•
Definition
–
Let
K
be the key space for a set of encryption transformations
–
A sequence of symbols e
1
e
2
e
3
. . . e
i
ϵ
K
, is called a
keystream
•
Definition
–
Let
A
be an alphabet of q symbols and let
E
e
be a simple
substitution cipher with block length 1 where e
ϵ
K
.
–
Let m
1
m
2
m
3
be a plaintext string and
–
let
e
1
e
2
e
3
be a keystream from
K
.
–
A
stream cipher
takes the plaintext string and produces a
ciphertext string c
1
c
2
c
3
where c
i
=
E
ei
(m
i
).
–
If d
i
denotes the inverse of e
i
, then
D
di
(c
i
) = m
i
decrypts the
ciphertext string.
95

Cont.
•
A stream cipher applies simple encryption
transformations according to the keystream being
used.
•
keystream generator
.
–
The keystream is generated by an algorithm which generates
the keystream from an initial
seed
value
96

The Vernam cipher
•
Definition
–
The
Vernam Cipher
is a stream cipher defined on the
alphabet A = {0, 1}.
–
A binary message m
1
m
2
. . . m
t
is operated on by a binary
key string k
1
k
2
. . . k
t
of the same length to produce a
ciphertext string c
1
c
2
. . .
c
t
where
c
i
= m
i
Xor k
i
1
≤
i
≤
t:
•
one-time system
or a
one-time pad
–
If the key string is randomly chosen and never used again
97

The key space
•
Size of the key space
–
It is the number of encryption/decryption key pairs that are
available in the cipher system.
•
A key is a compact way to specify the encryption
transformation (from the set of all encryption
transformations) to be used
–
For example, a transposition cipher of block length t has t!
encryption functions from which to select.
98

Cont.
•
Fact:
A necessary, but usually not sufficient, condition
for an encryption scheme to be secure is that the key
space be large enough to prevent exhaustive search.
•
For instance,
–
the simple substitution cipher in
slide 61
has a key space of
size 26! = 4 x 10
26
–
The polyalphabetic substitution cipher of has a key space of
size (26!)
3
= 7 x 10
79
.
–
Exhaustive search of either key space is completely
infeasible, yet both ciphers are relatively weak and provide
little security.
99

Digital signatures
•
A cryptographic primitive which is fundamental in
–
authentication,
–
authorization, and
–
nonrepudiation
•
Purpose
–
to provide a means for an entity to bind its identity to a piece
of information.
•
Process of
signing
transforming the message and some
secret information held by the entity into a tag called a
signature
.
100

A signing and verification function for a digital
signature scheme.
•
Setup
–
M
is the set of messages which can be signed.
–
S
is a set of elements called
signatures
, possibly binary strings
of a fixed length.
–
S
A
is a
signing transformation for entity A
from the message
set
M
to the signature set
S
.

#### You've reached the end of your free preview.

Want to read all 183 pages?

- Summer '19
- Cryptography, Alice