CYG Chapter 2 Classical Cryptography

Questions about the lecture 'Cryptography' of the RWTH Aachen Chapter 2 Classical Cryptography

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This flashcard set covers classical cryptography techniques at a university level, focusing on encryption and decryption methods like substitution, affine, Caesar, Vigenère, and Hill ciphers. It delves into tools such as alphabets, keys, and matrices, explaining how they are used in various cipher techniques. The set is beneficial for students and professionals in computer science who need a solid understanding of foundational cryptographic principles and their practical applications.

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21.03.2017 / 12.11.2017

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How does the encryption works?

[hill.classical]

e(m)=c=(c₁ … c_n) with (c_ik+1 … c_ik+k)’=U(m_ik+1 … m_ik+k)’ for i=0,…,n/k-1

How does the decryption works?

[hill.classical]

d(c)=m=(m₁ … m_n) with (m_ik+1 … m_ik+k)’=U^-1(c_ik+1 … c_ik+k)’ for i=0,…,n/k-1

What are the remarks?

[hill.classical, 2]

1. If p prime, Z_p is a field and det(U)!=0 then an inverse U^-1exists

2. If Invertibility of U can be assured then ring Z_n can be used to

What is the permutation cipher?

[hill.classical]

Special case of hill cipher

What are the two possebilites?

[alphabet.characteristics.classical]

1. In- and 2. output alphabet

What is the definition?

[input.alphabet.characteristics.classical]

X := {x₁, …, x_m}

What is the definition?

[output.alphabet.characteristics.classical]

Y := {y₁, …, y_d}

What is a property?

[alphabet.characteristics.classical, 2]

1. Mono- or 2. polyalphabetic

What is the definition?

[mono.alphabet.characteristics.classical]

Each character is mapped to a unique cipher character

What are examples?

[mono.alphabet.characteristics.classical]

Substitution ciphers

What is the definition?

[poly.alphabet.characteristics.classical]

Each character may be mapped onto different cipher characters

What are examples?

[poly.alphabet.characteristics.classical, 2]

1. Vigenère and 2. Vernam cipher

What is the definition?

[plains.text.characteristics.classical]

Plaintext messages M := Cup_l=0^infX^l

What is the definition?

[ciphers.text.characteristics.classical]

Ciphertext messages C := Cup_l=0^infY^l

What is the definition?

[plain.text.characteristics.classical]

Plaintext, message m \in M

What is the definition?

[cipher.text.characteristics.classical]

Ciphertext, cryptogram c \in C

What is the definition?

[keyspace.characteristics.classical]

Keyspace K is finite set of possible keys k \in K

What is the definition?

[encryption.characteristics.classical]

Encryption rule e : M x K → C : (m,k) → m

What is the definition?

[decryption.characteristics.classical]

Decryption rule d : C x K → M : (c,k) → c

What is the definition?

[cryptosystem.characteristics.classical]

(M,K,C,e,d) with d(e(m,k),k)=m for all (m,k) \in M x K

Who used the technique?

[scytale.classical]

Tastatur-Befehle:

= drehen,

= vor-/rückwärts,

= scrollen

Spartans around 400 BC

What is the tool?

[scytale.classical]

Tastatur-Befehle:

= drehen,

= vor-/rückwärts,

= scrollen

Wand with diameter d (So-called scytale)

How does the encryption works?

[scytale.classical, 3]

Tastatur-Befehle:

= drehen,

= vor-/rückwärts,

= scrollen

1. Blank stripe is wrapped around the wand

2. Letters of message are written column wise

3. Unwrapping the strip leaves a meaningless message

How does the decryption works?

[scytale.classical]

Tastatur-Befehle:

= drehen,

= vor-/rückwärts,

= scrollen

Use wand with same diameter d

What are the tools?

[substitution.classical, 2]

Tastatur-Befehle:

= drehen,

= vor-/rückwärts,

= scrollen

1. Alphabet Sigma={x₁,…,x_m}

2. Permutation pi \in S_m of {1,…,m}

How does the encryption works?

[substitution.classical]

Tastatur-Befehle:

= drehen,

= vor-/rückwärts,

= scrollen

Substitute letter x_i by x_pi(i) in the plain-text

How does the decryption works?

[substitution.classical]

Tastatur-Befehle:

= drehen,

= vor-/rückwärts,

= scrollen

Substitute letter x_jby x_pi’(j) in the cipher-text

What are the variants?

[substitution.classical, 2]

Tastatur-Befehle:

= drehen,

= vor-/rückwärts,

= scrollen

1. Caesar and 2. affine in Z_m

Who used the technique?

[caesar.substitution.classical, 2]

Tastatur-Befehle:

= drehen,

= vor-/rückwärts,

= scrollen

1. Caesar during the Gallic Wars 100-44 BC

2. Enhanced by Alberti with machine-assistance in 15^th century

What are the tools?

[caesar.substitution.classical, 2]

Tastatur-Befehle:

= drehen,

= vor-/rückwärts,

= scrollen

1. Alphabet Sigma=Z₂₆={0,…,25}

2. Key k \in Z₂₆

How does the encryption works?

[caesar.substitution.classical]

e((m₁ … m_n)) = c = (c₁ … c_n) with c_i=(m_i+k) mod 26

How does the decryption works?

[caesar.substitution.classical]

d((c₁ … c_n)) = m = (m₁ … m_n) with m_i=(c_i-k) mod 26

What are the tools?

[affine.substitution.classical, 2]

1. Alphabet Sigma=Z_m={0,…,m-1}

2. Key k=(a,b) \in Z_m* x Z_mwith Z_m* := {a \in Z_m | \exists a^-1 : a*a^-1=1 mod m}

How does the encryption works?

[affine.substitution.classical]

e((m₁ … m_n)) = c = (c₁ … c_n) with c_i=(a*m_i+b) mod m

How does the decryption works?

[affine.substitution.classical]

d((c₁ … c_n)) = m = (m₁ … m_n) with m_i=(a^-1(c_i-b)) mod m

What has to hold?

[affine.substitution.classical]

a must be multiplicatively invertible mod m, else it could happen that e(m₁)=e(m₂)

What is the condition?

[invertible.affine.substitution.classical]

a*i+b = a*j+b (mod m) ↔ m|(i-j) // gcd(a,m)=1

What are the tools?

[permutation.classical, 2]

1. Size of blocks k

2. Permutation pi \in S_k of {1,…,k}

How does the encryption works?

[permutation.classical]

e(m)) = (m_pi(1),…,m_pi(k)|m_k+pi(1),…,m_k+pi(k)|m_2k+pi(1),…,m_n-k+pi(k))

How does the decryption works?

[permutation.classical]

d(c)) = (c_pi’(1),…,c_pi’(k)|c_k+pi’(1),…,c_k+pi’(k)|c_2k+pi’(1),…,c_n-k+pi’(k))

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What is the definition?

[ciphers.text.characteristics.classical]

Ciphertext messages C := Cup_l=0^infY^l

What is the definition?

[plain.text.characteristics.classical]

Plaintext, message m \in M

What is the definition?

[cipher.text.characteristics.classical]

Ciphertext, cryptogram c \in C

What is the definition?

[keyspace.characteristics.classical]

Keyspace K is finite set of possible keys k \in K

What is the definition?

[encryption.characteristics.classical]

Encryption rule e : M x K → C : (m,k) → m

What is the definition?

[decryption.characteristics.classical]

Decryption rule d : C x K → M : (c,k) → c

What is the definition?

[cryptosystem.characteristics.classical]

(M,K,C,e,d) with d(e(m,k),k)=m for all (m,k) \in M x K

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CYG Chapter 2 Classical Cryptography

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