Problem 1 :

Calculate the hash value for the 21-character message: who wrote the book of love, or equivalently: WHOWROTETHEBOOKOFLOVE,after removing whitespace, and capitalizing.

Problem 2 :

Calculate the hash value for the 21-letter message: who wrote the book ov love, or equivalently: WHOWROTETHEBOOKOVLOVE, after removing whitespace and capitalizing.

At this point you may have noticed the hash values for the two messages are different by two characters, despite the fact that the messages differ by only one character. This is a desired property of a good hash function. However, it's mathematically impossible to ensure this: if two given messages are identical, their hash values will be identical too. If two messages are different then it's likely' their hash values will be different, but, it's not mathematically possible to design a hash function that has this property. (Think about why this is true and try to express this in your own words.)

Problem 3 :

To demonstrate the weakness of TTH, find a different block, of any size, that produces the same hash value as problem 1. Hint: Use lots of As. (The message that creates the collision doesn't needn't be intelligible, complete gibberish is acceptable.)

problem2HashFunctions (1) Compatibility Mode Microsoft Word Home nsert Page Layo Reteren Ma Review View ng A Find Aria A A sbocDdl AaBbc AaBbc AaBbc AaBboc AaBbccDd AaBbccDdl copy Replace Pa Chang I U abe x n Normal No Spaci... Heading 1 Heading 2 Subtit Select ormat Painte Style pboard Font diting Cryptograpnic Hasn runctions Round theggi Amenge block of textint 4* matrix and finally convertit to indi This proble HA cryptographic hashes, but stead of bytes, andits mpute by mple, for the blockABCDERGH JKLMNOP Toy Tetra-g ph HeshITH and just ke SHA, TTH mputes a foxed length value for Despiteitstriviality, it of the cryptographically ach you they operate familiarize you with th and you to think implications A 6 DC D 0 2 3 divdee a given Rage into blocks of 16 itters ignoring paces. and punctuat and capitalizes he letters. The lett his matrix to indi range 10.25. If the essage length is not divisible by 16, then the last blook is padded with A four-number tuple caled thestate of the hash. 24 2 10 sion tuncton conciata oftwo pplied to ry Mocha of the meyRFage til the entire meReage been processed. 16 indices add lumn modulo 26and add these results to the cument state. modulo 26. this example the statebe (24.2.5.10. ompressor Round 2 Using th dex matix it from Round 1. rotate thefirst left by 1. the second by 2 Round 1 Round 2 by 3. Sum1 N 13 12 4 indices (7,5,3, State 242G101 5, 1. you set ot 10 characterblocks B, B, B the folowing (And there autoequent blocks te given messag where all operations procee ed, comer na final leterek ths set of le the TTH hash of your message. In this example when the message le 3The value (5,T,9, 1) the sum of the state trom Round 1 p24,2.0, 10) and the mivate W (7.6, 3 d20,9 d 20.10 20.21 mod 20) https: ien wikipedia 2httperien wikipedia orgwkione-way compreRRion-function Go to Settings act vate Page: of 4 Word English (U.S 2.26 PM ENG Search the web and Windows problem2HashFunctions (1) Compatibility Mode Microsoft Word Home nsert Page Layo Reteren Ma Review View ng A Find Aria A A sbocDdl AaBbc AaBbc AaBbc AaBboc AaBbccDd AaBbccDdl copy Replace Pa Chang I U abe x n Normal No Spaci... Heading 1 Heading 2 Subtit Select ormat Painte Style pboard Font diting Cryptograpnic Hasn runctions Round theggi Amenge block of textint 4* matrix and finally convertit to indi This proble HA cryptographic hashes, but stead of bytes, andits mpute by mple, for the blockABCDERGH JKLMNOP Toy Tetra-g ph HeshITH and just ke SHA, TTH mputes a foxed length value for Despiteitstriviality, it of the cryptographically ach you they operate familiarize you with th and you to think implications A 6 DC D 0 2 3 divdee a given Rage into blocks of 16 itters ignoring paces. and punctuat and capitalizes he letters. The lett his matrix to indi range 10.25. If the essage length is not divisible by 16, then the last blook is padded with A four-number tuple caled thestate of the hash. 24 2 10 sion tuncton conciata oftwo pplied to ry Mocha of the meyRFage til the entire meReage been processed. 16 indices add lumn modulo 26and add these results to the cument state. modulo 26. this example the statebe (24.2.5.10. ompressor Round 2 Using th dex matix it from Round 1. rotate thefirst left by 1. the second by 2 Round 1 Round 2 by 3. Sum1 N 13 12 4 indices (7,5,3, State 242G101 5, 1. you set ot 10 characterblocks B, B, B the folowing (And there autoequent blocks te given messag where all operations procee ed, comer na final leterek ths set of le the TTH hash of your message. In this example when the message le 3The value (5,T,9, 1) the sum of the state trom Round 1 p24,2.0, 10) and the mivate W (7.6, 3 d20,9 d 20.10 20.21 mod 20) https: ien wikipedia 2httperien wikipedia orgwkione-way compreRRion-function Go to Settings act vate Page: of 4 Word English (U.S 2.26 PM ENG Search the web and Windows