How Are Cryptographic Algorithms Broken??? Presented By Bhavana Tapde June 19, 2006

Outline  Cryptographic Algorithms  Cryptographic Hash Algorithms  Applications of Hash Functions  Properties of Hash Functions  Case Study of MD5  Wang’s Method  Klima’s Method  Demo  Case Study of SHA-1  Conclusion

What is Cryptographic Algorithm?  Cryptography – process of scrambling information in a manner that is difficult to unscramble, and making scrambled information intelligible.  Cryptographic Algorithm – any algorithm written to achieve cryptography, and consequently confidentiality, integrity, and authentication.  Types of Cryptographic Algorithms  Symmetric Key Algorithms – DES, Triple DES  Asymmetric Key Algorithms – RSA  Cryptographic Hash Algorithms – MD5, SHA-1

Cryptographic Hash Algorithm  Hashing Algorithm – a protocol for using the hash function, specifying how the message will be broken up and how the results from previous message blocks are chained together.  Hash Function  is effectively computable.  compresses information of arbitrary length to some information of fixed length (“digital fingerprint”).  possesses Avalanche (Ripple Effect) – when a input is changed slightly, output changes significantly Hash function

How hashes are used?  Digitally Signed Documents

How hashes are used? (…cont)  Hashing Passwords

How hashes are used? (…cont)  Verifying File Integrity  If you have just downloaded a large piece of software from a website, how do you know that you've received it correctly and that it has not been tampered with?  The website publishes the hash values of its download bundles, and you can compare a published hash (e.g.MD5 sum) with checksum of downloaded file.  Utilities Unix OS – includes MD5 utilities in their distribution packages. Windows – third party applications like FastSum (

When a Cryptographic Hash Function is Secured? When it satisfies following three properties  Preimage-resistance: “Given V, find M such that h(M)= V” is infeasible.  2 nd -preimage-resistance: “Given M, find M’ M such that h(M’)=h(M)” is infeasible.  Collision-resistance: “Find M’ M such that h(M’)=h(M)” is infeasible.

Case Study of MD5

Description of MD5  MD5 (message digest algorithm) – developed at RSA Data Security, Inc.  Improved version of MD4.  Takes any message and outputs an 128-bit hash.  A message is padded so the length is multiple of 512.  Each 512-bit block is processed individually. MD5

Description of MD5 (…cont)  The 512-bit block is divided into bit words.  There are 4 32-bit registers A, B, C and D. These are initially loaded with IV 0 and carry the hash values from one 512-bit block to the next.  It works in an iterative (chaining) process: H i+1 = f(H i,M i ) IV 0 =H 0 where M i is a 512-bit block. MD5

Hash Chaining f H 0 =IV 0 fixed M1M1 H1H1 f H2H2 … f H n = H M2M2 MnMn M i 512 bits H i 128 bits MD5

One Small Step  A,B,C,D – 4 registers.  F – nonlinear function; there are total 4 functions and one function is used in each round.  Each round has 16 steps (so, total 64 steps).  Mi – 32-bit block of the message input. (512/16=32)  Ki – 32-bit constant, different for each step.  s – Left bit rotation by s places; s varies for each operation.  – Addition modulo MD5

The Rounds and Non-Linear Functions  M i =(w 0,…,w 15 )  For fixed i, 4 consecutive steps will yield a i+4 =b i +((a i +F i (b i,c i,d i )+w i +k i )<<<s i ) d i+4 =a i +((d i +F i+1 (a i,b i,c i )+w i+1 +k i+1 )<<<s i+1 ) c i+4 =d i +((c i +F i+2 (d i,a i,b i )+w i+2 +k i+2 )<<<s i+2 ) b i+4 =c i +((b i +F i+3 (c i,d i,a i )+w i+3 +k i+3 )<<<s i+3 ) k i and s i are predefined step dependant constants  F i changes every 16 steps F i (X,Y,Z)=(X^Y)ν(~X^Z) 0 ≤ i ≤ 15 F i (X,Y,Z)=(X^Z)ν(Y^~Z)16 ≤ i ≤ 31 F i (X,Y,Z)=X  Y  Z32 ≤ i ≤ 47 F i (X,Y,Z)=Y  (X ν ~Z) 48 ≤ i ≤ 63 MD5

Finding Collisions  MD5 does 64 rounds of scrambling, so a brute force attack to find a collision requires at most 2 64 operations. Brute Force Attack – method of defeating cryptographic scheme by exhaustively working through all possible keys.  Xiaoyun Wang and her team – have an attack that requires 2 39 operations. This attack takes at most an hour and 5 minutes on a IBM P690 (supercomputer).  Vlastimil Klima and his team – have an attack that can find collisions on a Notebook PC within a minute. MD5

Wang’s Method (August 2004)  Use of Differential Cryptanalysis: find a statistical correlation between key values and cipher transformations (typically Exclusive-OR of text pairs), then use sufficient defined plaintext to develop the key.  Find a particular M such that a particular H occurs with high probability.  In collision case, want H=0. MD5 - Wang

Differentials  The attack uses two types of differentials  XOR differential: ΔX=X  X’  Modular differential: ΔX=X-X’ mod 2 32  For M=(m 0,…,m n-1 ) and M’=(m’ 0,…m’ n-1 ) the full hash differential is for a message of length 512n bits ΔH 0 -> ΔH 1 ->…-> ΔH n= ΔH If M and M’ are a collision pair ΔH=0  Round Differentials  ΔH i -> ΔH i+1 can be split into round differentials as well  ΔH i ΔR 0 ΔR 1 ΔR 2 ΔR 3 = ΔH i+1 P0P0 P1P1 P2P2 P3P3 MD5 - Wang

Probability  Each of these differentials has a probabilistic relationship with the next.  Ideally, we’d like to be able to set up 2 messages where we can guarantee with probability 1 that ΔH=0.  This can be assured by modifying M so the first round differential will be what you want.  More modifications will improve the probability for the second, third and fourth round differentials. MD5 - Wang

The Attack with Message Modification  Find M=(M 0,M 1 ) and M’=(M’ 0,M’ 1 )  ΔM 0 =M’ 0 -M 0 =(0,0,0,0,2 31,0,0,0,0,0,0,2 15,0,0,2 31,0)  ΔM 1 =M’ 1 -M 1 =(0,0,0,0,2 31,0,0,0,0,0,0,-2 15,0,0,2 31,0)  M’ 0 differ in the 5 th, 12 th and 15 th words only.  Same for M 1 and M’ 1.  Message Modification Method – modify a message word so that the first non-zero step differential (after 5 th step) is anything you want with probability 1.  Modify multiple words to guarantee the round differentials with high probability. MD5 - Wang

Results - Actual Collisions M0 = 2dd31d1 c4eee6c5 69a3d69 5cf9af98 87b5ca2f ab7e4612 3e ffbb8 634ad55 2b3f e483 5a e fc9cdf7 f2bd1dd9 5b3c3780 M1 = d11d0b96 9c7b41dc f497d8e4 d555655a c79a7335 cfdebf0 66f fb109d1 797f2775 eb5cd530 baade822 5c15cc79 ddcb74ed 6dd3c55f d80a9bb1 e3a7cc35 M0’ = 2dd31d1 c4eee6c5 69a3d69 5cf9af98 7b5ca2f ab7e4612 3e ffbb8 634ad55 2b3f e483 5a41f125 e fc9cdf7 72bd1dd9 5b3c3780 M1’ = d11d0b96 9c7b41dc f497d8e4 d555655a 479a7335 cfdebf0 66f fb109d1 797f2775 eb5cd530 baade822 5c154c79 ddcb74ed 6dd3c55f 580a9bb1 e3a7cc35 Hash: f a30f9dbf 9f65ffbc f41fc7ef MD5 - Wang

Klima’s Method (March 2006)  “Tunnels in Hash Functions: MD5 Collisions Within a Minute”  Tunnel – a complex function written to find collision which takes into account individual bit of message instead of word.  Tunnels replaces multi-message modification method, and exponentially accelerate collision search.  Several tunnels are written in MD5 hash function.  Also uses ‘differential path’ – the effect of a single bit change tracked through the hash algorithm. MD5 - Klima

Speed Comparison to Find MD5 Collisions Software - MD5 - Klima Machine Specification Avg. Time Min. Time Max. Time Colli- sions CPU Intel Pentium III (1 GHz), 512MB RAM, Windows CPU Intel Pentium 4 (3 GHz), 512MB RAM, Windows XP Pentium M (1.7 GHz), 512MB RAM, debian AMD Athlon XP2000+(1.67 GHz), 256MB RAM, Windows XP Time in seconds.

Demo of Pack3  Pack3 – software developed by one of the team members of Klima.  “Give me three files and I will give you another three with the same MD5 hash!”  The program serves as a toy example of how to get around the necessity of creating the second preimage.  Usage: pack3 file1 file2 file3 file4 file5 file6 Will create two packages – package1.exe package2.exe, having same MD5 sum. package1 extracts files 1-3. package2 extracts files 4-6.  Pack3 is available at  Verification tool used is FastSum. MD5 - Klima

Screen Shots : FastSum Utility C:\Demo\fastsum>fsum "C:\Demo\pack3\selfextract-md5_coll\FileA.txt“ MD5 Checksum calculation and verification utility. [ ] EN (C) Kirill Zinov and Vitaly Rogotsevich. Web site: C:\Demo\pack3\selfextract-md5_coll\FileA.txt 12FABF28FF61D4AE9F7080F524CC3130 Calculation summary: Processed 1 files in 0 folders with total size 0.04 Kb. Elapsed time: 00:00:00 Average speed: 0.00 Kb\Sec. C:\Demo\fastsum>fsum "C:\Demo\pack3\selfextract-md5_coll\FileB.txt" MD5 Checksum calculation and verification utility. [ ] EN (C) Kirill Zinov and Vitaly Rogotsevich. Web site: C:\Demo\pack3\selfextract-md5_coll\FileB.txt 6DE787E2B6255B94B73DC39D32FC135C Calculation summary: Processed 1 files in 0 folders with total size 0.04 Kb. Elapsed time: 00:00:00 Average speed: 0.00 Kb\Sec.

Screen Shots : Pack3 C:\Demo\pack3\selfextract-md5_coll>pack3 file1.txt file2.txt file3.txt file4.txt file5.txt file6.txt

Screen Shots : Pack3 (…cont)  Verify results of Pack3 with FastSum C:\Demo\fastsum>fsum "C:\Demo\pack3\selfextract-md5_coll\package1.exe" MD5 Checksum calculation and verification utility. [ ] EN (C) Kirill Zinov and Vitaly Rogotsevich. Web site: C:\Demo\pack3\selfextract-md5_coll\package1.exe 0DAACC BD6B4345E Calculation summary: Processed 1 files in 0 folders with total size Kb. Elapsed time: 00:00:00 Average speed: 0.00 Kb\Sec. C:\Demo\fastsum>fsum "C:\Demo\pack3\selfextract-md5_coll\package2.exe" MD5 Checksum calculation and verification utility. [ ] EN (C) Kirill Zinov and Vitaly Rogotsevich. Web site: C:\Demo\pack3\selfextract-md5_coll\package2.exe 0DAACC BD6B4345E Calculation summary: Processed 1 files in 0 folders with total size Kb. Elapsed time: 00:00:00 Average speed: Mb\Sec.

Case Study of SHA-1

Description of SHA-1  SHA-1 (Secure Hash Algorithm) – developed by NIST (National Institute of Standards and Technology).  Improved version of SHA-0.  Takes any message of length of less than 2 64 bits and outputs 160 bit hash.  A message is padded so the length is multiple of 512.  Each 512-bit block is processed individually. SHA-1

Description of SHA-1 (…cont)  The 512-bit block is divided into bit words.  There are 5 32-bit registers A, B, C, D and E. These are initially loaded with IV0 and carry the hash value from one 512-bit block to the next.  It works in an iterative process. SHA-1

Hash Chaining Expansion Function 512 bit blocks Compression Function 2560 bits Initialization vector (fixed) 160 bit hash SHA-1

One Small Step  There are 4 rounds and each round has 20 steps (so, total 80 steps).  A,B,C,D,E – 5 registers.  F – Non-linear function.  W t – 32-bit word derived from current 512-bit input block.  t – Round number, 0 ≤ t ≤ 79.  K t – 32-bit constant, different for each step.  s – left bit rotation by s places; s varies for each step.  – Addition modulo SHA-1

SHA-1 Functions  Expansion Function: W i = (W i-3  W i-8  W i-14  W i-16 ) << 1 16 ≤i ≤79  F Functions: F t (B,C,D)=(B^C)v(~B^D) 0 ≤ t ≤ 19 F t (B,C,D)=B  C  D20 ≤ t ≤ 39 F t (B,C,D)=(B^C)v(B^D)v(C^D) 40 ≤ t ≤ 59 F t (B,C,D)= B  C  D 60 ≤ t ≤ 79 SHA-1

Finding Collisions  SHA-1 does 80 rounds of scrambling, so a brute force attack to find a collision requires at most 2 80 operations.  Xiaoyun Wang and her team – have an attack that requires 2 69 operations (i.e times faster than 2 80 brute force). SHA-1

Wang’s Method (February 2005) Wang found following short-comings in SHA-1  The message expansion does not offer enough avalanche effect in terms of spreading the input differences.  The structure of all the step functions is unexpectedly weak. Because of the simple step operation, the certain step properties of some Boolean functions combined with the carry effect actually facilitate, rather than prevent, differential attack. SHA-1

Final Attack  Wang’s attack on SHA-1 consisted following techniques:  Message Modification Method  Differential Attack  Local Collision Attack  Use of Differential Path ( effect of a single bit change tracked through the hash algorithm ) and Disturbance Vector (set of bit changes to the hash input designed to create a set of changes to the hash sequence). SHA-1

Differential Attack  Differential Cryptanalysis : the study of how differences in an input can affect the resultant difference at the output.  Fundamental Observations made by the team: A change in a bit j of word W i can be corrected by complementary changes in the following bits –  bit (j+6) mod 32 of word W i+1  bit j of word W i+2  bit (j+30) mod 32 of word W i+3  bit (j+30) mod 32 of word W i+4  bit (j+30) mod 32 of word W i+5 SHA-1

Local Collision Attack  Local Collision – a collision within a single message (or within a few steps of hash function), including intermediate hash results.  SHA-1 has a 6-step local collision that can start at any step. SHA-1

Local Collision Attack (…cont) ΔmΔmΔaΔaΔbΔbΔcΔcΔdΔdΔeΔe i i i i i i Collision SHA-1

Conclusion  MD5 is breakable – 2 39 complexity  SHA-1 is breakable – 2 69 complexity  So, it’s time to switch from MD5 and SHA-1.  What next? Longer variants published by NIST  SHA-224  SHA-256  SHA-384  SHA-512  Because “Attacks always get better; they never get worse…”

References  Xiaoyun Wang et. al. “Finding Collisions in the Full SHA-1”, yao.pdf yao.pdf  Xiaoyun Wang et. al. “Collisions for Hash Functions MD4, MD5, HAVAL-128 and RIPEMD”,  Vlastimil Klima “Tunnels in Hash Functions: MD5 Collisions Within a Minute”  Steve Friedl, “An Illustrated Guide to Cryptographic Hashes ”,  Hashing Function Lounge  

Thank You! Questions? What is she talking about? mmm… Z Z z…