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CM30173:
Cryptography

Part II

Outline

Combining basic
building blocks

Substitution-
permutation
networks

Example SPN

Attacks on SPNs

Part II

Private-key cryptography: block ciphers

CM30173:
Cryptography

Part II

Outline

Combining basic
building blocks

Substitution-
permutation
networks

Example SPN

Attacks on SPNs

Outline

Combining basic building blocks

Substitution-permutation networks

Example SPN

Attacks on SPNs

CM30173:
Cryptography

Part II

Outline

Combining basic
building blocks

Substitution-
permutation
networks

Example SPN

Attacks on SPNs

Outline

Combining basic building blocks

Substitution-permutation networks

Example SPN

Attacks on SPNs

CM30173:
Cryptography

Part II

Outline

Combining basic
building blocks

Substitution-
permutation
networks

Example SPN

Attacks on SPNs

Recall Alice and Bob

Alice Bob

Oscar

PlaintextPlaintext

Encryption Decryption

Unsecured channel
ek(x) = y dk(y) = x

CM30173:
Cryptography

Part II

Outline

Combining basic
building blocks

Substitution-
permutation
networks

Example SPN

Attacks on SPNs

Private-key cryptosystems

Alice Bob

Oscar

PlaintextPlaintext

Encryption Decryption

Unsecured channel

Secure channel

ek(x) = y dk(y) = x

k

k

xx

Key source

CM30173:
Cryptography

Part II

Outline

Combining basic
building blocks

Substitution-
permutation
networks

Example SPN

Attacks on SPNs

Private-key cryptography: Block ciphers

1 Combining basic components

2 Substitution-permutation networks

3 Attacks on substitution-permutation networks

4 The Data Encryption Standard (DES)

5 Modes of operation

6 After DES: 3DES and the Advanced Encryption
Standard (AES)

CM30173:
Cryptography

Part II

Outline

Combining basic
building blocks

Substitution-
permutation
networks

Example SPN

Attacks on SPNs

Outline

Combining basic building blocks

Substitution-permutation networks

Example SPN

Attacks on SPNs

CM30173
Cryptography

Useful information

Course outline

Confusion and Di↵usion

According to Claude Shannon, an ideal cipher should
satisfy:

Confusion The relationship between the key and
the ciphertext is as complex as possible.

Di↵usion The structure of the plaintext is
dissipated over the entire ciphertext.

More precisely (the strict avalanche criterion):

Confusion Flipping any fixed set of key bits causes
the ith bit of ciphertext to change with probability
0.5.

Di↵usion Flipping any fixed set of plaintext bits
causes the ith bit of ciphertext to change with
probability 0.5.

CM30173
Cryptography

Useful information

Course outline

Confusion and Di↵usion

According to Claude Shannon, an ideal cipher should
satisfy:

Confusion The relationship between the key and
the ciphertext is as complex as possible.

Di↵usion The structure of the plaintext is
dissipated over the entire ciphertext.

More precisely (the strict avalanche criterion):

Confusion Flipping any fixed set of key bits causes
the ith bit of ciphertext to change with probability
0.5.

Di↵usion Flipping any fixed set of plaintext bits
causes the ith bit of ciphertext to change with
probability 0.5.

CM30173:
Cryptography

Part II

Outline

Combining basic
building blocks

Substitution-
permutation
networks

Example SPN

Attacks on SPNs

Basic components

We already have some basic components…

Substitution to provide confusion.

CM30173:
Cryptography

Part II

Outline

Combining basic
building blocks

Substitution-
permutation
networks

Example SPN

Attacks on SPNs

Basic components

We already have some basic components…

Substitution to provide confusion.

Permutation to provide di!usion.

CM30173:
Cryptography

Part II

Outline

Combining basic
building blocks

Substitution-
permutation
networks

Example SPN

Attacks on SPNs

Basic components

We already have some basic components…

Substitution to provide confusion.

Permutation to provide di!usion.

Other components might include: x-or, linear
transformations, arithmetic operations, modular
multiplication

CM30173:
Cryptography

Part II

Outline

Combining basic
building blocks

Substitution-
permutation
networks

Example SPN

Attacks on SPNs

Combining components

Definition (Product cipher)

A product cipher combines two or more components
with the intention of producing a cipher that is more
secure than the basic parts of which it is made.

CM30173:
Cryptography

Part II

Outline

Combining basic
building blocks

Substitution-
permutation
networks

Example SPN

Attacks on SPNs

Example product cipher

Let P = C = K = (Z2)
m and for k1, k2 ! K we have

encryption functions:

e
(1)
k1

(x) = x ” k1

e
(2)
k2

(x) = permutation of the bits of x

(Decryption functions are the obvious inverse
operations).

CM30173:
Cryptography

Part II

Outline

Combining basic
building blocks

Substitution-
permutation
networks

Example SPN

Attacks on SPNs

Example product cipher

Cryptosystem (Product)

Our product cryptosystem is then (P, C,K #K, E ,D).

For each key (k1, k2) in the keyspace we have a member
of the set E of encryption functions:

e(k1,k2)(x) = e
(2)
k2

(e
(1)
k1

(x))

and a member of the set D:

d(k1,k2)(y) = d
(1)
k1

(d
(2)
k2

(y))

CM30173:
Cryptography

Part II

Outline

Combining basic
building blocks

Substitution-
permutation
networks

Example SPN

Attacks on SPNs

Iterated ciphers

Definition (Iterated block cipher)

An iterated block cipher is a block cipher is made up
from:

A key schedule of Nr round keys:
(k1, k2, . . . , kNr), derived, using a fixed public
algorithm, from the key k.

A round function f which takes a round key and
a current state

The encryption (and decryption) functions consist of
repetition of the round function Nr times.

Private-key cryptography: block ciphers
Outline
Combining basic building blocks
Substitution-permutation networks
Example SPN

Attacks on SPNs