Dr. Khalid A. Kaabneh Amman Arab University [email protected]

Dr. Khalid A. KaabnehAmman Arab University

[email protected]

04/19/23 © 2004 Dr. Khalid Kaabneh. 2

Encryption Systems Categories:

Symmetric encryption.

Asymmetric encryption.


Symmetric Encryption:

In a symmetric encryption system, both the sender and receiver must possess the same key value. The sender encrypts the plaintext message using the key and the receiver decrypts the cipher-text message using the same secret key.

The word “symmetric" here means that the same key is used for encryption and decryption.





The weaknesses:

• How you securely distribute the key to the needed parties and the fact that the number of keys required for secure pair-wise communication is given by (n2-n)/2 where n is is the number of communication endpoints.

• Symmetric key systems can be unmanageable for more than small groups of communicants.



Block - operates on plaintext input in blocks (usually 64 bits at a time) of bits to produce the ciphertext output; uses the key value to determine how the transformation algorithm is applied.

Stream - operates on plaintext input one bit at a time, often using a keystream generator to produce a series of bits which are XOR'd with the plaintext input.

Two classes of symmetric-key encryption algorithms:


Symmetric Encryption: Examples of Block:

– DES is a block cipher with a 64 bit block size. – AES is a block cipher with a 128 bit block size.– RSA and Diffie-Hellman are block ciphers with

variable block sizes.

Examples of Stream:– A5, the algorithm used to encrypt GSM communications,

is a stream cipher. – The RC4 cipher and the one-time pad are also stream

ciphers.


Stream Ciphers

C = P K, where is XOR Operation.

C K = (P K) K = P ( K K) = P 0 = P

0 1

0 0 1

1 1 0


Stream Ciphers

C = P K, where is XOR Operation.

C K = (P K) K = P ( K K) = P 0 = P

Plaintext 1 0 1 1 0 1 1 0 0

Key 1 1 0 1 0 0 0 1 1

Cipher 0 1 1 0 0 1 1 1 1


Asymmetric Encryption:

Known as "public key" encryption, each entity participating in the communication uses mathematical algorithms implemented in a software program to generate a "public key" and a "private key" which are related via the mathematical formulae. The private key must be kept secret and is never disclosed; this is a requirement for the security system to function. The public key, however, is intended to be freely distributed.


Asymmetric Encryption:


Public key cryptography characteristics:

Something encrypted with the public key can only be decrypted with the private key.

Something encrypted with the private key can only be decrypted with the public key.


Symmetric-key vs.

Public-key cryptography


Advantages of symmetric-key

Have high rates of data throughput . Keys for symmetric-key ciphers are

relatively short. Symmetric-key ciphers can be composed to

produce stronger ciphers.


Disadvantages of symmetric-key

In a two-party communication, the key must remain secret at both ends.

In a large network, there are many key pairs to be managed.

Digital signature mechanisms arising from symmetric-key encryption.


Advantages of Public-key

Only the private key must be kept secret. Depending on the mode of usage, a private

key/public key pair may remain unchanged for considerable periods of time.

Many public-key schemes yield relatively efficient digital signature mechanisms.


Disadvantages of Public-key

Slower than the best known symmetric-key schemes.

Key sizes are typically much larger. No public-key scheme has been proven to

be secure.


Symmetric Encryption Techniques

S-DES DES


Simplified DES

DES = Data Encryption Standard. Educational tool (not secure) 8-bit block cipher 10-bit key


Simplified DES

Encryption involves these Steps: IP = Initial Permutations. fk1 = complex function. SW = Switch the two halves. fk2 = complex function. IP-1 = inverse Permutation.


S-DES Details:

P10 = (3,5,2,7,4,10,1,9,8,6). P8 = (6,3,7,4,8,5,10,9). IP = (2,6,3,1,4,8,5,7). IP-1 =(4,1,3,5,7,2,8,6).


S-DES Details: (S0 Box)

S0

C0 C1 C2 C3

R0 1 0 3 2

R1 3 2 1 0

R2 0 2 1 3

R3 3 1 3 2


S-DES Details: (S1 Box)

S1

C0 C1 C2 C3

R0 0 1 2 3

R1 2 0 1 3

R2 3 0 1 0

R3 2 1 0 3


S-box Operation

(1) First and fourth bits give row number. (2) Second and third bits give column number. (3) Look up number in specified row and column. (4) Convert to binary.


SUBKEY GENERATION


SUBKEY GENERATION

Apply the P10 operation on the 10 bit input. Apply LS-1 (left shift 1) to each 5-bit

group. Apply permutation P8 K1. Apply LS-2 (left shift 2) to each 5-bit

group. K2.


S-DES


S-DES Example:

let K = 1010000010

Step (1): 10000|01100

Step (2): 00001|11000

Step (3): Apply permutation P8then K1 = 10100100

Step (4): Apply LS-2 (left shift 2)

00001 | 11000 LS2 00100 | 00011 P8 K2 = 01000011


S-DES Example:

let plaintext: 01101101

IP

1110 | 0110

IP = (2,6,3,1,4,8,5,7)

E/PApply expansion/permutation

E/P To right 4 bits of above result,

= 4 1 2 3 2 3 4 1

00111100


Perform binary XOR operation withsub key K1: 10100100

XOR

1001 | 1000From above:

For the row, combine bits 1 and 4 and convert to decimal.For the column, combine bits 2 and 3 and convert to decimal.

Left Side:

bits 1 & 4 11 Row: 3bits 2 & 3 00 Col: 0

therefore, get from S0 R3 & C0 3 11Right Side:

bits 1 & 4 10 Row: 2bits 2 & 3 00 Col: 0

therefore, get from S1 R2 & C0 3 11


S0 & S1

1111

P4 P4 = (2,4,3,1)

1111Perform binary XOR operation, combining it with the left 4-bits of our first result (application of IP to original plaintext input, blue cell above).

Result:

0001


Rewrite that first result with its left half replaced.

0001 | 0110Swap the two 4-bit halves of the above result.

0110 | 0001To right 4 bits of above, apply E/P

10000010Upon above result, perform binary XOR operation with sub-key K2: 01000011

11000001


From above:For the row, combine bits 1 and 4 and convert to decimal.

For the column, combine bits 2 and 3 and convert to decimal.

Left Side:

bits 1 & 4 10 Row: 2bits 2 & 3 10 Col: 2


Right Side:

bits 1 & 4 01 Row: 1bits 2 & 3 00 Col: 0


1100 | 0001


0110

P4 P4 = (2,4,3,1)

1010Perform binary XOR operation with the left 4-bits of the earlier swap result (0110).

1100Rewrite that first result with its left half replaced.

11000001


11000001

To above result, apply reverse of initial permutation

IP, which is IP-1 =(4,1,3,5,7,2,8,6).

Ciphertextis

01000110


How can we decrypt a ciphertext???

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Dr. Khalid A. Kaabneh Amman Arab University [email protected]