1
Lecture 1
INTRODUCTION
TO CRYPTOGRAPHY
Classic Definition of Cryptography
Cryptography
, or the art of "
hidden writing
", classically meant hiding the
contents or existence of messages from an adversary.
Steganography
,
or "
covered writing
"
,
is
concerned with hiding the existence
of a message

often in plain sight.
CRYPTOGRAPHY

science of information security

science of communicating and computing in the presence of an
adversary

derived from the Greek
kryptos
, meaning
hidden

before, it i
ncludes techniques such as microdots, merging words with
images

now, it is most often associated with scrambling
plaintext
(ordinary
text) into
ciphertext
(known as
encryption
) then back again (known as
decryption
) to plaintext

individuals who practice this field are known as
cryptographers
CRYPTANALYSIS

refers to the study of ciphers,
ciphertext
, or cryptosystems with a view
to finding weaknesses in them that will permit retrieval of the
plaintext
from the ciphertext, without necessarily knowing the
key
or the
2
algorithm
. This is known as
breaking
the cipher
,
ciphertext
, or
cryptosystem

relies on a knowledge of the encryption algorithm (that for civilian
applications should be in the public domain) and some knowledge of
the possible s
tructure of the plaintext (such as the structure of a
typical interbank financial transaction) for a partial or full
reconstruction of the plaintext from ciphertext

additionally, the goal is to also infer the key for decryption of future
messages.
The pre
cise methods used for cryptanalysis depend on whether the
“attacker” has just a piece of ciphertext, or pairs of plaintext and ciphertext,
how much structure is possessed by the plaintext, and how much of that
structure is known to the attacker.
All forms
of cryptanalysis for classical encryption exploit the fact that some
aspect of the structure of plaintext may survive in the ciphertext.
CRYPTOLOGY
is a science which incorporates both
cryptograph
y
and
cryptanalysis
.
CRYPTOLOGY
is the mathematics, such as number theory, and the
application of formulas and
algorithm
s, that add force to
cryptography
and
cryptanalysis
.
Brute force attack

when encryption and decryption algorithms are publicly available, as
they generally are, a brute

force attack means trying every possible
key on a piece of ciphertext until an intelligible transla
tion into
plaintext is obtained

when the
adversary tests all possible keys and checks which key
decrypts the message,
this assumes we can identify the correct
plaintext among all plaintexts generated by the attack
Example
:
3
Caesar cipher
key space = 26
The adversary tests these 26 keys
and 1 of these keys will give the
correct plaintext
Key space

the total number of all possible keys that can be used in a
cryptographic system

for example,
DES
uses a 56

bit key. So, the key space is of size 2
56
,
which is approximately the same as 7
.
2
×
10
16
STEGANOGRAPHY
Steganography
is the art and science of writing hidden messages in such a
way that no one, apart from the sender and intended recipient, suspects
the existence of the message, a form of
security through obscurity
.
CODES
Codes replace a specific piece of plaintext with a predefined
code word.
Codes are essentially a substitution cipher,
but can
replace strings of
symbols rather than just individual symbols.
Examples:
"One if by land, two if by sea."
Kerckhoffs' Principle
A cryptosystem should be secure even if everything about it is public
knowledge except the secret key.
“Do not re
ly on "security through obscurity".
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CRYPTOGRAPHY: ENCRYPTION & DECRYPTION
Encryption algorithm
:
The sequence of data processing steps that
transform plaintext into ciphertext.
In cryptography for commercial and other civilian applications, the
encryption and decryption algorithms are made public.
Secret key
:
A secret key is used to set some or all of the various
parameters used by the encryption algorithm.
The important thing to note is that, in classical cryptography,
the same
secret key is used for encryption and decryption.
It is for this reason that
classical cryptography is also referred to as
symmetric key cryptography
.
On the other hand, in the more modern cryptographic algorithms,
the
encryption and decryption
keys are not only different, but also one of them
is placed in the public
domain.
Such algorithms are commonly referred to
as
asymmetric key cryptography
.
Decryption algorithm
:
The sequence of data processing steps
that
transform
ciphertext
back into plaintext.
Encryption

the process of transforming plaintext using an algorithm (called
cipher
) to make it unreadable to anyone except those who has the
key to decrypt it.

the pr
ocess by which plaintext is converted into ciphertext
c
=
e
k
(
m
)
where
,
m
is the plaintext
e
is the cipher function (encryption algorithm)
k
is the secret key
5
c
is the ciphertext
Informally,
encryption
makes the contents of a message unintelligible to
anyone not possessing some secret information.
Decryption

the process to make the encrypted information readable again

r
ecovering plaintext from ciphertext
m
=
d
k
(
c
)
where,
d
is the decipher function (decryption algorithm)
Note that
e
is public, the secrecy of
m
given
c
depends totally on the
secrecy of
k.
NOTE:
Usually in cryptography the parties are denoted by:
Alice & Bob
Someone listening is denoted by:
Eve (Eavesdropper)
Cryptographic system

any single scheme for encryption
Cipher

a cipher means the same thing as a “cryptographic system”
Block cipher

a block cipher processes a block of input data at a time and produces
a ciphertext block of the same size
Stream cipher

a stream cipher encrypts data on the fly, usually one
byte at a time.
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Secret Key Cryptography or Symmetric Cryptography

Each communicating party needs access to the
secret key

This needs to
be known to both sides, but needs to be kept secret

This secret key is used for encryption and decryption
Public Key
or Asymmetric
Cryptography

The s
ender encrypts
the plaintext
using a
public key

The r
eceiver decrypts
the ciphertext
using a
private ke
y

T
he private key must be kept secret
, while the p
ubli
c key can be
distributed

It c
an be used for digital
signatures

Examples of public key cryptography:
o
RSA, El Gamal, DSA, various algorithms based on elliptic
curves
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