CYG Chapter 2 Classical Cryptography
Questions about the lecture 'Cryptography' of the RWTH Aachen Chapter 2 Classical Cryptography
Questions about the lecture 'Cryptography' of the RWTH Aachen Chapter 2 Classical Cryptography
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What is the definition?
[input.alphabet.characteristics.classical]
X := {x1, …, xm}
What is the definition?
[output.alphabet.characteristics.classical]
Y := {y1, …, yd}
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 := Cupl=0inf Xl
What is the definition?
[ciphers.text.characteristics.classical]
Ciphertext messages C := Cupl=0inf Yl
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]
Spartans around 400 BC
What is the tool?
[scytale.classical]
Wand with diameter d (So-called scytale)
How does the encryption works?
[scytale.classical, 3]
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]
Use wand with same diameter d
What are the tools?
[substitution.classical, 2]
1. Alphabet Sigma={x1,…,xm}
2. Permutation pi \in Sm of {1,…,m}
How does the encryption works?
[substitution.classical]
Substitute letter xi by xpi(i) in the plain-text
How does the decryption works?
[substitution.classical]
Substitute letter xj by xpi’(j) in the cipher-text
What are the variants?
[substitution.classical, 2]
1. Caesar and 2. affine in Zm
Who used the technique?
[caesar.substitution.classical, 2]
1. Caesar during the Gallic Wars 100-44 BC
2. Enhanced by Alberti with machine-assistance in 15th century
What are the tools?
[caesar.substitution.classical, 2]
1. Alphabet Sigma=Z26={0,…,25}
2. Key k \in Z26
How does the encryption works?
[caesar.substitution.classical]
e((m1 … mn)) = c = (c1 … cn) with ci=(mi+k) mod 26
How does the decryption works?
[caesar.substitution.classical]
d((c1 … cn)) = m = (m1 … mn) with mi=(ci-k) mod 26
What are the tools?
[affine.substitution.classical, 2]
1. Alphabet Sigma=Zm={0,…,m-1}
2. Key k=(a,b) \in Zm* x Zm with Zm* := {a \in Zm | \exists a-1 : a*a-1=1 mod m}
How does the encryption works?
[affine.substitution.classical]
e((m1 … mn)) = c = (c1 … cn) with ci=(a*mi+b) mod m
How does the decryption works?
[affine.substitution.classical]
d((c1 … cn)) = m = (m1 … mn) with mi=(a-1(ci-b)) mod m
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