Frage zu MD5

[ChrisM]

Hi,

ich poste das einfach mal unter Mathematik, denn ein Hashalgorithmus ist ja im Prinzip reine Mathematik.

Es heißt ja immer, dass man MD5 nicht umkehren kann, d.h. ich kann (außer mit Brute Force) keinen Datenblock errechnen, der einen bestimmten Hashwert beim Hashen ergibt. Darauf basieren ja nicht nur sehr viele Passwortspeicherverfahren, sondern auch die meisten Tauschbörsen, um Dateien eindeutig zu identifizieren.

Jetzt die Frage, MD5 ist ja ein festgelegter Algorithmus. Warum kann ich nicht den fertigen Hash nehmen und dann quasi rückwärts gehen, d.h. für jeden Schritt per (schnellem) Brute Force den vorherigen ausrechnen. Wenn ich beim Brute Forcen einfach immer die erste Lösung nehme, müsste ich doch am Ende schnell auf eine gültige Lösung kommen, oder?

ChrisM

[LiquidAcid]

Naja, MD5 ist ja eine Checksum und hat eine bestimmte Anzahl an Bits. Wenn du jetzt versuchst die 700MB AVI-Datei von der die Checksumme stammt mithilfe dieser wieder zu rekonstruieren und das schaffst, dann verdienste dir bestimmte ne goldene Nase für einen super Kompressionsalgo

Es geht einfach nicht, dass du aus so wenig Information so viel wiederherstellst (in den meisten Fällen jedenfalls).

cya
liquid

[Dasd]

Ich glaube nicht, dass ChrisM das so gemeint hat. Es geht darum, ob es möglich ist, aus dem Hash irgendeinen gültigen Ausangswert zu berechnen. Durchaus möglich, dass man aus der Checksum einer 700MB-Datei einen Fünf-Zeichen-String errechnen kann. Es geht lediglich darum, ob sie denselben Hash haben.

Die Idee, eine MD5-Umkehrung zu implementieren ist interessant. Ich kann hier nur raten, aber ich vermute, dass es nicht möglich ist. Sonst hätte man das bestimmt bereits getan...

[Jester]

Vielleicht nur als kleinen Denkanstoß:

In diesem Satz kommt die 0 _ mal vor, die 1 _ mal, die 2 _ mal, die 3 _ mal, die 4 _ mal, die 5 _ mal, die 6 _ mal, die 7 _ mal, die 8 _ mal, die 9 _ mal.

Bitte ausfüllen... Warum ist das so schwierig?
Weil jedes Teil der Lösung wieder das komplette Ergebnis beeinflußt. Man weiß sozusagen nicht so recht, wo man anfangen soll.

MfG Jester

[mwoidt]

Es ist übrigens auch nicht korrekt das gesagt wird MD5 lasse sich nicht umkehren. Korrekt ist: Es ist kein Weg bekannt die MD5 funktion umzukehren der gegenüber eines Brute Force Angriffs erheblich Rechenzeit spart. Man kann auch an älteren Hashverfahren sehen, dass manchmal doch solche Wege gefunden werden.

[ChrisM]

Hi,

@LiquidAcid: Ne, so blöd bin ich dann auch wieder nicht, ich meine genau das, was Dasd gesagt hat, also das ich gezielt eine Zeichenfolge suche, die einen bestimmten Hashwert erzeugt.

@Jester: Ja, aber in dem ich versuche ein Ergebnis zu errechnen, muss ich doch den Hash gar nicht verändern. Die Bedingungen bleiben also die gleichen.

Eine Einwegfunktion Binärdaten -> Hashwert zu schreiben, ist ja wirklich einfach (wenn man den Algorithmus verstanden hat), aber eine entsprechende Umkehrfunktion zu schreiben, verdammt schwer, wenn nicht unmöglich.
Wenn es nämlich ginge, könnte man MD5 ja nicht mehr zur Identifikation verwenden. User in Tauschbörsen könnten dann z.B: defekte Teile schicken und der Empfänger würde sie als richtig erkennen, weil der Hashwert ja stimmt. Also kann es nicht gehen, sonst würde es die Musikindustrie ja wohl so machen.

Korrekt ist: Es ist kein Weg bekannt die MD5 funktion umzukehren der gegenüber eines Brute Force Angriffs erheblich Rechenzeit spart.

Danke

ChrisM

[Jester]

ChrisM schrieb:

Ja, aber in dem ich versuche ein Ergebnis zu errechnen, muss ich doch den Hash gar nicht verändern.

Den nicht, aber den bisherigen Lösungsraum. Jede neue Zahl die Du einträgst verändert vielleicht wieder alte Werte. Und wenn Dir beim MD5 regelmäßig die gefundenen Teilergebnisse wieder kaputt gehen, dann ist das nicht so schön. Genau deswegen funktioniert ja (bis jetzt) nur ein Brute Force Angriff.

[Lawilog]

über genau das thema hab ich mir auch schon gedanken gemacht. und ich bin klar dafür, das das geht. es gibt keine rechenoperation die ncith umkehrbar ist. (auch wenn dabei mehrer lösungen möglich sind)

User in Tauschbörsen könnten dann z.B: defekte Teile schicken und der Empfänger würde sie als richtig erkennen, weil der Hashwert ja stimmt. Also kann es nicht gehen, sonst würde es die Musikindustrie ja wohl so machen.

GENAU DAS MACHT DIE MUSIKINDUSTRIE !!!

In diesem Satz kommt
die 0 6 mal vor,
die 1 2 mal,
die 2 1 mal,
die 3 0 mal,
die 4 0 mal,
die 5 0 mal,
die 6 1 mal,
die 7 0 mal,
die 8 0 mal,
die 9 0 mal.

mfg

um ne genaue antwort zu geben bräuchte man wohl mal den algorithmus an sich.

lw

[Abbadon]

Lawilog schrieb:

In diesem Satz kommt
die 0 6 mal vor,
die 1 2 mal,
die 2 1 mal,
die 3 0 mal,
die 4 0 mal,
die 5 0 mal,
die 6 1 mal,
die 7 0 mal,
die 8 0 mal,
die 9 0 mal.

Lügner!

[Lawilog]

HALLO ????!!!

einer von uns beiden kann nicht zählen.

lw

[LiquidAcid]

Ich sehe mindestens einmal die 9

[eagle2k]

versucht mal in einer textdatei den "eigenen" md5 wert zu speichern...

[Lawilog]

na gut...

In diesem Satz kommt
die 0 2 mal vor,
die 1 10 mal,
die 2 1 mal,
die 3 1 mal,
die 4 1 mal,
die 5 1 mal,
die 6 1 mal,
die 7 1 mal,
die 8 1 mal,
die 9 1 mal.

versucht mal in einer textdatei den "eigenen" md5 wert zu speichern...

den check ich net.

also hat mal jemand den md5-alogithmus zur hand ?
vielleicht stellt sich ja dann heraus, das ich (++ChrisM) unrecht hab. aber dazu will ich mir das erstmal angucken.

lw

[Lawilog]

ok, ich muss das erstmal verstehn, aber ich hab die beschreibung des algorithmuses gefunden:
RFC 1321, "The MD5 Message-Digest Algorithm ", April 1992
ich hab das schon nach errata korregiert:

(sorry, das das n bischen länger ist...)

Network Working Group                                          R. Rivest
Request for Comments: 1321           MIT Laboratory for Computer Science
                                             and RSA Data Security, Inc.
                                                              April 1992

                     The MD5 Message-Digest Algorithm

Status of this Memo

   This memo provides information for the Internet community.  It does
   not specify an Internet standard.  Distribution of this memo is
   unlimited.

Acknowlegements

   We would like to thank Don Coppersmith, Burt Kaliski, Ralph Merkle,
   David Chaum, and Noam Nisan for numerous helpful comments and
   suggestions.

Table of Contents

   1. Executive Summary                                                1
   2. Terminology and Notation                                         2
   3. MD5 Algorithm Description                                        3
   4. Summary                                                          6
   5. Differences Between MD4 and MD5                                  6
   References                                                          7
   APPENDIX A - Reference Implementation                               7
   Security Considerations                                            21
   Author's Address                                                   21

1. Executive Summary

   This document describes the MD5 message-digest algorithm. The
   algorithm takes as input a message of arbitrary length and produces
   as output a 128-bit "fingerprint" or "message digest" of the input.
   It is conjectured that it is computationally infeasible to produce
   two messages having the same message digest, or to produce any
   message having a given prespecified target message digest. The MD5
   algorithm is intended for digital signature applications, where a
   large file must be "compressed" in a secure manner before being
   encrypted with a private (secret) key under a public-key cryptosystem
   such as RSA.

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RFC 1321              MD5 Message-Digest Algorithm            April 1992

   The MD5 algorithm is designed to be quite fast on 32-bit machines. In
   addition, the MD5 algorithm does not require any large substitution
   tables; the algorithm can be coded quite compactly.

   The MD5 algorithm is an extension of the MD4 message-digest algorithm
   1,2]. MD5 is slightly slower than MD4, but is more "conservative" in
   design. MD5 was designed because it was felt that MD4 was perhaps
   being adopted for use more quickly than justified by the existing
   critical review; because MD4 was designed to be exceptionally fast,
   it is "at the edge" in terms of risking successful cryptanalytic
   attack. MD5 backs off a bit, giving up a little in speed for a much
   greater likelihood of ultimate security. It incorporates some
   suggestions made by various reviewers, and contains additional
   optimizations. The MD5 algorithm is being placed in the public domain
   for review and possible adoption as a standard.

   For OSI-based applications, MD5's object identifier is

   md5 OBJECT IDENTIFIER ::=
     iso(1) member-body(2) US(840) rsadsi(113549) digestAlgorithm(2) 5}

   In the X.509 type AlgorithmIdentifier [3], the parameters for MD5
   should have type NULL.

2. Terminology and Notation

   In this document a "word" is a 32-bit quantity and a "byte" is an
   eight-bit quantity. A sequence of bits can be interpreted in a
   natural manner as a sequence of bytes, where each consecutive group
   of eight bits is interpreted as a byte with the high-order (most
   significant) bit of each byte listed first. Similarly, a sequence of
   bytes can be interpreted as a sequence of 32-bit words, where each
   consecutive group of four bytes is interpreted as a word with the
   low-order (least significant) byte given first.

   Let x_i denote "x sub i". If the subscript is an expression, we
   surround it in braces, as in x_{i+1}. Similarly, we use ^ for
   superscripts (exponentiation), so that x^i denotes x to the i-th
   power.

   Let the symbol "+" denote addition of words (i.e., modulo-2^32
   addition). Let X <<< s denote the 32-bit value obtained by circularly
   shifting (rotating) X left by s bit positions. Let not(X) denote the
   bit-wise complement of X, and let X v Y denote the bit-wise OR of X
   and Y. Let X xor Y denote the bit-wise XOR of X and Y, and let XY
   denote the bit-wise AND of X and Y.

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RFC 1321              MD5 Message-Digest Algorithm            April 1992

3. MD5 Algorithm Description

   We begin by supposing that we have a b-bit message as input, and that
   we wish to find its message digest. Here b is an arbitrary
   nonnegative integer; b may be zero, it need not be a multiple of
   eight, and it may be arbitrarily large. We imagine the bits of the
   message written down as follows:

          m_0 m_1 ... m_{b-1}

   The following five steps are performed to compute the message digest
   of the message.

3.1 Step 1. Append Padding Bits

   The message is "padded" (extended) so that its length (in bits) is
   congruent to 448, modulo 512. That is, the message is extended so
   that it is just 64 bits shy of being a multiple of 512 bits long.
   Padding is always performed, even if the length of the message is
   already congruent to 448, modulo 512.

   Padding is performed as follows: a single "1" bit is appended to the
   message, and then "0" bits are appended so that the length in bits of
   the padded message becomes congruent to 448, modulo 512. In all, at
   least one bit and at most 512 bits are appended.

3.2 Step 2. Append Length

   A 64-bit representation of b (the length of the message before the
   padding bits were added) is appended to the result of the previous
   step. In the unlikely event that b is greater than 2^64, then only
   the low-order 64 bits of b are used. (These bits are appended as two
   32-bit words and appended low-order word first in accordance with the
   previous conventions.)

   At this point the resulting message (after padding with bits and with
   b) has a length that is an exact multiple of 512 bits. Equivalently,
   this message has a length that is an exact multiple of 16 (32-bit)
   words. Let M[0 ... N-1] denote the words of the resulting message,
   where N is a multiple of 16.

3.3 Step 3. Initialize MD Buffer

   A four-word buffer (A,B,C,D) is used to compute the message digest.
   Here each of A, B, C, D is a 32-bit register. These registers are
   initialized to the following values in hexadecimal, low-order bytes
   first):

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RFC 1321              MD5 Message-Digest Algorithm            April 1992

          word A: 01 23 45 67
          word B: 89 ab cd ef
          word C: fe dc ba 98
          word D: 76 54 32 10

3.4 Step 4. Process Message in 16-Word Blocks

   We first define four auxiliary functions that each take as input
   three 32-bit words and produce as output one 32-bit word.

          F(X,Y,Z) = XY v not(X) Z
          G(X,Y,Z) = XZ v Y not(Z)
          H(X,Y,Z) = X xor Y xor Z
          I(X,Y,Z) = Y xor (X v not(Z))

   In each bit position F acts as a conditional: if X then Y else Z.
   The function F could have been defined using + instead of v since XY
   and not(X)Z will never have 1's in the same bit position.) It is
   interesting to note that if the bits of X, Y, and Z are independent
   and unbiased, then each bit of F(X,Y,Z) will be independent and
   unbiased.

   The functions G, H, and I are similar to the function F, in that they
   act in "bitwise parallel" to produce their output from the bits of X,
   Y, and Z, in such a manner that if the corresponding bits of X, Y,
   and Z are independent and unbiased, then each bit of G(X,Y,Z),
   H(X,Y,Z), and I(X,Y,Z) will be independent and unbiased. Note that
   the function H is the bit-wise "xor" or "parity" function of its
   inputs.

   This step uses a 64-element table T[1 ... 64] constructed from the
   sine function. Let T[i] denote the i-th element of the table, which
   is equal to the integer part of 4294967296 times abs(sin(i)), where i
   is in radians. The elements of the table are given in the appendix.

   Do the following:

   /* Process each 16-word block. */
   For i = 0 to N/16-1 do

     /* Copy block i into X. */
     For j = 0 to 15 do
       Set X[j] to M[i*16+j].
     end /* of loop on j */

     /* Save A as AA, B as BB, C as CC, and D as DD. */
     AA = A
     BB = B

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RFC 1321              MD5 Message-Digest Algorithm            April 1992

     CC = C
     DD = D

     /* Round 1. */
     /* Let [abcd k s i] denote the operation
          a = b + ((a + F(b,c,d) + X[k] + T[i]) <<< s). */
     /* Do the following 16 operations. */
     [ABCD  0  7  1]  [DABC  1 12  2]  [CDAB  2 17  3]  [BCDA  3 22  4]
     [ABCD  4  7  5]  [DABC  5 12  6]  [CDAB  6 17  7]  [BCDA  7 22  8]
     [ABCD  8  7  9]  [DABC  9 12 10]  [CDAB 10 17 11]  [BCDA 11 22 12]
     [ABCD 12  7 13]  [DABC 13 12 14]  [CDAB 14 17 15]  [BCDA 15 22 16]

     /* Round 2. */
     /* Let [abcd k s i] denote the operation
          a = b + ((a + G(b,c,d) + X[k] + T[i]) <<< s). */
     /* Do the following 16 operations. */
     [ABCD  1  5 17]  [DABC  6  9 18]  [CDAB 11 14 19]  [BCDA  0 20 20]
     [ABCD  5  5 21]  [DABC 10  9 22]  [CDAB 15 14 23]  [BCDA  4 20 24]
     [ABCD  9  5 25]  [DABC 14  9 26]  [CDAB  3 14 27]  [BCDA  8 20 28]
     [ABCD 13  5 29]  [DABC  2  9 30]  [CDAB  7 14 31]  [BCDA 12 20 32]

     /* Round 3. */
     /* Let [abcd k s i] denote the operation
          a = b + ((a + H(b,c,d) + X[k] + T[i]) <<< s). */
     /* Do the following 16 operations. */
     [ABCD  5  4 33]  [DABC  8 11 34]  [CDAB 11 16 35]  [BCDA 14 23 36]
     [ABCD  1  4 37]  [DABC  4 11 38]  [CDAB  7 16 39]  [BCDA 10 23 40]
     [ABCD 13  4 41]  [DABC  0 11 42]  [CDAB  3 16 43]  [BCDA  6 23 44]
     [ABCD  9  4 45]  [DABC 12 11 46]  [CDAB 15 16 47]  [BCDA  2 23 48]

     /* Round 4. */
     /* Let [abcd k s i] denote the operation
          a = b + ((a + I(b,c,d) + X[k] + T[i]) <<< s). */
     /* Do the following 16 operations. */
     [ABCD  0  6 49]  [DABC  7 10 50]  [CDAB 14 15 51]  [BCDA  5 21 52]
     [ABCD 12  6 53]  [DABC  3 10 54]  [CDAB 10 15 55]  [BCDA  1 21 56]
     [ABCD  8  6 57]  [DABC 15 10 58]  [CDAB  6 15 59]  [BCDA 13 21 60]
     [ABCD  4  6 61]  [DABC 11 10 62]  [CDAB  2 15 63]  [BCDA  9 21 64]

     /* Then perform the following additions. (That is increment each
        of the four registers by the value it had before this block
        was started.) */
     A = A + AA
     B = B + BB
     C = C + CC
     D = D + DD

   end /* of loop on i */

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RFC 1321              MD5 Message-Digest Algorithm            April 1992

3.5 Step 5. Output

   The message digest produced as output is A, B, C, D. That is, we
   begin with the low-order byte of A, and end with the high-order byte
   of D.

   This completes the description of MD5. A reference implementation in
   C is given in the appendix.

4. Summary

   The MD5 message-digest algorithm is simple to implement, and provides
   a "fingerprint" or message digest of a message of arbitrary length.
   It is conjectured that the difficulty of coming up with two messages
   having the same message digest is on the order of 2^64 operations,
   and that the difficulty of coming up with any message having a given
   message digest is on the order of 2^128 operations. The MD5 algorithm
   has been carefully scrutinized for weaknesses. It is, however, a
   relatively new algorithm and further security analysis is of course
   justified, as is the case with any new proposal of this sort.

5. Differences Between MD4 and MD5

     The following are the differences between MD4 and MD5:

       1.   A fourth round has been added.

       2.   Each step now has a unique additive constant.

       3.   The function g in round 2 was changed from (XY v XZ v YZ) to
       (XZ v Y not(Z)) to make g less symmetric.

       4.   Each step now adds in the result of the previous step.  This
       promotes a faster "avalanche effect".

       5.   The order in which input words are accessed in rounds 2 and
       3 is changed, to make these patterns less like each other.

       6.   The shift amounts in each round have been approximately
       optimized, to yield a faster "avalanche effect." The shifts in
       different rounds are distinct.

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RFC 1321              MD5 Message-Digest Algorithm            April 1992

References

   [1] Rivest, R., "The MD4 Message Digest Algorithm", RFC 1320, MIT and
       RSA Data Security, Inc., April 1992.

   [2] Rivest, R., "The MD4 message digest algorithm", in A.J.  Menezes
       and S.A. Vanstone, editors, Advances in Cryptology - CRYPTO '90
       Proceedings, pages 303-311, Springer-Verlag, 1991.

   [3] CCITT Recommendation X.509 (1988), "The Directory -
       Authentication Framework."

APPENDIX A - Reference Implementation

   This appendix contains the following files taken from RSAREF: A
   Cryptographic Toolkit for Privacy-Enhanced Mail:

     global.h -- global header file

     md5.h -- header file for MD5

     md5c.c -- source code for MD5

   For more information on RSAREF, send email to <rsaref@rsa.com>.

   The appendix also includes the following file:

     mddriver.c -- test driver for MD2, MD4 and MD5

   The driver compiles for MD5 by default but can compile for MD2 or MD4
   if the symbol MD is defined on the C compiler command line as 2 or 4.

   The implementation is portable and should work on many different
   plaforms. However, it is not difficult to optimize the implementation
   on particular platforms, an exercise left to the reader. For example,
   on "little-endian" platforms where the lowest-addressed byte in a 32-
   bit word is the least significant and there are no alignment
   restrictions, the call to Decode in MD5Transform can be replaced with
   a typecast.

A.1 global.h

/* GLOBAL.H - RSAREF types and constants
 */

/* PROTOTYPES should be set to one if and only if the compiler supports
  function argument prototyping.
The following makes PROTOTYPES default to 0 if it has not already

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RFC 1321              MD5 Message-Digest Algorithm            April 1992

  been defined with C compiler flags.
 */
#ifndef PROTOTYPES
#define PROTOTYPES 0
#endif

/* POINTER defines a generic pointer type */
typedef unsigned char *POINTER;

/* UINT2 defines a two byte word */
typedef unsigned short int UINT2;

/* UINT4 defines a four byte word */
typedef unsigned long int UINT4;

/* PROTO_LIST is defined depending on how PROTOTYPES is defined above.
If using PROTOTYPES, then PROTO_LIST returns the list, otherwise it
  returns an empty list.
 */
#if PROTOTYPES
#define PROTO_LIST(list) list
#else
#define PROTO_LIST(list) ()
#endif

A.2 md5.h

/* MD5.H - header file for MD5C.C
 */

/* Copyright (C) 1991-2, RSA Data Security, Inc. Created 1991. All
rights reserved.

License to copy and use this software is granted provided that it
is identified as the "RSA Data Security, Inc. MD5 Message-Digest
Algorithm" in all material mentioning or referencing this software
or this function.

License is also granted to make and use derivative works provided
that such works are identified as "derived from the RSA Data
Security, Inc. MD5 Message-Digest Algorithm" in all material
mentioning or referencing the derived work.

RSA Data Security, Inc. makes no representations concerning either
the merchantability of this software or the suitability of this
software for any particular purpose. It is provided "as is"
without express or implied warranty of any kind.

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RFC 1321              MD5 Message-Digest Algorithm            April 1992

These notices must be retained in any copies of any part of this
documentation and/or software.
 */

/* MD5 context. */
typedef struct {
  UINT4 state[4];                                   /* state (ABCD) */
  UINT4 count[2];        /* number of bits, modulo 2^64 (lsb first) */
  unsigned char buffer[64];                         /* input buffer */
} MD5_CTX;

void MD5Init PROTO_LIST ((MD5_CTX *));
void MD5Update PROTO_LIST
  ((MD5_CTX *, unsigned char *, unsigned int));
void MD5Final PROTO_LIST ((unsigned char [16], MD5_CTX *));

A.3 md5c.c

/* MD5C.C - RSA Data Security, Inc., MD5 message-digest algorithm
 */

/* Copyright (C) 1991-2, RSA Data Security, Inc. Created 1991. All
rights reserved.

License to copy and use this software is granted provided that it
is identified as the "RSA Data Security, Inc. MD5 Message-Digest
Algorithm" in all material mentioning or referencing this software
or this function.

License is also granted to make and use derivative works provided
that such works are identified as "derived from the RSA Data
Security, Inc. MD5 Message-Digest Algorithm" in all material
mentioning or referencing the derived work.

RSA Data Security, Inc. makes no representations concerning either
the merchantability of this software or the suitability of this
software for any particular purpose. It is provided "as is"
without express or implied warranty of any kind.

These notices must be retained in any copies of any part of this
documentation and/or software.
 */

#include "global.h"
#include "md5.h"

/* Constants for MD5Transform routine.
 */

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RFC 1321              MD5 Message-Digest Algorithm            April 1992

#define S11 7
#define S12 12
#define S13 17
#define S14 22
#define S21 5
#define S22 9
#define S23 14
#define S24 20
#define S31 4
#define S32 11
#define S33 16
#define S34 23
#define S41 6
#define S42 10
#define S43 15
#define S44 21

static void MD5Transform PROTO_LIST ((UINT4 [4], unsigned char [64]));
static void Encode PROTO_LIST
  ((unsigned char *, UINT4 *, unsigned int));
static void Decode PROTO_LIST
  ((UINT4 *, unsigned char *, unsigned int));
static void MD5_memcpy PROTO_LIST ((POINTER, POINTER, unsigned int));
static void MD5_memset PROTO_LIST ((POINTER, int, unsigned int));

static unsigned char PADDING[64] = {
  0x80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
};

/* F, G, H and I are basic MD5 functions.
 */
#define F(x, y, z) (((x) & (y)) | ((~x) & (z)))
#define G(x, y, z) (((x) & (z)) | ((y) & (~z)))
#define H(x, y, z) ((x) ^ (y) ^ (z))
#define I(x, y, z) ((y) ^ ((x) | (~z)))

/* ROTATE_LEFT rotates x left n bits.
 */
#define ROTATE_LEFT(x, n) (((x) << (n)) | ((x) >> (32-(n))))

/* FF, GG, HH, and II transformations for rounds 1, 2, 3, and 4.
Rotation is separate from addition to prevent recomputation.
 */
#define FF(a, b, c, d, x, s, ac) { \
 (a) += F ((b), (c), (d)) + (x) + (UINT4)(ac); \
 (a) = ROTATE_LEFT ((a), (s)); \

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RFC 1321              MD5 Message-Digest Algorithm            April 1992

 (a) += (b); \
  }
#define GG(a, b, c, d, x, s, ac) { \
 (a) += G ((b), (c), (d)) + (x) + (UINT4)(ac); \
 (a) = ROTATE_LEFT ((a), (s)); \
 (a) += (b); \
  }
#define HH(a, b, c, d, x, s, ac) { \
 (a) += H ((b), (c), (d)) + (x) + (UINT4)(ac); \
 (a) = ROTATE_LEFT ((a), (s)); \
 (a) += (b); \
  }
#define II(a, b, c, d, x, s, ac) { \
 (a) += I ((b), (c), (d)) + (x) + (UINT4)(ac); \
 (a) = ROTATE_LEFT ((a), (s)); \
 (a) += (b); \
  }

/* MD5 initialization. Begins an MD5 operation, writing a new context.
 */
void MD5Init (context)
MD5_CTX *context;                                        /* context */
{
  context->count[0] = context->count[1] = 0;
  /* Load magic initialization constants.
*/
  context->state[0] = 0x67452301;
  context->state[1] = 0xefcdab89;
  context->state[2] = 0x98badcfe;
  context->state[3] = 0x10325476;
}

/* MD5 block update operation. Continues an MD5 message-digest
  operation, processing another message block, and updating the
  context.
 */
void MD5Update (context, input, inputLen)
MD5_CTX *context;                                        /* context */
unsigned char *input;                                /* input block */
unsigned int inputLen;                     /* length of input block */
{
  unsigned int i, index, partLen;

  /* Compute number of bytes mod 64 */
  index = (unsigned int)((context->count[0] >> 3) & 0x3F);

  /* Update number of bits */
  if ((context->count[0] += ((UINT4)inputLen << 3))

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RFC 1321              MD5 Message-Digest Algorithm            April 1992

   < ((UINT4)inputLen << 3))
 context->count[1]++;
  context->count[1] += ((UINT4)inputLen >> 29);

  partLen = 64 - index;

  /* Transform as many times as possible.
*/
  if (inputLen >= partLen) {
 MD5_memcpy
   ((POINTER)&context->buffer[index], (POINTER)input, partLen);
 MD5Transform (context->state, context->buffer);

 for (i = partLen; i + 63 < inputLen; i += 64)
   MD5Transform (context->state, &input[i]);

 index = 0;
  }
  else
 i = 0;

  /* Buffer remaining input */
  MD5_memcpy
 ((POINTER)&context->buffer[index], (POINTER)&input[i],
  inputLen-i);
}

/* MD5 finalization. Ends an MD5 message-digest operation, writing the
  the message digest and zeroizing the context.
 */
void MD5Final (digest, context)
unsigned char digest[16];                         /* message digest */
MD5_CTX *context;                                       /* context */
{
  unsigned char bits[8];
  unsigned int index, padLen;

  /* Save number of bits */
  Encode (bits, context->count, 8);

  /* Pad out to 56 mod 64.
*/
  index = (unsigned int)((context->count[0] >> 3) & 0x3f);
  padLen = (index < 56) ? (56 - index) : (120 - index);
  MD5Update (context, PADDING, padLen);

  /* Append length (before padding) */
  MD5Update (context, bits, 8);

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RFC 1321              MD5 Message-Digest Algorithm            April 1992

  /* Store state in digest */
  Encode (digest, context->state, 16);

  /* Zeroize sensitive information.
*/
  MD5_memset ((POINTER)context, 0, sizeof (*context));
}

/* MD5 basic transformation. Transforms state based on block.
 */
static void MD5Transform (state, block)
UINT4 state[4];
unsigned char block[64];
{
  UINT4 a = state[0], b = state[1], c = state[2], d = state[3], x[16];

  Decode (x, block, 64);

  /* Round 1 */
  FF (a, b, c, d, x[ 0], S11, 0xd76aa478); /* 1 */
  FF (d, a, b, c, x[ 1], S12, 0xe8c7b756); /* 2 */
  FF (c, d, a, b, x[ 2], S13, 0x242070db); /* 3 */
  FF (b, c, d, a, x[ 3], S14, 0xc1bdceee); /* 4 */
  FF (a, b, c, d, x[ 4], S11, 0xf57c0faf); /* 5 */
  FF (d, a, b, c, x[ 5], S12, 0x4787c62a); /* 6 */
  FF (c, d, a, b, x[ 6], S13, 0xa8304613); /* 7 */
  FF (b, c, d, a, x[ 7], S14, 0xfd469501); /* 8 */
  FF (a, b, c, d, x[ 8], S11, 0x698098d8); /* 9 */
  FF (d, a, b, c, x[ 9], S12, 0x8b44f7af); /* 10 */
  FF (c, d, a, b, x[10], S13, 0xffff5bb1); /* 11 */
  FF (b, c, d, a, x[11], S14, 0x895cd7be); /* 12 */
  FF (a, b, c, d, x[12], S11, 0x6b901122); /* 13 */
  FF (d, a, b, c, x[13], S12, 0xfd987193); /* 14 */
  FF (c, d, a, b, x[14], S13, 0xa679438e); /* 15 */
  FF (b, c, d, a, x[15], S14, 0x49b40821); /* 16 */

 /* Round 2 */
  GG (a, b, c, d, x[ 1], S21, 0xf61e2562); /* 17 */
  GG (d, a, b, c, x[ 6], S22, 0xc040b340); /* 18 */
  GG (c, d, a, b, x[11], S23, 0x265e5a51); /* 19 */
  GG (b, c, d, a, x[ 0], S24, 0xe9b6c7aa); /* 20 */
  GG (a, b, c, d, x[ 5], S21, 0xd62f105d); /* 21 */
  GG (d, a, b, c, x[10], S22,  0x2441453); /* 22 */
  GG (c, d, a, b, x[15], S23, 0xd8a1e681); /* 23 */
  GG (b, c, d, a, x[ 4], S24, 0xe7d3fbc8); /* 24 */
  GG (a, b, c, d, x[ 9], S21, 0x21e1cde6); /* 25 */
  GG (d, a, b, c, x[14], S22, 0xc33707d6); /* 26 */
  GG (c, d, a, b, x[ 3], S23, 0xf4d50d87); /* 27 */

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RFC 1321              MD5 Message-Digest Algorithm            April 1992

  GG (b, c, d, a, x[ 8], S24, 0x455a14ed); /* 28 */
  GG (a, b, c, d, x[13], S21, 0xa9e3e905); /* 29 */
  GG (d, a, b, c, x[ 2], S22, 0xfcefa3f8); /* 30 */
  GG (c, d, a, b, x[ 7], S23, 0x676f02d9); /* 31 */
  GG (b, c, d, a, x[12], S24, 0x8d2a4c8a); /* 32 */

  /* Round 3 */
  HH (a, b, c, d, x[ 5], S31, 0xfffa3942); /* 33 */
  HH (d, a, b, c, x[ 8], S32, 0x8771f681); /* 34 */
  HH (c, d, a, b, x[11], S33, 0x6d9d6122); /* 35 */
  HH (b, c, d, a, x[14], S34, 0xfde5380c); /* 36 */
  HH (a, b, c, d, x[ 1], S31, 0xa4beea44); /* 37 */
  HH (d, a, b, c, x[ 4], S32, 0x4bdecfa9); /* 38 */
  HH (c, d, a, b, x[ 7], S33, 0xf6bb4b60); /* 39 */
  HH (b, c, d, a, x[10], S34, 0xbebfbc70); /* 40 */
  HH (a, b, c, d, x[13], S31, 0x289b7ec6); /* 41 */
  HH (d, a, b, c, x[ 0], S32, 0xeaa127fa); /* 42 */
  HH (c, d, a, b, x[ 3], S33, 0xd4ef3085); /* 43 */
  HH (b, c, d, a, x[ 6], S34,  0x4881d05); /* 44 */
  HH (a, b, c, d, x[ 9], S31, 0xd9d4d039); /* 45 */
  HH (d, a, b, c, x[12], S32, 0xe6db99e5); /* 46 */
  HH (c, d, a, b, x[15], S33, 0x1fa27cf8); /* 47 */
  HH (b, c, d, a, x[ 2], S34, 0xc4ac5665); /* 48 */

  /* Round 4 */
  II (a, b, c, d, x[ 0], S41, 0xf4292244); /* 49 */
  II (d, a, b, c, x[ 7], S42, 0x432aff97); /* 50 */
  II (c, d, a, b, x[14], S43, 0xab9423a7); /* 51 */
  II (b, c, d, a, x[ 5], S44, 0xfc93a039); /* 52 */
  II (a, b, c, d, x[12], S41, 0x655b59c3); /* 53 */
  II (d, a, b, c, x[ 3], S42, 0x8f0ccc92); /* 54 */
  II (c, d, a, b, x[10], S43, 0xffeff47d); /* 55 */
  II (b, c, d, a, x[ 1], S44, 0x85845dd1); /* 56 */
  II (a, b, c, d, x[ 8], S41, 0x6fa87e4f); /* 57 */
  II (d, a, b, c, x[15], S42, 0xfe2ce6e0); /* 58 */
  II (c, d, a, b, x[ 6], S43, 0xa3014314); /* 59 */
  II (b, c, d, a, x[13], S44, 0x4e0811a1); /* 60 */
  II (a, b, c, d, x[ 4], S41, 0xf7537e82); /* 61 */
  II (d, a, b, c, x[11], S42, 0xbd3af235); /* 62 */
  II (c, d, a, b, x[ 2], S43, 0x2ad7d2bb); /* 63 */
  II (b, c, d, a, x[ 9], S44, 0xeb86d391); /* 64 */

  state[0] += a;
  state[1] += b;
  state[2] += c;
  state[3] += d;

  /* Zeroize sensitive information.

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RFC 1321              MD5 Message-Digest Algorithm            April 1992

*/
  MD5_memset ((POINTER)x, 0, sizeof (x));
}

/* Encodes input (UINT4) into output (unsigned char). Assumes len is
  a multiple of 4.
 */
static void Encode (output, input, len)
unsigned char *output;
UINT4 *input;
unsigned int len;
{
  unsigned int i, j;

  for (i = 0, j = 0; j < len; i++, j += 4) {
 output[j] = (unsigned char)(input[i] & 0xff);
 output[j+1] = (unsigned char)((input[i] >> 8) & 0xff);
 output[j+2] = (unsigned char)((input[i] >> 16) & 0xff);
 output[j+3] = (unsigned char)((input[i] >> 24) & 0xff);
  }
}

/* Decodes input (unsigned char) into output (UINT4). Assumes len is
  a multiple of 4.
 */
static void Decode (output, input, len)
UINT4 *output;
unsigned char *input;
unsigned int len;
{
  unsigned int i, j;

  for (i = 0, j = 0; j < len; i++, j += 4)
 output[i] = ((UINT4)input[j]) | (((UINT4)input[j+1]) << 8) |
   (((UINT4)input[j+2]) << 16) | (((UINT4)input[j+3]) << 24);
}

/* Note: Replace "for loop" with standard memcpy if possible.
 */

static void MD5_memcpy (output, input, len)
POINTER output;
POINTER input;
unsigned int len;
{
  unsigned int i;

  for (i = 0; i < len; i++)

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RFC 1321              MD5 Message-Digest Algorithm            April 1992

 output[i] = input[i];
}

/* Note: Replace "for loop" with standard memset if possible.
 */
static void MD5_memset (output, value, len)
POINTER output;
int value;
unsigned int len;
{
  unsigned int i;

  for (i = 0; i < len; i++)
 ((char *)output)[i] = (char)value;
}

A.4 mddriver.c

/* MDDRIVER.C - test driver for MD2, MD4 and MD5
 */

/* Copyright (C) 1990-2, RSA Data Security, Inc. Created 1990. All
rights reserved.

RSA Data Security, Inc. makes no representations concerning either
the merchantability of this software or the suitability of this
software for any particular purpose. It is provided "as is"
without express or implied warranty of any kind.

These notices must be retained in any copies of any part of this
documentation and/or software.
 */

/* The following makes MD default to MD5 if it has not already been
  defined with C compiler flags.
 */
#ifndef MD
#define MD 5
#endif

#include <stdio.h>
#include <time.h>
#include <string.h>
#include "global.h"
#if MD == 2
#include "md2.h"
#endif
#if MD == 4

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RFC 1321              MD5 Message-Digest Algorithm            April 1992

#include "md4.h"
#endif
#if MD == 5
#include "md5.h"
#endif

/* Length of test block, number of test blocks.
 */
#define TEST_BLOCK_LEN 1000
#define TEST_BLOCK_COUNT 1000

static void MDString PROTO_LIST ((char *));
static void MDTimeTrial PROTO_LIST ((void));
static void MDTestSuite PROTO_LIST ((void));
static void MDFile PROTO_LIST ((char *));
static void MDFilter PROTO_LIST ((void));
static void MDPrint PROTO_LIST ((unsigned char [16]));

#if MD == 2
#define MD_CTX MD2_CTX
#define MDInit MD2Init
#define MDUpdate MD2Update
#define MDFinal MD2Final
#endif
#if MD == 4
#define MD_CTX MD4_CTX
#define MDInit MD4Init
#define MDUpdate MD4Update
#define MDFinal MD4Final
#endif
#if MD == 5
#define MD_CTX MD5_CTX
#define MDInit MD5Init
#define MDUpdate MD5Update
#define MDFinal MD5Final
#endif

/* Main driver.

Arguments (may be any combination):
  -sstring - digests string
  -t       - runs time trial
  -x       - runs test script
  filename - digests file
  (none)   - digests standard input
 */
int main (argc, argv)
int argc;

Rivest                                                         [Page 17]

RFC 1321              MD5 Message-Digest Algorithm            April 1992

char *argv[];
{
  int i;

  if (argc > 1)
 for (i = 1; i < argc; i++)
   if (argv[i][0] == '-' && argv[i][1] == 's')
     MDString (argv[i] + 2);
   else if (strcmp (argv[i], "-t") == 0)
     MDTimeTrial ();
   else if (strcmp (argv[i], "-x") == 0)
     MDTestSuite ();
   else
     MDFile (argv[i]);
  else
 MDFilter ();

  return (0);
}

/* Digests a string and prints the result.
 */
static void MDString (string)
char *string;
{
  MD_CTX context;
  unsigned char digest[16];
  unsigned int len = strlen (string);

  MDInit (&context);
  MDUpdate (&context, string, len);
  MDFinal (digest, &context);

  printf ("MD%d (\"%s\") = ", MD, string);
  MDPrint (digest);
  printf ("\n");
}

/* Measures the time to digest TEST_BLOCK_COUNT TEST_BLOCK_LEN-byte
  blocks.
 */
static void MDTimeTrial ()
{
  MD_CTX context;
  time_t endTime, startTime;
  unsigned char block[TEST_BLOCK_LEN], digest[16];
  unsigned int i;

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RFC 1321              MD5 Message-Digest Algorithm            April 1992

  printf
 ("MD%d time trial. Digesting %d %d-byte blocks ...", MD,
  TEST_BLOCK_LEN, TEST_BLOCK_COUNT);

  /* Initialize block */
  for (i = 0; i < TEST_BLOCK_LEN; i++)
 block[i] = (unsigned char)(i & 0xff);

  /* Start timer */
  time (&startTime);

  /* Digest blocks */
  MDInit (&context);
  for (i = 0; i < TEST_BLOCK_COUNT; i++)
 MDUpdate (&context, block, TEST_BLOCK_LEN);
  MDFinal (digest, &context);

  /* Stop timer */
  time (&endTime);

  printf (" done\n");
  printf ("Digest = ");
  MDPrint (digest);
  printf ("\nTime = %ld seconds\n", (long)(endTime-startTime));
  printf
 ("Speed = %ld bytes/second\n",
  (long)TEST_BLOCK_LEN * (long)TEST_BLOCK_COUNT/(endTime-startTime));
}

/* Digests a reference suite of strings and prints the results.
 */
static void MDTestSuite ()
{
  printf ("MD%d test suite:\n", MD);

  MDString ("");
  MDString ("a");
  MDString ("abc");
  MDString ("message digest");
  MDString ("abcdefghijklmnopqrstuvwxyz");
  MDString
 ("ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789");
  MDString
 ("1234567890123456789012345678901234567890\
1234567890123456789012345678901234567890");
}

/* Digests a file and prints the result.

Rivest                                                         [Page 19]

RFC 1321              MD5 Message-Digest Algorithm            April 1992

 */
static void MDFile (filename)
char *filename;
{
  FILE *file;
  MD_CTX context;
  int len;
  unsigned char buffer[1024], digest[16];

  if ((file = fopen (filename, "rb")) == NULL)
 printf ("%s can't be opened\n", filename);

  else {
 MDInit (&context);
 while (len = fread (buffer, 1, 1024, file))
   MDUpdate (&context, buffer, len);
 MDFinal (digest, &context);

 fclose (file);

 printf ("MD%d (%s) = ", MD, filename);
 MDPrint (digest);
 printf ("\n");
  }
}

/* Digests the standard input and prints the result.
 */
static void MDFilter ()
{
  MD_CTX context;
  int len;
  unsigned char buffer[16], digest[16];

  MDInit (&context);
  while (len = fread (buffer, 1, 16, stdin))
 MDUpdate (&context, buffer, len);
  MDFinal (digest, &context);

  MDPrint (digest);
  printf ("\n");
}

/* Prints a message digest in hexadecimal.
 */
static void MDPrint (digest)
unsigned char digest[16];
{

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RFC 1321              MD5 Message-Digest Algorithm            April 1992

  unsigned int i;

  for (i = 0; i < 16; i++)
 printf ("%02x", digest[i]);
}

A.5 Test suite

   The MD5 test suite (driver option "-x") should print the following
   results:

MD5 test suite:
MD5 ("") = d41d8cd98f00b204e9800998ecf8427e
MD5 ("a") = 0cc175b9c0f1b6a831c399e269772661
MD5 ("abc") = 900150983cd24fb0d6963f7d28e17f72
MD5 ("message digest") = f96b697d7cb7938d525a2f31aaf161d0
MD5 ("abcdefghijklmnopqrstuvwxyz") = c3fcd3d76192e4007dfb496cca67e13b
MD5 ("ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789") =
d174ab98d277d9f5a5611c2c9f419d9f
MD5 ("123456789012345678901234567890123456789012345678901234567890123456
78901234567890") = 57edf4a22be3c955ac49da2e2107b67a

Security Considerations

   The level of security discussed in this memo is considered to be
   sufficient for implementing very high security hybrid digital-
   signature schemes based on MD5 and a public-key cryptosystem.

Author's Address

   Ronald L. Rivest
   Massachusetts Institute of Technology
   Laboratory for Computer Science
   NE43-324
   545 Technology Square
   Cambridge, MA  02139-1986

   Phone: (617) 253-5880
   EMail: rivest@theory.lcs.mit.edu

Rivest                                                         [Page 21]

[PMrogan]

Lawilog schrieb:

In diesem Satz kommt
die 0 2 mal vor,
die 1 10 mal,
die 2 1 mal,
die 3 1 mal,
die 4 1 mal,
die 5 1 mal,
die 6 1 mal,
die 7 1 mal,
die 8 1 mal,
die 9 1 mal.

Besser, aber immer noch falsch.. die 2 gibts mehr als 1 mal

[Lawilog]

mist.
aber jetzt: :p

In diesem Satz kommt
die 0 1 mal vor,
die 1 7 mal,
die 2 3 mal,
die 3 2 mal,
die 4 1 mal,
die 5 1 mal,
die 6 1 mal,
die 7 2 mal,
die 8 1 mal,
die 9 1 mal.

[Jester]

Lawilog schrieb:

über genau das thema hab ich mir auch schon gedanken gemacht. und ich bin klar dafür, das das geht. es gibt keine rechenoperation die ncith umkehrbar ist. (auch wenn dabei mehrer lösungen möglich sind)

Das ist die falsche Frage: Es geht darum, ob sie effizient umkehrbar ist. Und das kann auf mit hoher Wahrscheinlichkeit negativ beantwortet werden:

Kennst Du 3SAT? Du hast ne Aussagenlogische Formel, die aus je 3 mit "Oder "Verknüpften Literalen besteht (den sogenannten Klauseln) und diese Klauseln sind dann mit "und" verknüpft. Jetzt ist die Frage, ob diese Formel erfüllbar ist.
Für jede der Klauseln ist das furchtbar einfach nachzuprüfen: Man kann direkt ne Belegung angeben, daß sie wahr wird. Der Haken: Die Frage, ob es möglich ist, daß alle gleichzeitig wahr werden ist dennoch NP-vollständig. Das heißt mit großer Wahrscheinlichkeit gibt es keinen polynomialen Algorithmus der dieses Problem lösen kann. Man geht davon aus, daß nur exponentielle Lösungen existieren... man grob gesprochen also nur durchprobieren kann.

MfG Jester