1. Chapter 3
Public Key Cryptography and Message authentication.

2. Introduction Approaches to message authentication
Public key cryptography principles
Public key cryptography algorithms
Digital signatures

3. Block vs Stream Ciphers
block ciphers process messages in into blocks, each of which is then en/decrypted
like a substitution on very big characters
64-bits or more
stream ciphers process messages a bit or byte at a time when en/decrypting
many current ciphers are block ciphers
hence are focus of course
Block ciphers work a on block / word at a time, which is some number of bits. All of these bits have to be available before the block can be processed. Stream ciphers work on a bit or byte of the message at a time, hence process it as a “stream”.

4. Authentication Requirements - must be able to verify that:
1. Message came from apparent source or author,
2. Contents have not been altered,
3. Sometimes, it was sent at a certain time or sequence.
Protection against active attack (falsification of data and transactions)

5. Approaches to Message Authentication
Authentication Using Conventional Encryption
Only the sender and receiver should share a key
Message Authentication without Message Encryption
An authentication tag is generated and appended to each message
Message Authentication Code
Calculate the MAC as a function of the message and the key. MAC = F(K, M)

6. MAC

7. One way HASH function

8. One-way HASH function
Secret value is added before the hash and removed before transmission.

9. Secure HASH functions
Purpose of the HASH function is to produce a ”fingerprint.
Properties of a HASH function H :
H can be applied to a block of data at any size
H produces a fixed length output
H(x) is easy to compute for any given x.
For any given block x, it is computationally infeasible to find x such that H(x) = h
For any given block x, it is computationally infeasible to find with H(y) = H(x).
It is computationally infeasible to find any pair (x, y) such that H(x) = H(y)

10. Simple HASH function
One-bit circular shift on the hash value after each block is processed would improve

12. Public-key cryptography principles
A public-key encryption scheme has 6 ingredients
Plaintext: This is readable message or data that is fed into the algorithm
as input
Encryption algorithm: The encryption algorithm performs various transformation on the plain text
Public and private key: pair of keys that have been selected where one is used for encryption and other is decryption.
Ciphertext: scrambled message produced as output
Decryption algorithm: accepts ciphertext and matching key and produces the original plain text

13. Public key Cryptography

14. Applications for Public-Key Cryptosystems
Three categories:
Encryption/decryption: The sender encrypts a message with the recipient’s public key.
Digital signature: The sender ”signs” a message with its private key.
Key echange: Two sides cooperate two exhange a session key.

15. Requirements for Public-Key Cryptography
Computationally easy for a party B to generate a pair (public key KUb, private key KRb)
Easy for sender to generate ciphertext:
Easy for the receiver to decrypt ciphertect using private key:

16. Requirements for Public-Key Cryptography
Computationally infeasible to determine private key (KRb) knowing public key (KUb)
Computationally infeasible to recover message M, knowing KUb and ciphertext C
Either of the two keys can be used for encryption, with the other used for decryption:

17. Public-Key Cryptographic Algorithms
RSA and Diffie-Hellman
RSA - Ron Rives, Adi Shamir and Len Adleman at MIT, in 1977.
RSA is a block cipher
The most widely implemented
Diffie-Hellman
Echange a secret key securely
Compute discrete logarithms

18. The RSA Algorithm – Key Generation
Select p,q p and q both prime
Calculate n = p x q
Calculate
Select integer e
Calculate d
Public Key KU = {e,n}
Private key KR = {d,n}

19. Example of RSA Algorithm

20. The RSA Algorithm - Encryption
Plaintext: M<n
Ciphertext: C = Me (mod n)

21. The RSA Algorithm - Decryption
Ciphertext: C
Plaintext: M = Cd (mod n)

22. Other Public-Key Cryptographic Algorithms
Digital Signature Standard (DSS)
Makes use of the SHA-1
Not for encryption or key echange
Elliptic-Curve Cryptography (ECC)
Good for smaller bit size
Low confidence level, compared with RSA
Very complex

23. Digital signatures
Bob wants to send a message to alice and wants to maintain secret.
Bob has private key and no one could have created a cipher text that could be decrypted bob’s public key.
This is not possible to alter the message without access.
This emphasis that the encryption process just described does not provide confidentiality.
Even in this case of complete encryption, there is no protection of confidentiality because any observer can decrypt the message by using the sender’s public key.

24. Key management Public key certificates:
A certificate consists of a public key + a user id of the key owner, with the whole block singed by a trusted third party.
The third party should be a government agency or financial institution
Public key distribution of secret keys
Sharing a secret key between 2 parties is the conventional method to share the information

25. Key Management Public-Key Certificate Uses