Cipher Block Chaining. Take the following figure below, representing the structure for a block ciphe in Cipher Block Chaining or CBC mode. The below figure is only for a 2-stage CBC structure, with each stage processing 8-bits at a time. It also provides some reference information on how hexadecim digits can be converted to binary and vice versa as well as how the “XOR" operation is performed bit- by-bit.

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7. Cipher Block Chaining. Take the following figure below, representing the structure for a block cipher
in Cipher Block Chaining or CBC mode. The below figure is only for a 2-stage CBC structure, with
each stage processing 8-bits at a time. It also provides some reference information on how hexadecimal
digits can be converted to binary and vice versa as well as how the “XOR" operation is performed bit-
by-bit.
P:
P2
0 = 0000
1= 0001
2 = 0010
ХOR
0 xor 0 = 0
1 = 1
0 xor
0 = 1
IV
3 = 0011
4 = 0100
5 = 0101
1 хor
1 xor 1 = 0
6 = 0110
7 = 0111
8 = 1000
9 = 1001
A = 1010
B = 1011
C = 1100
D= 1101
E = 1110
K
K
Encrypt
Encrypt
C;
E = 1111
CBC works with ANY encryption algorithm. Suppose that we have a really, really, dumb encryption
algorithm which simply performs the following:
comp(x), if k = 1
comp(x), if k = 1
E(r, k) =
D(r, k) =
otherwise
otherwise
and
where, "comp(x)" simply performs the binary "1's complement" of x. For example, the hexadecimal
value F2 can be expressed in binary as 11110010 (see the table). The “l’s complement" of this is
obtained by simply flipping the bits to give us 00001101, which in hexadecimal is OD. In other words
E(F2, 1) = OD. Note the 'key' is simply a single bit that, when it is 1, the complementation is
performed, and when it is 0, it is simply left "as is". That is, E(F2,0) = F2 (no change). The circular
plus symbol in the above diagram, recall, represents the bitwise XOR operation. For example, the
bitwise XOR of two 4-bit values 1010 and 1000 is 0010. CBC shows that for the first stage, we must
perform the XOR operation of P1 with an Initial Vector (IV) value prior to encrypting.
For this problem, suppose that the plaintext data Pı is the byte 7A (in hexadecimal), and P2 is the byte
2C (in hexadecimal). Use the above diagram, encryption algorithms, with an IV = 55 (in
hexadecimal) and a key value of K = 1, to determine the enciphered bytes C1 and C2 (also in
НЕХADECIMAL).
State your answer as "C1 = ??, C2 = ??".
Note for this problem you HAVE to convert form hexadecimal to binary so that everything can be done
in binary. Once you get your final answers, reconvert them back to hexadecimal. So, if you compute
"11101110" (in binary), then the answer in Hexadecimal is "EE".
Transcribed Image Text:7. Cipher Block Chaining. Take the following figure below, representing the structure for a block cipher in Cipher Block Chaining or CBC mode. The below figure is only for a 2-stage CBC structure, with each stage processing 8-bits at a time. It also provides some reference information on how hexadecimal digits can be converted to binary and vice versa as well as how the “XOR" operation is performed bit- by-bit. P: P2 0 = 0000 1= 0001 2 = 0010 ХOR 0 xor 0 = 0 1 = 1 0 xor 0 = 1 IV 3 = 0011 4 = 0100 5 = 0101 1 хor 1 xor 1 = 0 6 = 0110 7 = 0111 8 = 1000 9 = 1001 A = 1010 B = 1011 C = 1100 D= 1101 E = 1110 K K Encrypt Encrypt C; E = 1111 CBC works with ANY encryption algorithm. Suppose that we have a really, really, dumb encryption algorithm which simply performs the following: comp(x), if k = 1 comp(x), if k = 1 E(r, k) = D(r, k) = otherwise otherwise and where, "comp(x)" simply performs the binary "1's complement" of x. For example, the hexadecimal value F2 can be expressed in binary as 11110010 (see the table). The “l’s complement" of this is obtained by simply flipping the bits to give us 00001101, which in hexadecimal is OD. In other words E(F2, 1) = OD. Note the 'key' is simply a single bit that, when it is 1, the complementation is performed, and when it is 0, it is simply left "as is". That is, E(F2,0) = F2 (no change). The circular plus symbol in the above diagram, recall, represents the bitwise XOR operation. For example, the bitwise XOR of two 4-bit values 1010 and 1000 is 0010. CBC shows that for the first stage, we must perform the XOR operation of P1 with an Initial Vector (IV) value prior to encrypting. For this problem, suppose that the plaintext data Pı is the byte 7A (in hexadecimal), and P2 is the byte 2C (in hexadecimal). Use the above diagram, encryption algorithms, with an IV = 55 (in hexadecimal) and a key value of K = 1, to determine the enciphered bytes C1 and C2 (also in НЕХADECIMAL). State your answer as "C1 = ??, C2 = ??". Note for this problem you HAVE to convert form hexadecimal to binary so that everything can be done in binary. Once you get your final answers, reconvert them back to hexadecimal. So, if you compute "11101110" (in binary), then the answer in Hexadecimal is "EE".
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