![Subject: How to crack Netrek RSA binary verification system
Date: September 19, 2004
From: J Corrales
-----------------------------------------------------
The RSA Algorithm
Select two primes p and q
Calculate n = p q
Calculate f(n) = (p-1)(q-1)
Select e such that 1 < e < f(n) and gcd(f(n),e) = 1
Calculate d = e^-1 mod f(n)
Public key KU = {e,n}
Private key KR = {d,n}
Example
Select two primes p=7 and q=17
Calculate n = p q = 119
Calculate f(n) = (p-1)(q-1) = 96
Select e such that 1 < e < f(n) and gcd(f(n),e) = 1, e.g., e = 5
Calculate d = e^-1 mod f(n), e.g., d = 77
Public key KU = {e,n} = {5,119}
Private key KR = {d,n} = {77,119}
Cracking RSA
Factor n, which is public, yielding p and q
Calculate f(n) = (p-1)(q-1)
Calculate d = e^-1 mod f(n) (e is public)
Private key KR = {d,n}
Note: you can check your calculation of d because d e = 1 mod f(n)
Cracking RSA (Example)
Factor 119, which is public, yielding 7 and 17
Calculate f(119) = (7-1)(17-1) = 96
Calculate 5^-1 = 77 mod 96
Private key KR = {77,119}
Plaintext M = 19
Ciphertext C = Me mod n = 195 mod 119 = 66
Plaintext M = Cd mod n = 6677 mod 119 = 19
-------------------------------------------
Netrek RSA Specifics:
Go to http://65.193.17.240:3530/ and select a key. Try:
key.brmh2.sun4:ct=BRM-Hadley:cr=hadley@uci.edu:
:cd=September 1994:ar=Sun4 / SunOS 4.1.2:cl=inl,standard2:
:cm=At cad.ics.uci.edu-/pub/netrek:
:gk=636a5977da5ce59948885d1003e983deabf405ed0cb952a5b42930523909f901:
:pk=0dfc24f1d19398586dafa37e985163290eb01f139c03f90affc5d458a7f6b800:
Convert gk and pk to integers. Note gk and pk are little endian, so
they must be reversed and converted. I used java:
//be2i.java : converts gk and pk to plain integers
//
import java.math.BigInteger;
public class be2i {
static BigInteger GLOBAL_KEY = new
BigInteger(swapEndian("636a5977da5ce59948885d1003e983deabf405ed0cb952a5b42930523909f901"),
16);
static BigInteger PUBLIC_KEY = new
BigInteger(swapEndian("0dfc24f1d19398586dafa37e985163290eb01f139c03f90affc5d458a7f6b800"),
16);
static String swapEndian(String s)
{
char c[] = s.toCharArray();
StringBuffer buffer = new StringBuffer(c.length);
for(int i = c.length; (i -= 2) >= 0;)
{
buffer.append(c[i]);
buffer.append(c[i + 1]);
}
return buffer.toString();
}
public static void main(String args[]) {
System.out.println(GLOBAL_KEY.toString(10));
System.out.println(PUBLIC_KEY.toString(10));
}
}
E:be2i>javac -d . be2i.java
E:be2i>java be2i
892321428802586219001502719778378451271677716961403333724586529659410803299
326802201186638185587649392739171025726846542356328056267675213531974007821
Note:
gk=892321428802586219001502719778378451271677716961403333724586529659410803299
pk=326802201186638185587649392739171025726846542356328056267675213531974007821
Factor gk. Download PARI/GP http://pari.math.u-bordeaux.fr/ Install
it, then run it:
Reading GPRC: /cygdrive/c/Program Files/PARI/.gprc ...Done.
GP/PARI CALCULATOR Version 2.2.8 (development CHANGES-1.887)
i686 running cygwin (ix86 kernel) 32-bit version
compiled: Jan 13 2004, gcc-3.3.1 (cygming special)
(readline v4.3 enabled, extended help available)
Copyright (C) 2003 The PARI Group
PARI/GP is free software, covered by the GNU General Public License,
and
comes WITHOUT ANY WARRANTY WHATSOEVER.](https://image.slidesharecdn.com/45dba361-9560-4b85-b2db-4b0ddcf92ab7-161211154030/85/How-To-Crack-RSA-Netrek-Binary-Verification-System-1-320.jpg)
![Type ? for help, q to quit.
Type ?12 for how to get moral (and possibly technical) support.
realprecision = 28 significant digits
seriesprecision = 16 significant terms
format = g0.28
parisize = 4000000, primelimit = 500000
(19:29) gp > factorint(892321428802586219001502719778378451271677716961403333724586529659410803299)
*** Warning: MPQS: the factorization of this number will take
several hours.
%1 =
[6158427920916659824908651606478252183 1]
[144894352951973396937037531927458847253 1]
(21:29) gp >
Calculate d = e^-1 mod f(n) (e is public)
Download res-rsa-2.9.2
ftp://ftp.netrek.org/pub/netrek/rsa/res-rsa-2.9.2.tar.gz
Modify mkkey.c as follows:
/* mpz_set_ui(x, 0); */
/* mpz_set_ui(y, 0); */
/* mpz_set_ui(global, 0); */
mpz_set_str(x,"6158427920916659824908651606478252183", 0);
mpz_set_str(y, "144894352951973396937037531927458847253", 0);
mpz_set_str
(global, "892321428802586219001502719778378451271677716961403333724586529659410803299",
0);
mpz_set_str
(private, "326802201186638185587649392739171025726846542356328056267675213531974007821",
0);
/* mpz_set_ui(public, 0); */
mpz_set_ui(public, 0);
mpz_set_ui(xyminus1, 0);
/* here we find x and y, two large primes */
rand_raw(temp, HALF);
temp[0] |= 1; /* force odd */
/* raw_to_num(x, temp); */
while (!is_prime(x))
mpz_add(x, x, two);
check_positive(x);
assert(is_prime(x));
rand_raw(temp, HALF);
temp[0] |= 1; /* force odd */
/* raw_to_num(y, temp); */
while (!is_prime(y))
mpz_add(y, y, two);
check_positive(y);
assert(is_prime(y));
/* the private key is a large prime (it should be the larger than
* x & y) */
rand_raw(temp, HALF + 1);
temp[0] |= 1; /* force odd */
//raw_to_num(private, temp);
// while (!is_prime(private))
// mpz_add(private, private, two);
check_positive(private);
//assert(is_prime(private));
Note rest of mkkeys.c is unchanged.
cherry:/home/bd/netrek/mkkey/res-rsa-2.9.2$ diff mkkey.c mkkey-mine.c
1103,1106c1119,1129
< mpz_set_ui(x, 0);
< mpz_set_ui(y, 0);
< mpz_set_ui(global, 0);
< mpz_set_ui(private, 0);
---
> /* mpz_set_ui(x, 0); */
> /* mpz_set_ui(y, 0); */
> /* mpz_set_ui(global, 0); */
>
> mpz_set_str(x,"6158427920916659824908651606478252183", 0);
> mpz_set_str(y, "144894352951973396937037531927458847253", 0);
> mpz_set_str
> (global, "892321428802586219001502719778378451271677716961403333724586529659410803299", 0);
> mpz_set_str
> (private, "326802201186638185587649392739171025726846542356328056267675213531974007821", 0);
> /* mpz_set_ui(public, 0); */
1114c1137
< raw_to_num(x, temp);
---
> /* raw_to_num(x, temp); */
1124c1147
< raw_to_num(y, temp);
---
> /* raw_to_num(y, temp); */
1137c1160
< raw_to_num(private, temp);
---
> //raw_to_num(private, temp);
1139,1140c1162,1163
< while (!is_prime(private))
< mpz_add(private, private, two);
---
> // while (!is_prime(private))
> // mpz_add(private, private, two);](https://image.slidesharecdn.com/45dba361-9560-4b85-b2db-4b0ddcf92ab7-161211154030/85/How-To-Crack-RSA-Netrek-Binary-Verification-System-2-320.jpg)
![1143c1166
< assert(is_prime(private));
---
> //assert(is_prime(private));
cherry:/home/bd/netrek/mkkey/res-rsa-2.9.2$ make
gcc -O2 -c mkkey.c
gcc -O2 -o mkkey mkkey.o -lgmp
cherry:/home/bd/netrek/mkkey/res-rsa-2.9.2$ ./mkkey foo foo foo foo
foo
mkkey version [RES-RSA 2.9.2: Mar. 13, 2000][GMP]
Source basename: "rsa_box"
Number of shells: 3
Number of steps between swaps: 2
Number of files: 5
Ratio of computation in files to main file: 0.8
Making new key, hold on....
Testing key .................................................. key
seems OK
Writing...
240 bits left, 5 files left, 37 bits in rsa_box_0.c
202 bits left, 4 files left, 7 bits in main file
194 bits left, 4 files left, 42 bits in rsa_box_1.c
151 bits left, 3 files left, 11 bits in main file
139 bits left, 3 files left, 29 bits in rsa_box_2.c
109 bits left, 2 files left, 10 bits in main file
98 bits left, 2 files left, 32 bits in rsa_box_3.c
65 bits left, 1 files left, 13 bits in main file
51 bits left, 1 files left, 39 bits in rsa_box_4.c
cherry:/home/bd/netrek/mkkey/res-rsa-2.9.2$ cat foo.secret
foo:ct=foo:cr=foo:
:cd=September 2004:ar=foo:
:cm=foo:
:gk=636a5977da5ce59948885d1003e983deabf405ed0cb952a5b42930523909f901:
:pk=057505d6c5b0b5ccd0f7819a7670da469e000000000000000000000000000000:
:sk=0dfc24f1d19398586dafa37e985163290eb01f139c03f90affc5d458a7f6b800:
Note pk and sk are reversed. Edit foo.secret to correct the order to:
foo:ct=foo:cr=foo:
:cd=September 2004:ar=foo:
:cm=foo:
:gk=636a5977da5ce59948885d1003e983deabf405ed0cb952a5b42930523909f901:
:pk=0dfc24f1d19398586dafa37e985163290eb01f139c03f90affc5d458a7f6b800:
:sk=057505d6c5b0b5ccd0f7819a7670da469e000000000000000000000000000000:
Rerun mkkey with the edited secret key file:
cherry:/home/bd/netrek/mkkey/res-rsa-2.9.2$ ./mkkey -k foo.secret
mkkey version [RES-RSA 2.9.2: Mar. 13, 2000][GMP]
Source basename: "rsa_box"
Number of shells: 3
Number of steps between swaps: 2
Number of files: 5
Ratio of computation in files to main file: 0.8
Reading key from keycap file "foo.secret"...
Testing key .................................................. key
seems OK
Writing...
128 bits left, 5 files left, 19 bits in rsa_box_0.c
108 bits left, 4 files left, 6 bits in main file
101 bits left, 4 files left, 20 bits in rsa_box_1.c
80 bits left, 3 files left, 5 bits in main file
74 bits left, 3 files left, 15 bits in rsa_box_2.c
58 bits left, 2 files left, 6 bits in main file
51 bits left, 2 files left, 21 bits in rsa_box_3.c
29 bits left, 1 files left, 5 bits in main file
23 bits left, 1 files left, 14 bits in rsa_box_4.c
cherry:/home/bd/netrek/mkkey/res-rsa-2.9.2$ ls -aFl rsa_box_?.c
-rw-r--r-- 1 bd bd 3856 Sep 19 20:02 rsa_box_0.c
-rw-r--r-- 1 bd bd 4093 Sep 19 20:02 rsa_box_1.c
-rw-r--r-- 1 bd bd 3222 Sep 19 20:02 rsa_box_2.c
-rw-r--r-- 1 bd bd 4368 Sep 19 20:02 rsa_box_3.c
-rw-r--r-- 1 bd bd 3130 Sep 19 20:02 rsa_box_4.c
cherry:/home/bd/netrek/mkkey/res-rsa-2.9.2$
Copy rsa_box_?.c files into your own custom client source directory,
compile, and login to any public netrek server, including INL server
of your choice.](https://image.slidesharecdn.com/45dba361-9560-4b85-b2db-4b0ddcf92ab7-161211154030/85/How-To-Crack-RSA-Netrek-Binary-Verification-System-3-320.jpg)
How To Crack RSA Netrek Binary Verification System
- 1. Subject: How to crack Netrek RSA binary verification system Date: September 19, 2004 From: J Corrales ----------------------------------------------------- The RSA Algorithm Select two primes p and q Calculate n = p q Calculate f(n) = (p-1)(q-1) Select e such that 1 < e < f(n) and gcd(f(n),e) = 1 Calculate d = e^-1 mod f(n) Public key KU = {e,n} Private key KR = {d,n} Example Select two primes p=7 and q=17 Calculate n = p q = 119 Calculate f(n) = (p-1)(q-1) = 96 Select e such that 1 < e < f(n) and gcd(f(n),e) = 1, e.g., e = 5 Calculate d = e^-1 mod f(n), e.g., d = 77 Public key KU = {e,n} = {5,119} Private key KR = {d,n} = {77,119} Cracking RSA Factor n, which is public, yielding p and q Calculate f(n) = (p-1)(q-1) Calculate d = e^-1 mod f(n) (e is public) Private key KR = {d,n} Note: you can check your calculation of d because d e = 1 mod f(n) Cracking RSA (Example) Factor 119, which is public, yielding 7 and 17 Calculate f(119) = (7-1)(17-1) = 96 Calculate 5^-1 = 77 mod 96 Private key KR = {77,119} Plaintext M = 19 Ciphertext C = Me mod n = 195 mod 119 = 66 Plaintext M = Cd mod n = 6677 mod 119 = 19 ------------------------------------------- Netrek RSA Specifics: Go to http://65.193.17.240:3530/ and select a key. Try: key.brmh2.sun4:ct=BRM-Hadley:cr=hadley@uci.edu: :cd=September 1994:ar=Sun4 / SunOS 4.1.2:cl=inl,standard2: :cm=At cad.ics.uci.edu-/pub/netrek: :gk=636a5977da5ce59948885d1003e983deabf405ed0cb952a5b42930523909f901: :pk=0dfc24f1d19398586dafa37e985163290eb01f139c03f90affc5d458a7f6b800: Convert gk and pk to integers. Note gk and pk are little endian, so they must be reversed and converted. I used java: //be2i.java : converts gk and pk to plain integers // import java.math.BigInteger; public class be2i { static BigInteger GLOBAL_KEY = new BigInteger(swapEndian("636a5977da5ce59948885d1003e983deabf405ed0cb952a5b42930523909f901"), 16); static BigInteger PUBLIC_KEY = new BigInteger(swapEndian("0dfc24f1d19398586dafa37e985163290eb01f139c03f90affc5d458a7f6b800"), 16); static String swapEndian(String s) { char c[] = s.toCharArray(); StringBuffer buffer = new StringBuffer(c.length); for(int i = c.length; (i -= 2) >= 0;) { buffer.append(c[i]); buffer.append(c[i + 1]); } return buffer.toString(); } public static void main(String args[]) { System.out.println(GLOBAL_KEY.toString(10)); System.out.println(PUBLIC_KEY.toString(10)); } } E:be2i>javac -d . be2i.java E:be2i>java be2i 892321428802586219001502719778378451271677716961403333724586529659410803299 326802201186638185587649392739171025726846542356328056267675213531974007821 Note: gk=892321428802586219001502719778378451271677716961403333724586529659410803299 pk=326802201186638185587649392739171025726846542356328056267675213531974007821 Factor gk. Download PARI/GP http://pari.math.u-bordeaux.fr/ Install it, then run it: Reading GPRC: /cygdrive/c/Program Files/PARI/.gprc ...Done. GP/PARI CALCULATOR Version 2.2.8 (development CHANGES-1.887) i686 running cygwin (ix86 kernel) 32-bit version compiled: Jan 13 2004, gcc-3.3.1 (cygming special) (readline v4.3 enabled, extended help available) Copyright (C) 2003 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER.
- 2. Type ? for help, q to quit. Type ?12 for how to get moral (and possibly technical) support. realprecision = 28 significant digits seriesprecision = 16 significant terms format = g0.28 parisize = 4000000, primelimit = 500000 (19:29) gp > factorint(892321428802586219001502719778378451271677716961403333724586529659410803299) *** Warning: MPQS: the factorization of this number will take several hours. %1 = [6158427920916659824908651606478252183 1] [144894352951973396937037531927458847253 1] (21:29) gp > Calculate d = e^-1 mod f(n) (e is public) Download res-rsa-2.9.2 ftp://ftp.netrek.org/pub/netrek/rsa/res-rsa-2.9.2.tar.gz Modify mkkey.c as follows: /* mpz_set_ui(x, 0); */ /* mpz_set_ui(y, 0); */ /* mpz_set_ui(global, 0); */ mpz_set_str(x,"6158427920916659824908651606478252183", 0); mpz_set_str(y, "144894352951973396937037531927458847253", 0); mpz_set_str (global, "892321428802586219001502719778378451271677716961403333724586529659410803299", 0); mpz_set_str (private, "326802201186638185587649392739171025726846542356328056267675213531974007821", 0); /* mpz_set_ui(public, 0); */ mpz_set_ui(public, 0); mpz_set_ui(xyminus1, 0); /* here we find x and y, two large primes */ rand_raw(temp, HALF); temp[0] |= 1; /* force odd */ /* raw_to_num(x, temp); */ while (!is_prime(x)) mpz_add(x, x, two); check_positive(x); assert(is_prime(x)); rand_raw(temp, HALF); temp[0] |= 1; /* force odd */ /* raw_to_num(y, temp); */ while (!is_prime(y)) mpz_add(y, y, two); check_positive(y); assert(is_prime(y)); /* the private key is a large prime (it should be the larger than * x & y) */ rand_raw(temp, HALF + 1); temp[0] |= 1; /* force odd */ //raw_to_num(private, temp); // while (!is_prime(private)) // mpz_add(private, private, two); check_positive(private); //assert(is_prime(private)); Note rest of mkkeys.c is unchanged. cherry:/home/bd/netrek/mkkey/res-rsa-2.9.2$ diff mkkey.c mkkey-mine.c 1103,1106c1119,1129 < mpz_set_ui(x, 0); < mpz_set_ui(y, 0); < mpz_set_ui(global, 0); < mpz_set_ui(private, 0); --- > /* mpz_set_ui(x, 0); */ > /* mpz_set_ui(y, 0); */ > /* mpz_set_ui(global, 0); */ > > mpz_set_str(x,"6158427920916659824908651606478252183", 0); > mpz_set_str(y, "144894352951973396937037531927458847253", 0); > mpz_set_str > (global, "892321428802586219001502719778378451271677716961403333724586529659410803299", 0); > mpz_set_str > (private, "326802201186638185587649392739171025726846542356328056267675213531974007821", 0); > /* mpz_set_ui(public, 0); */ 1114c1137 < raw_to_num(x, temp); --- > /* raw_to_num(x, temp); */ 1124c1147 < raw_to_num(y, temp); --- > /* raw_to_num(y, temp); */ 1137c1160 < raw_to_num(private, temp); --- > //raw_to_num(private, temp); 1139,1140c1162,1163 < while (!is_prime(private)) < mpz_add(private, private, two); --- > // while (!is_prime(private)) > // mpz_add(private, private, two);
- 3. 1143c1166 < assert(is_prime(private)); --- > //assert(is_prime(private)); cherry:/home/bd/netrek/mkkey/res-rsa-2.9.2$ make gcc -O2 -c mkkey.c gcc -O2 -o mkkey mkkey.o -lgmp cherry:/home/bd/netrek/mkkey/res-rsa-2.9.2$ ./mkkey foo foo foo foo foo mkkey version [RES-RSA 2.9.2: Mar. 13, 2000][GMP] Source basename: "rsa_box" Number of shells: 3 Number of steps between swaps: 2 Number of files: 5 Ratio of computation in files to main file: 0.8 Making new key, hold on.... Testing key .................................................. key seems OK Writing... 240 bits left, 5 files left, 37 bits in rsa_box_0.c 202 bits left, 4 files left, 7 bits in main file 194 bits left, 4 files left, 42 bits in rsa_box_1.c 151 bits left, 3 files left, 11 bits in main file 139 bits left, 3 files left, 29 bits in rsa_box_2.c 109 bits left, 2 files left, 10 bits in main file 98 bits left, 2 files left, 32 bits in rsa_box_3.c 65 bits left, 1 files left, 13 bits in main file 51 bits left, 1 files left, 39 bits in rsa_box_4.c cherry:/home/bd/netrek/mkkey/res-rsa-2.9.2$ cat foo.secret foo:ct=foo:cr=foo: :cd=September 2004:ar=foo: :cm=foo: :gk=636a5977da5ce59948885d1003e983deabf405ed0cb952a5b42930523909f901: :pk=057505d6c5b0b5ccd0f7819a7670da469e000000000000000000000000000000: :sk=0dfc24f1d19398586dafa37e985163290eb01f139c03f90affc5d458a7f6b800: Note pk and sk are reversed. Edit foo.secret to correct the order to: foo:ct=foo:cr=foo: :cd=September 2004:ar=foo: :cm=foo: :gk=636a5977da5ce59948885d1003e983deabf405ed0cb952a5b42930523909f901: :pk=0dfc24f1d19398586dafa37e985163290eb01f139c03f90affc5d458a7f6b800: :sk=057505d6c5b0b5ccd0f7819a7670da469e000000000000000000000000000000: Rerun mkkey with the edited secret key file: cherry:/home/bd/netrek/mkkey/res-rsa-2.9.2$ ./mkkey -k foo.secret mkkey version [RES-RSA 2.9.2: Mar. 13, 2000][GMP] Source basename: "rsa_box" Number of shells: 3 Number of steps between swaps: 2 Number of files: 5 Ratio of computation in files to main file: 0.8 Reading key from keycap file "foo.secret"... Testing key .................................................. key seems OK Writing... 128 bits left, 5 files left, 19 bits in rsa_box_0.c 108 bits left, 4 files left, 6 bits in main file 101 bits left, 4 files left, 20 bits in rsa_box_1.c 80 bits left, 3 files left, 5 bits in main file 74 bits left, 3 files left, 15 bits in rsa_box_2.c 58 bits left, 2 files left, 6 bits in main file 51 bits left, 2 files left, 21 bits in rsa_box_3.c 29 bits left, 1 files left, 5 bits in main file 23 bits left, 1 files left, 14 bits in rsa_box_4.c cherry:/home/bd/netrek/mkkey/res-rsa-2.9.2$ ls -aFl rsa_box_?.c -rw-r--r-- 1 bd bd 3856 Sep 19 20:02 rsa_box_0.c -rw-r--r-- 1 bd bd 4093 Sep 19 20:02 rsa_box_1.c -rw-r--r-- 1 bd bd 3222 Sep 19 20:02 rsa_box_2.c -rw-r--r-- 1 bd bd 4368 Sep 19 20:02 rsa_box_3.c -rw-r--r-- 1 bd bd 3130 Sep 19 20:02 rsa_box_4.c cherry:/home/bd/netrek/mkkey/res-rsa-2.9.2$ Copy rsa_box_?.c files into your own custom client source directory, compile, and login to any public netrek server, including INL server of your choice.