1 files changed, 73 insertions, 18 deletions

diff --git a/src/lib/libcrypto/bn/bn.h b/src/lib/libcrypto/bn/bn.h
index cd94e39345..cc1f467523 100644
--- a/src/lib/libcrypto/bn/bn.h
+++ b/src/lib/libcrypto/bn/bn.h
@@ -1,4 +1,4 @@
-/* $OpenBSD: bn.h,v 1.38 2018/02/20 17:13:14 jsing Exp $ */
+/* $OpenBSD: bn.h,v 1.39 2019/08/25 19:23:59 schwarze Exp $ */
 /* Copyright (C) 1995-1997 Eric Young (eay@cryptsoft.com)
  * All rights reserved.
  *
@@ -308,24 +308,79 @@ int BN_GENCB_call(BN_GENCB *cb, int a, int b);
 #define BN_prime_checks 0 /* default: select number of iterations
                              based on the size of the number */
 
-/* number of Miller-Rabin iterations for an error rate  of less than 2^-80
- * for random 'b'-bit input, b >= 100 (taken from table 4.4 in the Handbook
- * of Applied Cryptography [Menezes, van Oorschot, Vanstone; CRC Press 1996];
- * original paper: Damgaard, Landrock, Pomerance: Average case error estimates
- * for the strong probable prime test. -- Math. Comp. 61 (1993) 177-194) */
-#define BN_prime_checks_for_size(b) ((b) >= 1300 ?  2 : \
-                                (b) >=  850 ?  3 : \
-                                (b) >=  650 ?  4 : \
-                                (b) >=  550 ?  5 : \
-                                (b) >=  450 ?  6 : \
-                                (b) >=  400 ?  7 : \
-                                (b) >=  350 ?  8 : \
-                                (b) >=  300 ?  9 : \
-                                (b) >=  250 ? 12 : \
-                                (b) >=  200 ? 15 : \
-                                (b) >=  150 ? 18 : \
-                                /* b >= 100 */ 27)
+/*
+ * BN_prime_checks_for_size() returns the number of Miller-Rabin
+ * iterations that will be done for checking that a random number
+ * is probably prime.  The error rate for accepting a composite
+ * number as prime depends on the size of the prime |b|.  The error
+ * rates used are for calculating an RSA key with 2 primes, and so
+ * the level is what you would expect for a key of double the size
+ * of the prime.
+ *
+ * This table is generated using the algorithm of FIPS PUB 186-4
+ * Digital Signature Standard (DSS), section F.1, page 117.
+ * (https://dx.doi.org/10.6028/NIST.FIPS.186-4)
+ *
+ * The following magma script was used to generate the output:
+ * securitybits:=125;
+ * k:=1024;
+ * for t:=1 to 65 do
+ *   for M:=3 to Floor(2*Sqrt(k-1)-1) do
+ *     S:=0;
+ *     // Sum over m
+ *     for m:=3 to M do
+ *       s:=0;
+ *       // Sum over j
+ *       for j:=2 to m do
+ *         s+:=(RealField(32)!2)^-(j+(k-1)/j);
+ *       end for;
+ *       S+:=2^(m-(m-1)*t)*s;
+ *     end for;
+ *     A:=2^(k-2-M*t);
+ *     B:=8*(Pi(RealField(32))^2-6)/3*2^(k-2)*S;
+ *     pkt:=2.00743*Log(2)*k*2^-k*(A+B);
+ *     seclevel:=Floor(-Log(2,pkt));
+ *     if seclevel ge securitybits then
+ *       printf "k: %5o, security: %o bits  (t: %o, M: %o)\n",k,seclevel,t,M;
+ *       break;
+ *     end if;
+ *   end for;
+ *   if seclevel ge securitybits then break; end if;
+ * end for;
+ *
+ * It can be run online at:
+ * http://magma.maths.usyd.edu.au/calc
+ *
+ * And will output:
+ * k:  1024, security: 129 bits  (t: 6, M: 23)
+ *
+ * k is the number of bits of the prime, securitybits is the level
+ * we want to reach.
+ *
+ * prime length | RSA key size | # MR tests | security level
+ * -------------+--------------|------------+---------------
+ *  (b) >= 6394 |     >= 12788 |          3 |        256 bit
+ *  (b) >= 3747 |     >=  7494 |          3 |        192 bit
+ *  (b) >= 1345 |     >=  2690 |          4 |        128 bit
+ *  (b) >= 1080 |     >=  2160 |          5 |        128 bit
+ *  (b) >=  852 |     >=  1704 |          5 |        112 bit
+ *  (b) >=  476 |     >=   952 |          5 |         80 bit
+ *  (b) >=  400 |     >=   800 |          6 |         80 bit
+ *  (b) >=  347 |     >=   694 |          7 |         80 bit
+ *  (b) >=  308 |     >=   616 |          8 |         80 bit
+ *  (b) >=   55 |     >=   110 |         27 |         64 bit
+ *  (b) >=    6 |     >=    12 |         34 |         64 bit
+ */
 
+#define BN_prime_checks_for_size(b) ((b) >= 3747 ?  3 : \
+                                (b) >=  1345 ?  4 : \
+                                (b) >=  476 ?  5 : \
+                                (b) >=  400 ?  6 : \
+                                (b) >=  347 ?  7 : \
+                                (b) >=  308 ?  8 : \
+                                (b) >=  55  ? 27 : \
+                                /* b >= 6 */ 34)
+ 
 #define BN_num_bytes(a) ((BN_num_bits(a)+7)/8)
 
 /* Note that BN_abs_is_word didn't work reliably for w == 0 until 0.9.8 */