Lecture 1 INTRODUCTION TO CRYPTOGRAPHY

AI and Robotics

Nov 21, 2013 (4 years and 7 months ago)

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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

-

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
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".

4

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.

6

Secret Key Cryptography or Symmetric Cryptography

-

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