PROGRAMME: ICE
COURSE CODE: EIE 524
ASSIGNMENT 2
Review Questions
2.1 Plaintext, encryption algorithm, secret key, cipher text, decryption algorithm.
2.2 Permutation and substitution.
2.3 One key for symmetric ciphers, two keys for asymmetric ciphers.
2.4 A stream cipher is one that encrypts a digital data stream one bit or one byte at a time. A
block cipher is one in which a block of plaintext is treated as a whole and used to
produce a cipher text block of equal length.
2.5 Cryptanalysis and brute force.
2.6 Ciphertext only. One possible attack under these circumstances is the brute-force
approach of trying all possible keys. If the key space is very large, this becomes
impractical. Thus, the opponent must rely on an analysis of the ciphertext itself, generally
applying various statistical tests to it. Known plaintext. The analyst may be able to
capture one or more plaintext messages as well as their encryptions. With this knowledge,
the analyst may be able to deduce the key on the basis of the way in which the known
plaintext is transformed. Chosen plaintext. If the analyst is able to choose the messages to
encrypt, the analyst may deliberately pick patterns that can be expected to reveal the
structure of the key.
2.7 An encryption scheme is unconditionally secure if the cipher text generated by the scheme
does not contain enough information to determine uniquely the corresponding plaintext, no
matter how much cipher text is available. An encryption scheme is said to be
computationally secure if: (1) the cost of breaking the cipher exceeds the value of the
encrypted information, and (2) the time required to break the cipher exceeds the useful
lifetime of the information.
2.8 The Caesar cipher involves replacing each letter of the alphabet with the letter standing
k places further down the alphabet, for k in the range 1 through 25.
2.9 A mono-alphabetic substitution cipher maps a plaintext alphabet to a ciphertext alphabet,
so that each letter of the plaintext alphabet maps to a single unique letter of the cipher text
, alphabet.
2.10 The Playfair algorithm is based on the use of a 5 ´ 5 matrix of letters constructed using a
keyword. Plaintext is encrypted two letters at a time using this matrix.
2.11 A polyalphabetic substitution cipher uses a separate mono-alphabetic
substitution cipher for each successive letter of plaintext, depending on a key.
2.12 1. There is the practical problem of making large quantities of random keys. Any
heavily used system might require millions of random characters on a regular basis.
Supplying truly random characters in this volume is a significant task.
2. Even more daunting is the problem of key distribution and protection. For every
message to be sent, a key of equal length is needed by both sender and receiver.
Thus, a mammoth key distribution problem exists.
2.13 A transposition cipher involves a permutation of the plaintext letters.
2.14 Steganography involves concealing the existence of a message.
Problems
2.1 a. No. A change in the value of b shifts the relationship between plaintext letters and
ciphertext letters to the left or right uniformly, so that if the mapping is one-to-one it
remains one-to-one.
b. 2, 4, 6, 8, 10, 12, 13, 14, 16, 18, 20, 22, 24. Any value of a larger than 25 is
equivalent to a mod 26.
c. The values of a and 26 must have no common positive integer factor other than 1. This
is equivalent to saying that a and 26 are relatively prime, or that the greatest common
divisor of a and 26 is 1. To see this, first note that E(a, p) = E(a, q) (0 ≤ p ≤ q < 26) if and
only if a(p – q) is divisible by 26.
1. Suppose that a and 26 are relatively prime. Then, a(p – q) is not divisible by 26, because
there is no way to reduce the fraction a/26 and (p – q) is less than 26.
2. Suppose that a and 26 have a common factor k > 1. Then E(a, p) = E(a, q), if q = p +
m/k≠ p.
COURSE CODE: EIE 524
ASSIGNMENT 2
Review Questions
2.1 Plaintext, encryption algorithm, secret key, cipher text, decryption algorithm.
2.2 Permutation and substitution.
2.3 One key for symmetric ciphers, two keys for asymmetric ciphers.
2.4 A stream cipher is one that encrypts a digital data stream one bit or one byte at a time. A
block cipher is one in which a block of plaintext is treated as a whole and used to
produce a cipher text block of equal length.
2.5 Cryptanalysis and brute force.
2.6 Ciphertext only. One possible attack under these circumstances is the brute-force
approach of trying all possible keys. If the key space is very large, this becomes
impractical. Thus, the opponent must rely on an analysis of the ciphertext itself, generally
applying various statistical tests to it. Known plaintext. The analyst may be able to
capture one or more plaintext messages as well as their encryptions. With this knowledge,
the analyst may be able to deduce the key on the basis of the way in which the known
plaintext is transformed. Chosen plaintext. If the analyst is able to choose the messages to
encrypt, the analyst may deliberately pick patterns that can be expected to reveal the
structure of the key.
2.7 An encryption scheme is unconditionally secure if the cipher text generated by the scheme
does not contain enough information to determine uniquely the corresponding plaintext, no
matter how much cipher text is available. An encryption scheme is said to be
computationally secure if: (1) the cost of breaking the cipher exceeds the value of the
encrypted information, and (2) the time required to break the cipher exceeds the useful
lifetime of the information.
2.8 The Caesar cipher involves replacing each letter of the alphabet with the letter standing
k places further down the alphabet, for k in the range 1 through 25.
2.9 A mono-alphabetic substitution cipher maps a plaintext alphabet to a ciphertext alphabet,
so that each letter of the plaintext alphabet maps to a single unique letter of the cipher text
, alphabet.
2.10 The Playfair algorithm is based on the use of a 5 ´ 5 matrix of letters constructed using a
keyword. Plaintext is encrypted two letters at a time using this matrix.
2.11 A polyalphabetic substitution cipher uses a separate mono-alphabetic
substitution cipher for each successive letter of plaintext, depending on a key.
2.12 1. There is the practical problem of making large quantities of random keys. Any
heavily used system might require millions of random characters on a regular basis.
Supplying truly random characters in this volume is a significant task.
2. Even more daunting is the problem of key distribution and protection. For every
message to be sent, a key of equal length is needed by both sender and receiver.
Thus, a mammoth key distribution problem exists.
2.13 A transposition cipher involves a permutation of the plaintext letters.
2.14 Steganography involves concealing the existence of a message.
Problems
2.1 a. No. A change in the value of b shifts the relationship between plaintext letters and
ciphertext letters to the left or right uniformly, so that if the mapping is one-to-one it
remains one-to-one.
b. 2, 4, 6, 8, 10, 12, 13, 14, 16, 18, 20, 22, 24. Any value of a larger than 25 is
equivalent to a mod 26.
c. The values of a and 26 must have no common positive integer factor other than 1. This
is equivalent to saying that a and 26 are relatively prime, or that the greatest common
divisor of a and 26 is 1. To see this, first note that E(a, p) = E(a, q) (0 ≤ p ≤ q < 26) if and
only if a(p – q) is divisible by 26.
1. Suppose that a and 26 are relatively prime. Then, a(p – q) is not divisible by 26, because
there is no way to reduce the fraction a/26 and (p – q) is less than 26.
2. Suppose that a and 26 have a common factor k > 1. Then E(a, p) = E(a, q), if q = p +
m/k≠ p.
