Author : Prof Bill Buchanan · Author : Prof Bill Buchanan RC 2 . RC 2 . RC 2 (" Rivest Cipher ")...

Author: Prof Bill Buchanan

Advanced

CryptoAlice

2. Public key, private key and key exchange.

http://asecuritysite.com/crypto

Key Entropy. Key generators. Private key (AES, Twofish, CAST, IDEA, Blowfish, DES, 3DES, RC2, RC4/RC5, Skipjack, Camellia, Affine). Stream or block? ECB/CBC/OFB. Salting. Public key (RSA, DSA, ElGamal). Elliptic curve. Diffie-Hellman. FIPS.

ion Trusted third party

Intruder

Privacy (Private Key)

Identity (Public Key)

Integrity (Public/Private Key)

Encryption/

Decryption

Public key

Private key Public key

Private keyUsed to authenticate (RSA)

Key exchange (Diffie-Hellman)

Secret key used to encrypt/decrypt

(DES/3DES/AES)

Communications

Channel

Encryption/

Decryption

Encryption/

Decryption

BobAlice

Public key

Private key Public key

Private key

Typical application:

Diffie-Hellman used to generate private-key.

Public-key used for authentication.

Private-key used for encryption.

Used to authenticate (RSA)

Key exchange (Diffie-Hellman)

Secret key used to encrypt/decrypt

(DES/3DES/AES)

RSA 2048 bits

Replace by:

ElGamal 160bits

Advanced

CryptoAlice

Block or stream?

RC4. This is a stream encryption algorithm, and is used in wireless

communications (such as in WEP) and SSL (Secure Sockets).

RC4IV and

Data stream

(eg 0101010 …. 010)

Pseudo infinite stream

(eg 1110000 … 100)

The IV (Initiation Vector)

gives variation in the

output for the same key

Cipher stream

(eg 1010110 … 110)

Data stream 0101010 … 010

Pseudo infinite stream 1110000 … 100

Cipher stream 1010110 … 110

Ex-OR operator

Advanced

CryptoAlice

Private Key

RC2. RC2. RC2 ("Rivest Cipher") is

a block cipher, and is seen as a

replacement for DES. It was created

by Ron Rivest in 1987, and is a 64-

bit block code and can have a key

size from 40 bits to 128-bits (in

increments of 8 bits). The 40-bit key

version is seen as weak, as the

encryption key is so small, but is

favoured by governments for export

purposes, as it can be easily

cracked. In this case the key is

created from a Key and an IV

(Initialisation Vector). The key has

12 characters (96 bits), and the IV

has 8 characters (64 bits), which go

to make the overall key.

DES. DES encryption algorithm is

block cipher and uses a 64-bit block

and a 64-bit encryption key.

3DES. DES encryption algorithm is

block cipher and uses a 64-bit block

and a 64-bit encryption key (of which

only 56 bits are actively used in the

encryption process). Unfortunately

DES has been around for a long

time, and the 56-bit version is now

easily crackable (in less than a day,

on fairly modest equipment). An

enhancement, and one which is still

fairly compatible with DES, is the 3-

DES algorithm. It has three phases,

and splits the key into two. Overall

the key size is typically 112 bits

(2x54 bits - with a combination of the

three keys - of which two of the keys

are typically the same). The

algorithm is EncryptK3( DecryptK2(

EncryptK1(message), where K1 and

K3 are typically the same (to keep

compatibility).

Bruce Schneier created Twofish with

a general-purpose private key block

cipher encryption algorithm.

AES. AES (or Rijndael) is a new

block cipher, and is the new

replacement for DES, and uses 128-

bit blocks with 128, 192 and 256 bit

encryption keys. It was selected by

NIST in 2001 (after a five year

standardisation process). The name

Rijndael comes from its Belgium

creators: Joan Daemen and Vincent

Rijmen.

Blowfish

Blowfish. Bruce Schneier created

Blowfish with a general-purpose

private key block cipher encryption

algorithm.

Blowfish (with CBC). Blowfishcbc.

With CBC we split the message into

blocks and encrypt each block. The

input from the first stage is the IV

(Initialisation Vector), and the input

to the following stages is the output

from the previous stage. In this

example we will use Blowfish to

encrypt, using CBC.

Twofish

Skipjack. Skip jack. Skipjack is a

block cipher, using private-key

encryption algorithm, and

designed by NSA.

Camellia. Camillia is a block

cipher created by Mitsubishi and

RC4. RC4 is a stream cipher

used in WEP (in wireless

encryption).

Affine. Affine is a stream cipher

which uses an equation to

encrypt.

Others

Advanced

CryptoAlice

Key Exchange

BobAlice

(Ax)y Axy

A(x+y)

BobAlice

Private key

yx AAgreed number

Random value Random value

BobAlice

yx AAgreed number

Random value Random value

(AY)x (Ax)y

Advanced

CryptoAlice

Public Key

Select two primes (p,q)

Next, the n value is calculated. Thus:

n = p x q = 11 x 3 = 33

Next PHI is calculated by:

PHI = (p-1)(q-1) = 20

e selected so that GCD(e,PHI)=1

Public key: (n,e)

Bob Select two prime numbers: a and b

n = a x b

e is chosen so that e and (a-1)x(b-1)

are relatively prime (no common

factor greater than 1)

Public key is now: <e,n>

d = e-1 mod [(a-1)x(b-1)]

Private key is now: <d,n>

Generating public and private keys

Public key are keys which

relate to extremely large prime

numbers (as it is difficult to

factorise large prime

numbers). It is extremely

difficult to determine a private

key from a public key.

Public-key

Communications

ChannelEncryption Decryption

BobAlice

Public key

Private key

Public key

Private key

Public key generates two keys: A

public key and a private one. These are

special in that if one is applied to encrypt,

the other can be used to decrypt

Once Bob encrypts the

message, the only key

which can decrypt it is

Alice’s private key.

Bob and Alice keep their

private keys secret.

Public-key

Communications

ChannelEncryption Decryption

BobAlice

Public key

Private key

Public key

Private key

A. Bob creates the message.

B. Bob encrypts with Alice’s public key

and sends Alice the encrypted message

C. Alice decrypts with her private key

D. Alice receives the message

Using Bob’s private key to authenticate himself

Message

Encrypted

Bob’s

private

Bob’s

public

Bob encrypts the message/hash with Alice’s public key

Message

Encrypted

Bob’s

private

Bob’s

public

Alice’s

private

Alice’s

public

Encrypted

Content

Bob encrypts the message/hash with Alice’s public key

Message

Encrypted

Bob’s

private

Bob’s

public

Alice’s

private

Alice’s

public

Encrypted

Content

Encrypted

Content

Alice decrypts the message

Message

Encrypted

Bob’s

private

Bob’s

public

Alice’s

private

Alice’s

public

Encrypted

Content

Encrypted

Content

Message

Encrypted

Alice decrypts the message

Message

Encrypted

Bob’s

private

Bob’s

public

Encrypted

Content

Encrypted

Content

Message

Encrypted

MD5 (message)

MD5 (result)Alice compares the MD5

values. If they are the

same … Bob sent the

message

Advanced

CryptoAlice

Key Entropy. Key generators. Private key (AES, Twofish, CAST, IDEA, Blowfish, DES, 3DES, RC2, RC4/RC5, Skipjack, Camellia, Affine). Stream or block? ECB/CBC/OFB. Salting. Public key (RSA, DSA, ElGamal). Elliptic curve. Diffie-Hellman. FIPS.

Discrete logarithms

within computer and

network securityProf Bill Buchanan, Edinburgh Napier

http://asecuritysite.com @billatnapier

Introduction.

Encryption:

Public/Private Key.

Key Exchange.

Authentication.

Signatures.

ElGamal.

AliceTrent

ElGamal

ier’s

g = a.b

log(g) = log(a)+log(b)

g = Inverse Log (log(a)+log(b))

g = a/b

log(g) = log(a)-log(b)

g = Inverse Log (log(a)-log(b))

g = ax

log(g) = x.log(a)

g = Inverse Log (x.log(a))

g = 103

log10(g) = 3.log10(10)

g = 10(3x1)

= 1,000

g = ax mod P

For example:

a=5, x=3, P=7

g = 53 mod 7

= 125 mod 7

Y = gx mod p

Extremely difficult to the value

of x, and there can be many

solutions

Y = 34 mod 17 -> 13

Y = gx mod p

First Bob generates a prime number (p) and a number (g) which

is between 1 and (p-1):

Bob select a random number (x) which will be his private key:

Bob selects a random number(x):

He then calculates Y:

Bob sends g, p and Y to Alice. x

AliceJohn

M (message)

K (random)

a=gk mod P

b=yk M mod P

Author : Prof Bill Buchanan · Author : Prof Bill Buchanan RC 2 . RC 2 . RC 2 (" Rivest Cipher ")...

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