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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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
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 Sk of {1,…,k}
How does the encryption works?
[permutation.classical]
e(m)) = (mpi(1),…,mpi(k)|mk+pi(1),…,mk+pi(k)|m2k+pi(1),…,mn-k+pi(k))
How does the decryption works?
[permutation.classical]
d(c)) = (cpi’(1),…,cpi’(k)|ck+pi’(1),…,ck+pi’(k)|c2k+pi’(1),…,cn-k+pi’(k))
On which idea is the technique based on?
[vigenère.classical]
Enhancement of Alberti’s idea by Vignère in 16th century
What are the tools?
[vigenère.classical, 2]
1. Alphabet Sigma=Z26={0,…,25}
2. Word s of length k: s:=(s0,…, sk-1) \in Sigmak
How does the encryption works?
[vigenère.classical]
e((m1 … mn)) = c = (c1 … cn) with ci=(mi+s(i-1 mod k)) mod 26
How does the decryption works?
[vigenère.classical]
d((c1 … cn)) = m = (m1 … mn) with mi=(ci-s(i-1 mod k)) mod 26
Who extended this technique?
[vigenère.classical]
Vernam in 1917 is choosing k=n (length of plaintext)
When was the technique developed?
[hill.classical]
1929
What are the tools?
[hill.classical, 3]
1. Alphabet Sigma=Zp={0,…,p-1} with p prime // Alphabet merged with {, . |_|} (29 elements) or with {Numbers |_|} (37 elements)
2. Size of blocks k (If k does not divide n use padding)
3. Matrix U \in Zpkxk with det(U)!=0
How does the encryption works?
[hill.classical]
e(m)=c=(c1 … cn) with (cik+1 … cik+k)’=U(mik+1 … mik+k)’ for i=0,…,n/k-1
How does the decryption works?
[hill.classical]
d(c)=m=(m1 … mn) with (mik+1 … mik+k)’=U-1(cik+1 … cik+k)’ for i=0,…,n/k-1
What are the remarks?
[hill.classical, 2]
1. If p prime, Zp is a field and det(U)!=0 then an inverse U-1 exists
2. If Invertibility of U can be assured then ring Zn 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, …, 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
