that we want of it is that it be a good non-cryptographic hash;
- * i.e. it not produce collisions when fed "random" data of the sort
- * we expect to see. As long as the pool state differs for different
- * inputs, we have preserved the input entropy and done a good job.
- * The fact that an intelligent attacker can construct inputs that
- * will produce controlled alterations to the pool's state is not
- * important because we don't consider such inputs to contribute any
- * randomness. The only property we need with respect to them is that
- * the attacker can't increase his/her knowledge of the pool's state.
- * Since all additions are reversible (knowing the final state and the
- * input, you can reconstruct the initial state), if an attacker has
- * any uncertainty about the initial state, he/she can only shuffle
- * that uncertainty about, but never cause any collisions (which would
- * decrease the uncertainty).
- *
- * The chosen system lets the state of the pool be (essentially) the input
- * modulo the generator polymnomial. Now, for random primitive polynomials,
- * this is a universal class of hash functions, meaning that the chance
- * of a collision is limited by the attacker's knowledge of the generator
- * polynomail, so if it is chosen at random, an attacker can never force
- * a collision. Here, we use a fixed polynomial, but we *can* assume that
- * ###--> it is unknown to the processes generating the input entropy. <-###
- * Because of this important property, this is a good, collision-resistant
- * hash; hash collisions will occur no more often than chance.
- */
-
-/*
* Static global variables
*/
static DECLARE_WAIT_QUEUE_HEAD(random_read_wait);
--
1.7.12.rc0.22.gcdd159b


\
 
 \ /
  Last update: 2013-09-22 23:01    [W:1.850 / U:0.640 seconds]
©2003-2020 Jasper Spaans|hosted at Digital Ocean and TransIP|Read the blog|Advertise on this site