2.7 This problem introduces a hash function similar in spirit to SHA that operates on lettersinstead of binary data. It is called the toy tetragraph hash (tth).8 Given a messageconsisting of a sequence of letters, tth produces a hash value consisting of four letters.First, tth divides the message into blocks of 16 letters, ignoring spaces, punctuation, andcapitalization. If the message length is not divisible by 16, it is padded out with nulls. Afour-number running total is maintained that starts out with the value (0, 0, 0, 0); this isinput to a function, known as a compression function, for processing the first block. Thecompression function consists of two rounds. Round 1: Get the next block of text andarrange it as a row-wise 4x4 block of text and convert it to numbers (A=0, B=1), forexample, for the block ABCDEFGHIJKLMNOP, we have81 thank William K. Mason and The American Cryptogram Association for providing this example.AB C D0 1 2 3EFG H46 758 9 10 11IJKLMNOP12 13 14 15Then, add each column mod 26 and add the result to the running total, mod 26. In thisexample, the running total is (24, 2, 6, 10). Round 2: Using the matrix from round 1, rotatethe first row left by 1, second row left by 2, third row left by 3, and reverse the order of thefourth row. In our example, BCD AG HEFLIJKPON M1 26 71115 14304 51013 128 9Now, add each column mod 26 and add the result to the running total. The new runningtotal is (5, 7, 9, 11). This running total is now the input into the first round of thecompression function for the next block of text. After the final block is processed, convertthe final running total to letters. For example, if the message is ABCDEFGHIJKLMNOP,then the hash is FHJL.a. Draw figures of the overall tth logic and the compression function logic.b. Calculate the hash function for the 48-letter message "I leave twenty million dollarsto my friendly cousin Bill."c. To demonstrate the weakness of tth, find a 48-letter block that produces the samehash as that just derived. Hint: Use lots of As.

the solution is an given below :

instead of binary data. It is called the toy tetragraph hash (tth).8 Given a message consisting of a sequence of letters, tth produces a hash value consisting of four letters. First, tth divides the message into blocks of 16 letters, ignoring spaces, punctuation, and capitalization. If the message length is not divisible by 16, it is padded out with nulls. A four-number running total is maintained that starts out with the value (0, 0, 0, 0); this is input to a function, known as a compression function, for processing the first block. The compression function consists of two rounds Pound 1: Get the next block of text and

instead of binary data. It is called the toy tetragraph hash (tth).8 Given a message consisting of a sequence of letters, tth produces a hash value consisting of four letters. First, tth divides the message into blocks of 16 letters, ignoring spaces, punctuation, and capitalization. If the message length is not divisible by 16, it is padded out with nulls. A four-number running total is maintained that starts out with the value (0, 0, 0, 0); this is input to a function, known as a compression function, for processing the first block. The compression function consists of two rounds Pound 1: Get the next block of text and

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Concept explainers

Hash Table

A hash table also called a hash map, is a data structure that maps key-value pairs. The hash table can be used in complex systems to provide fast access and compact storage. A hash table is a structure that stores data in an abstract data type kind of associative array. It keeps data in an array format, with a distinct index value for every data value. If the index of the required data is known, then the data can be accessed very easily.

Question

2.7 This problem introduces a hash function similar in spirit to SHA that operates on letters
instead of binary data. It is called the toy tetragraph hash (tth).8 Given a message
consisting of a sequence of letters, tth produces a hash value consisting of four letters.
First, tth divides the message into blocks of 16 letters, ignoring spaces, punctuation, and
capitalization. If the message length is not divisible by 16, it is padded out with nulls. A
four-number running total is maintained that starts out with the value (0, 0, 0, 0); this is
input to a function, known as a compression function, for processing the first block. The
compression function consists of two rounds. Round 1: Get the next block of text and
arrange it as a row-wise 4x4 block of text and convert it to numbers (A=0, B=1), for
example, for the block ABCDEFGHIJKLMNOP, we have
81 thank William K. Mason and The American Cryptogram Association for providing this example.
A
B C D
0 1 2 3
E
F
G H
4
6 7
5
8 9 10 11
I
J
K
L
M
N
OP
12 13 14 15
Then, add each column mod 26 and add the result to the running total, mod 26. In this
example, the running total is (24, 2, 6, 10). Round 2: Using the matrix from round 1, rotate
the first row left by 1, second row left by 2, third row left by 3, and reverse the order of the
fourth row. In our example,

BCD A
G HEF
LIJK
PON M
1 2
6 7
11
15 14
3
0
4 5
10
13 12
8 9
Now, add each column mod 26 and add the result to the running total. The new running
total is (5, 7, 9, 11). This running total is now the input into the first round of the
compression function for the next block of text. After the final block is processed, convert
the final running total to letters. For example, if the message is ABCDEFGHIJKLMNOP,
then the hash is FHJL.
a. Draw figures of the overall tth logic and the compression function logic.
b. Calculate the hash function for the 48-letter message "I leave twenty million dollars
to my friendly cousin Bill."
c. To demonstrate the weakness of tth, find a 48-letter block that produces the same
hash as that just derived. Hint: Use lots of As.

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