Cryptography: Principles, Techniques, and Applications, Slides of Digital Communication Systems

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Encryption and Decryption

Unit - V

Security Goals

 Consider the following security risks that could face two

communicating entities in an unprotected environment:

A B

C could view the secret message by eavesdropping on the communication. Loss of privacy / confidentiality

C

(1)^ m

A m B

A might repudiate having sent m to B

Hence, some possible goals for communication:

• Privacy/confidentiality - information not disclosed to unauthorized entities
• Integrity - information not altered deliberately or accidentally
• Authentication - validation of identity of source of information
• Non-repudiation – Sender should not be able to deny sending a message

(4)

What is Cryptography

 Cryptography is the study of mathematical techniques related

to aspects of information security such as confidentiality, data

integrity, authentication, and non-repudiation.

Attack classification

(encryption)

(key)

C

P

 Ciphertext Alone attack: The attacker has available only the

intercepted cryptogram C.

From C , try to find P or (even better) the key.

Attack classification

 Known Plaintext attack: The attacker knows a small amount of

plaintext (Pi) and its ciphertext Equivalent (Ci).

(encryption)

(key)

Ci

Pi

Ci+

Pi+

Attacker tries to find key or to infer Pi+1 (next plaintext)

Forms of Cryptosystems

• Private Key (symmetric) :
  • A single key ( K ) is used for both encryption and decryption and must

be kept secret.

• Key distribution problem a secure channel is needed to transmit the

key before secure communication can take place over an unsecure

channel.

(encryption)

( K )

C M (decryption) M

Sender Receiver

( K )

E K (M) = C D K (C) = M

Forms of Cryptosystems

• Public Key (asymmetric):
  • The encryption procedure (key) is public while the decryption procedure (key) is private.
  • Each participant has a public key and a private key.
  • May allow for both encryption of messages and creation of digital signatures.

Combining Public/Private Key Systems

• Public key encryption is more expensive than symmetric key encryption
• For efficiency, combine the two approaches
  1. Use public key encryption for authentication; once authenticated, transfer a shared secret symmetric key
  2. Use symmetric key for encrypting subsequent data transmissions

A (2) B

Rivest Shamir Adelman (RSA) Method

 Named after the designers: Rivest, Shamir, and Adleman

 Public-key cryptosystem and digital signature scheme.

 Based on difficulty of factoring large integers

 For large primes p & q, n = pq  Public key e and private key d calculated

Rivest Shamir Adelman (RSA) Method

Assume A wants to send something confidentially to B:

• A takes M, computes C = Me^ mod n, where (e, n) is B’s public key. Sends C to B
• B takes C, finds M = Cd^ mod n, where (d, n) is B’s private key

A

M e^ mod n C d^ mod^ n

Encryption Key for user B

(B’s Public Key)

Decryption Key for user B

(B’s PrivateKey)

C

( e, n ) ( d, n )

B

M M

+ Confidentiality

RSA Method

Example:

1. p = 5, q = 11 and n = 55. (p1)x(q1) = 4 x 10 = 40
2. A valid d is 23 since GCD(40, 23) = 1
3. Then e = 7 since: 23 x 7 = 161 modulo 40 = 1

in other words

e = 23-1^ (mod 40) = 7

Digital Signatures (Public Key)

• Public Key System:

sender, A: (EA : public, DA : private)

receiver, B: (EB : public, DB : private)

• A signs the message m using its private key, the result is then encrypted

with B’s public key, and the resulting ciphertext is sent to B:

• C= EB (DA (M))
• B receives ciphertext C decrypts it using its private key, the result is then

encrypted with the senders public key (A’s public key) and the message m

is retrieved.

• M = EA (DB (C))

Hashing

• A one-way hash function h is a public function h (which should be simple and fast to compute) that satisfies three properties:
• A message m of arbitrary length must be able to be converted into a message digest h(m) of fixed length.
• It must be one-way, that is given y = h(m) it must be computationally infeasible to find m.
• It must be collision free, that is it should be computationally infeasible to find m and m2 such that h(m1) = h(m2).

Examples: MD5 , SHA-