From 94b791198b35ae093106d6ee9478a4ff1ab3a1ef Mon Sep 17 00:00:00 2001
From: Dario Lombardo <lomato@gmail.com>
Date: Tue, 22 Apr 2014 18:02:32 +0200
Subject: [PATCH] Added prime number offset generation

---
 Makefile.am   |  2 +-
 millerrabin.c | 80 +++++++++++++++++++++++++++++++++++++++++++++++++++
 millerrabin.h | 11 +++++++
 scanner.c     | 18 ++++++++----
 4 files changed, 104 insertions(+), 7 deletions(-)
 create mode 100644 millerrabin.c
 create mode 100644 millerrabin.h

diff --git a/Makefile.am b/Makefile.am
index 93c0255..e6a9829 100644
--- a/Makefile.am
+++ b/Makefile.am
@@ -1,3 +1,3 @@
 bin_PROGRAMS = namescan
-namescan_SOURCES = main.c radar.c scanner.c sock.c dns.c fingerprint.c log.c cmdline.c cmdline.h config.h dns.h  fingerprint.h log.h radar.h scanner.h sock.h list.c list.h
+namescan_SOURCES = main.c radar.c scanner.c sock.c dns.c fingerprint.c log.c cmdline.c cmdline.h config.h dns.h  fingerprint.h log.h radar.h scanner.h sock.h list.c list.h millerrabin.c millerrabin.h
 AM_CPPFLAGS = -Wall -Werror
diff --git a/millerrabin.c b/millerrabin.c
new file mode 100644
index 0000000..bd7b4d8
--- /dev/null
+++ b/millerrabin.c
@@ -0,0 +1,80 @@
+
+#include <millerrabin.h>
+
+/* 
+    Code taken from 
+    http://rosettacode.org/wiki/Miller-Rabin_primality_test#Deterministic_up_to_341.2C550.2C071.2C728.2C321
+*/
+
+// calcul a^n%mod
+size_t power(size_t a, size_t n, size_t mod)
+{
+    size_t power = a;
+    size_t result = 1;
+ 
+    while (n)
+    {
+        if (n & 1)
+            result = (result * power) % mod;
+        power = (power * power) % mod;
+        n >>= 1;
+    }
+    return result;
+}
+ 
+// n−1 = 2^s * d with d odd by factoring powers of 2 from n−1
+bool witness(size_t n, size_t s, size_t d, size_t a)
+{
+    size_t x = power(a, d, n);
+    size_t y = 0;
+ 
+    while (s) {
+        y = (x * x) % n;
+        if (y == 1 && x != 1 && x != n-1)
+            return false;
+        x = y;
+        --s;
+    }
+    if (y != 1)
+        return false;
+    return true;
+}
+ 
+/*
+ * if n < 1,373,653, it is enough to test a = 2 and 3;
+ * if n < 9,080,191, it is enough to test a = 31 and 73;
+ * if n < 4,759,123,141, it is enough to test a = 2, 7, and 61;
+ * if n < 1,122,004,669,633, it is enough to test a = 2, 13, 23, and 1662803;
+ * if n < 2,152,302,898,747, it is enough to test a = 2, 3, 5, 7, and 11;
+ * if n < 3,474,749,660,383, it is enough to test a = 2, 3, 5, 7, 11, and 13;
+ * if n < 341,550,071,728,321, it is enough to test a = 2, 3, 5, 7, 11, 13, and 17.
+ */
+ 
+bool is_prime_mr(size_t n)
+{
+    if (((!(n & 1)) && n != 2 ) || (n < 2) || (n % 3 == 0 && n != 3))
+        return false;
+    if (n <= 3)
+        return true;
+ 
+    size_t d = n / 2;
+    size_t s = 1;
+    while (!(d & 1)) {
+        d /= 2;
+        ++s;
+    }
+ 
+    if (n < 1373653)
+        return witness(n, s, d, 2) && witness(n, s, d, 3);
+    if (n < 9080191)
+        return witness(n, s, d, 31) && witness(n, s, d, 73);
+    if (n < 4759123141)
+        return witness(n, s, d, 2) && witness(n, s, d, 7) && witness(n, s, d, 61);
+    if (n < 1122004669633)
+        return witness(n, s, d, 2) && witness(n, s, d, 13) && witness(n, s, d, 23) && witness(n, s, d, 1662803);
+    if (n < 2152302898747)
+        return witness(n, s, d, 2) && witness(n, s, d, 3) && witness(n, s, d, 5) && witness(n, s, d, 7) && witness(n, s, d, 11);
+    if (n < 3474749660383)
+        return witness(n, s, d, 2) && witness(n, s, d, 3) && witness(n, s, d, 5) && witness(n, s, d, 7) && witness(n, s, d, 11) && witness(n, s, d, 13);
+    return witness(n, s, d, 2) && witness(n, s, d, 3) && witness(n, s, d, 5) && witness(n, s, d, 7) && witness(n, s, d, 11) && witness(n, s, d, 13) && witness(n, s, d, 17);
+}
diff --git a/millerrabin.h b/millerrabin.h
new file mode 100644
index 0000000..eb773b5
--- /dev/null
+++ b/millerrabin.h
@@ -0,0 +1,11 @@
+
+#ifndef __MILLERRABIN_H__
+#define __MILLERRABIN_H__
+
+#include <stdbool.h>
+#include <unistd.h>
+
+/* Returns true is n is prime, using the Miller-Rabin algorhytm */
+bool is_prime_mr(size_t n);
+
+#endif
diff --git a/scanner.c b/scanner.c
index 3476e0b..64f1dad 100644
--- a/scanner.c
+++ b/scanner.c
@@ -2,6 +2,7 @@
 #include <scanner.h>
 #include <fingerprint.h>
 #include <dns.h>
+#include <millerrabin.h>
 
 #include <stdio.h>
 #include <stdlib.h>
@@ -111,12 +112,6 @@ void scanner(scanner_params_t* sp)
         return;
     }
 
-    if (sp->randomize == false) {
-        off = 1;
-    } else {
-        off = 7; // TODO
-    }
-
     struct sockaddr_in sin;
     memset(&sin, 0x0, sizeof(sin));
     sin.sin_family = AF_INET;
@@ -145,6 +140,17 @@ void scanner(scanner_params_t* sp)
         diff = ntohl(sp->ranges[i].ip_to) - ntohl(sp->ranges[i].ip_from) + 1;
         ptr = ntohl(sp->ranges[i].ip_from);
 
+        if (sp->randomize == false) {
+            off = 1;
+        } else {
+            do {
+                off = rand() % diff;
+                if (off == 0)
+                    off = 1;
+            } while(!is_prime_mr(off));
+            LOG_DEBUG("Using %u as offset\n", off);
+        }
+
         if (diff % off == 0 && off > 1) {
             printf("%u %u\n", diff, off);
             LOG_ERROR("Collision detected. Specify another offset\n");