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# Hash Function & Analysis

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About the theory behind hash functions and analysis from the computer security prospective

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### Hash Function & Analysis

1. 1. Hash Functions & Analysis for CCM 4332 Seminar (Network Security) Presented By, Bhavesh Kumar Hari Pawandeep Kaur Manish Hatkar Prateek Goli Vipul Agarwal
2. 2. What is a hash function? A hash function is a set of procedures and steps or a mathematical function that can be used to convert a a large amount of data into a small data string and integers that can be used as an index as an array. Output of a hash function, Hash Values Hash Codes Hash Sums Checksums Hashes
3. 3. Applications of Hash Functions There are various applications of hash functions and the most common one is using hash tables.  Hash Tables Hash tables are mainly used to quickly search a data record using a given search key where the the hash function is used to map the search key using a generated hash.  Eliminate Redundancy
4. 4. Applications of Hash Functions • Caches Hash function are used with hash tables to build caches for large datasets that are stored in slow media. This highly improves the performance and reliability.  Bloom filters A compact data structure that uses hash function and hashes.
5. 5. Applications of Hash Functions • Pattern Matching String search algorithms like Rabin-karp uses hashing to compare strings with time complexity of O(n) on average.  Geometric Hashing Used to solve many proximity problems in a plane or in 3D space. This is further used to to image recognition, processing and matching. It's even used in telecommunication to encode and compress multi- dimensional signals and it's knows as vector quantization.
6. 6. Cryptographic Hash Functions A cryptographic hash function is a special hash function that has the following three properties,  Preimage resistance The function should be irreversible or one-way where a given hash h where it'll be difficult to find any message m such that, h = hash(m)  Second preimage resistance The function should not produce same hash for two different message. Given a message m1, it should be difficult to find another message m2 where m1 != m2 such that hash(m1) = hash(m2)
7. 7. Cryptographic Hash Functions  Collision Resistance The function should be collision resistant where it should be difficult to find two different messages m1, and m2, such that hash(m1) = hash(m2). Birthday attack maybe used against the hash functions to find a collision.  Some examples are, MD2, MD4, MD5, SHA-0, SHA-1, SHA-2, SHA-2, crypt
8. 8. Applications of Cryptographic Hash Function There are various applications of cryptographic has functions and few are mentioned as follows,  Integrity of files & messages A hash value of a file and message can be calculated and transferred to the destination via different forms to later ensure if the file or message is not tampered. It's used with digital signatures where, the hash of the message is generated and then encrypted using the private key. Later on the receiver can decrypt it using the sender's public key and compare the hash with the message. This helps in generating short signatures.
9. 9. Applications of Cryptographic Hash Function  Pseudorandom generation Hash functions can also be used in the generation of pseudorandom bits, or to derive new keys or passwords from a single, secure key or password.  SSL  IPSec  File or data identifier
10. 10. Description of Cryptographic Hash Function We'll be discussing few popular cryptographic function and their advantages/limitations.  MD2  MD4  MD5  SHA-1  SHA-2
11. 11. MD 2 (Message Digest) •Cryptographic hash function developed by Renald Rivest 1989. •Takes input as a message of arbitrary length and output of 128 bits •This algorithm is optimized for 8 bit computers •Message is padded according to specified conventions, to be a multiple of 16 bytes •These 16 bytes calls as checksum and added at the end.
12. 12. MD 2 •Final pass is processed in 16 bytes at same time with intermediate result for, each intermediate value depends on previous intermediate value. •No longer contained as secured algorithm. •First attack was pre image attack by F.Muller (2004) . •Second result was collision attack found by Rogier and Chauvaud on compression function. •This attack was not able to extend immediately because of checksum.
13. 13. MD 4 •Cryptographic hash function developed by Ronald Rivest in 1990. •Arbitrary length is 128 bits. •This algorithm is optimized for 32 bit computers. •It needs more intermediate state than MD 2 •Weakness of MD4 were demonstrated in1991by Den Boer & Bosselaers.
14. 14. MD 4 •Later collision attack were found 1995 and after that hashing function were designed in MD 5, SHA-1 •MD4 collision resistance were reduced, pre image and second pre image resistance attack on MD 4 are practical, •Cannot be used to hash a cryptography of 80 bits or longer. •MD 4 is used to complete hash password on Microsoft like windows NT, XP, Vista and 7.
15. 15. Discussed Topics: •Information about MD5 •MD5 Vs MD4 •Attacks on MD5
16. 16. Introduction •It is widely used cryptographic hash functions •Message is processed in 512 bits (16*32 bit words) block. Ex: if message is M then blocks are {m0,m1,m2…. M15} of 32bits •Digest is 128-bit quantity i.e. 4* 32-bit words having the predefined hex constant value. Ex digests : d0=67543201,d1= efcdab89, d2=85bacade, d3= 10325476 •It make 4 passes over each message word.
17. 17. •Every pass has a specific functions to blend on message digest •Each word of the processed message digest is added to pre-stage value(constant) to obtain the post- stage value. •This post- stage value will be the pre-stage value for the next stage •The final result is the Message Digest of entire message.
18. 18. Functional Steps for Algorithm 1) Padding: A arbitrary length message is first padded by 1s followed by 0s to make it 448bit(512-64)long. The 64 bit is then used to store the length of the message before padding.
19. 19. 2) Initialization: 4 digests(word buffer) are initialized to constant Hex value. Below A,B,C,D is 32-bit register 3)Process Message:- m0,m1…..m15 is processed in 4passes with 64 rounds
20. 20. .
21. 21. continued Pass1: F(x,y,z) = (x^y)v(~x^z) Pass2: G(x,y,z) = (x^z) v(y^~y) Pass3: H(x,y,z) = x xor y xor z Pass 4: I(x,y,z) = y xor( x v ~ z) here ^,v,~ denotes the AND, OR and NOT operations respectively 4) The message digest produced is A,B,C,D where A is lowest order bit and D is highest order bit.
22. 22. MD4 Vs MD5 •MD5 make 4 passes whereas it was 3 in MD4, making it more secure but less faster. •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 •Each step has unique addictive constant •Each step adds in the result of previous step to promote the faster avalanche effect.
23. 23. Attacks on MD5 •Chosen-prefix collision attack •Pre-image attack •Vulnerable CAs
24. 24. SHA-1 •Developed by National Security Agency (NSA) for use with NIST’s Digital Signature Standard. •It produces 160 bit (20 byte) Message Digest. •SHA1 is mostly used to secure protocol as SSH, TLS, SSL, PGP, and IPSec. •It is used to provide authenticity and integrity. •Key has to be destroyed upon Implementation.
25. 25. SHA 1 Digest •SHA1 (“Middlesex University“) = e9efe518 85e13e90 ff37c753 d96421f8 2c1bc9d4 •SHA1 (“Middlesex Univercity”) = 0773a83f 705a95ee 5827bd06 ea9b26cd e96dbe2e •Hash of Zero Length String is • SHA1 (“”) = da39a3ee 5e6b4b0d 3255bfef 95601890 afd80709
26. 26. SHA1 vs MD5 •MD5 – Vulnerable to Brute force Attack. •MD5 creates 128-bit String, SHA1 creates 256-bit String. •MD5 hash for "asdf": 912ec803b2ce49e4a541068d495ab570 •SHA1 hash for "asdf": 3da541559918a808c2402bba5012f6c60b27661c
27. 27. Limitations Collision - First successful collision was done in 2005. - The research team of Xiaoyun Wang, Yiqun Lisa Yin, and Hongbo Yu have been circulating a paper describing their results: - Collisions in the the full SHA-1 in 2**69 hash operations, much less than the brute-force attack of 2**80 operations based on the hash length. - Collisions in SHA-0 in 2**39 operations.
28. 28. SHA-2 •SHA stands for Secure Hash Algorithm. •It is a set of cryptographic hash functions which include SHA-224 , SHA-256 , SHA-384 and SHA-512 designed by the national security agency. •The SHA-256 and SHA-512 are considered as two similar hash functions with different block sizes , they vary in the word size like SHA-256 uses 32-bytes of words and SHA-512 uses 64-bytes of words.
29. 29. Advantages in SHA-2 •The SHA-2 is considered as a very secure hash standard with four secure hash algorithms used in it like SHA-224, SHA-256, SHA-384, and SHA-512. •It is a one way hash function that processes a message to produce a hash representation which is called as a Message digest •All the four algorithms used are iterative.
30. 30. Limitations • There are very limited known attacks for SHA-2 • Two meet-in-the-middle preimage attacks are possible against SHA-2 with reduced number of rounds. It has time complexity of 2^253.5 which can’t be practically implemented at the moment.against SHA-2 with a reduced number of rounds
31. 31. Questions?
32. 32. Thank You!