# Cryptography

Τεχνίτη Νοημοσύνη και Ρομποτική

21 Νοε 2013 (πριν από 4 χρόνια και 5 μήνες)

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Cryptography

Jill Tolentino

Introduction

Cryptography in Greek means “secret writing.”

Today, it refers to the science and art of transforming
messages to make them secure and immune to attacks.

Cryptography is used to achieve:

confidentiality .............. only authorized persons can access information

integrity ...................... information that was sent is what was received

authentication ............. guarantee of originator and of electronic
transmission

non
-
repudiation ........... originator of information cannot deny content or
transmission

Cryptography components

Original message is called
plaintext.

An
encryption algorithm

transforms the plaintext to
ciphertext
.

A
decryption algorithm

tranforms the ciphertext back to
plaintext.

Sender uses an encryption
a decryption algorithm.

Encryption and Decryption

An encryption/decryption
algorithm is referred to as
ciphers
.

Through the use of public
ciphers with secret keys, one
cipher can serve millions of
communicating pairs.

A
key

is a number (value) that
the cipher, as an algorithm,
operates on.

The encryption and decryption
algorithms are public; the keys
are secret.

Cryptography

Cryptography algorithms are divided into
two groups:

Symmetric
-
key (secret
-
key) cryptography
algorithms

Public
-
key(asymmetric) cryptography algorithms

Symmetric
-
key Cryptography

The same key is shared and used by
the sender and receiver to encrypt
and decrypt the message.

The decryption algorithm is the
inverse of the encryption algorithm.

Example: If encryption algorithm
uses a combination of addition and
multiplication, the decryption
algorithm uses a combination of
division and subtraction.

Symmetric
-
key Cryptography

Efficient
-

takes less time to encrypt a
message using a symmetric
-
key algorithm
than a public
-
key algorithm.

Key is smaller

Can encrypt and decrypt long messages

Symmetric
-
key Cryptography

Each pair of users must have a unique
symmetric key.
This means if N people in the world want to
use this method, there needs to be N(N
-
1)/2 symmetric keys. For
example, for 1 million people to communicate, 500 billion symmetric
keys are needed.

Distribution of the keys between two parties
can be difficult.

Symmetric
-
key Cryptography

Traditional ciphers use a character or symbol as the unit of
encryption/decryption.

Block ciphers use a block of bits as the unit of
encryption/decryption.

Traditional ciphers involve either substitution or
transposition.

Substitution Cipher

bit
-
level encryption method in which n bits
substitute for another n bits as defined by P
-
boxes, encoders, and
decoders.

Transposition Cipher

A character
-
level encryption method in
which the position of the character changes.

Examples:

Public
-
key Cryptography

There are two keys:
a private key and a
public key.

The sender uses the
public key to
encrypt the
message and the
private key to
decrypt the
message.

Public
-
key Cryptography

More efficient for short messages.

Removes the restriction of a shared symmetric key
between two entities.

Each entity is independent, and the pair of keys
created can be used to communicate with any
other entity.

Number of keys needed is reduced: For 1 million
users to communicate, only 2 million keys are
needed, not 500 billion, as in symmetric
-
key
cryptography.

Public
-
key Cryptography

:

Complexity of the algorithm…the algorithm needs
large numbers to be effective.

Association between entity and its public key,
must be verified. (Can be overcome using a
certification authority)

Public
-
key Cryptography

The most common public
-
key algorithm is
called the RSA method after its inventors

The sender uses the following algorithm to
encrypt the message: C=P
e
mod N

The receiver uses the following algorithm to
decrypt the message: P=C
d
mod N

Example: