PULIC –KEY CRYPTOGRAPHY AND MESSAGE AUTHENTICATION

Approaches to message Authentication Secure Hash Functions and HMAC Public – Key Cryptography Principles Public – Key Cryptography Algorithms 2NETWORK SECURITY By: Homera Durani

Approaches To Message Authentication Confidentiality – protection from passive attacks Authentication – you are who you say you are Integrity – received as sent, no modifications, insertions, shuffling or replays 3NETWORK SECURITY By: Homera Durani

Security Attacks Message authentication helps prevents these Protection against attacks is known as message authentication. MasqueradeDenial of service Active threats ReplayModification of message contents 4NETWORK SECURITY By: Homera Durani

What is Message Authentication It’s the “source,” of course! Procedure that allows communicating parties to verify that received messages are authentic Characteristics: source is authentic – masquerading contents unaltered – message modification timely sequencing – replay 5NETWORK SECURITY By: Homera Durani

Use of Conventional Encryption? Only sender and receiver share a key Include a time stamp Include error detection code and sequence number 6NETWORK SECURITY By: Homera Durani

Message Authentication without Confidentiality Application that broadcasts a message – only one destination needs to monitor for authentication Too heavy a load to decrypt – random authentication checking, messages are chosen at random for checking. Computer executables and files – checked when assurance required. 7NETWORK SECURITY By: Homera Durani

Life Without Authentication 8NETWORK SECURITY By: Homera Durani

Message Authentication Code Message Authentication Code (MAC) – use a secret key to generate a small block of data that is appended to the message Assume: A and B share a common secret key K AB MAC M = F(K AB,M) 9NETWORK SECURITY By: Homera Durani

10NETWORK SECURITY By: Homera Durani

Receiver assured that message is not altered – no modification Receiver assured that the message is from the alleged sender – no masquerading Include a sequence number, assured proper sequence – no replay 11NETWORK SECURITY By: Homera Durani

DES is used Need not be reversible Checksum Stands up to attack But there is an alternative... 12NETWORK SECURITY By: Homera Durani

One Way Hash Function Hash function accepts a variable size message M as input and produces a fixed-size message digest H(M) as output No secret key as input Message digest is sent with the message for authentication Produces a fingerprint of the message 13NETWORK SECURITY By: Homera Durani

Message digest H(M)Shared key Authenticity is assured 14NETWORK SECURITY By: Homera Durani

Digital signatureNo key distribution Less computation since message does not have to be encrypted 15NETWORK SECURITY By: Homera Durani

Encryption software is slow Encryption hardware costs aren’t cheap Hardware optimized toward large data sizes Algorithms covered by patents Algorithms subject to export control Thus ONE AVOID ENCRYPTION 16NETWORK SECURITY By: Homera Durani

No encryption for message authentication Secret value never sent; can’t modify the message Important technique for Digital Signatures Assumes secret value S AB MD M = H(S AB ||M) MD M ||M 17NETWORK SECURITY By: Homera Durani

18NETWORK SECURITY By: Homera Durani

HASH Function Requirements The purpose of a hash function is to produce a “fingerprint” of a file, message, or other block of data, a hash function H must have the following properties: 1. H can be applied to a block of data at any size 2. H produces a fixed length output 3. H(x) is easy to compute for any given x. 4. For any given block x, it is computationally infeasible to find x such that H(x) = h 5. For any given block x, it is computationally infeasible to find with H(y) = H(x). 6. It is computationally infeasible to find any pair (x, y) such that H(x) = H(y) 19NETWORK SECURITY By: Homera Durani

20NETWORK SECURITY By: Homera Durani

One of the simplest hash functions is the bit – by – bit exclusive OR(XOR) of every block which can be expressed as follows: Ci= bi1 ⊕ bi2 ⊕ … ⊕ bim. Where Ci= ith bit of the hash code, 1<= i<= n M = number of n- bit blocks in the input. Bij = ith bit in jth block ⊕ = XOR operation 21NETWORK SECURITY By: Homera Durani

22NETWORK SECURITY By: Homera Durani

A simple way to improve is to perform a one- bit circular shift, or rotation on the hash value after each block is processed. The procedure can be summarized as follows : 1. Initially set the n- bit hash value to zero. 2. Process each successive n – bit block of the data as follows: a. Rotate the current hash value to the left by one bit. b. XOR the block into the hash value. 23NETWORK SECURITY By: Homera Durani

24NETWORK SECURITY By: Homera Durani

SHA (Secure Hash Algorithm ) was developed by the National Institute of Standards and Technology (NIST) and published as a federal information processing standard (FIPS 180) in SHA -1 produces a hash value of 160 bits. In 2002, NIST produced a new version of the standard, FIPS 180-2, defined three new version of SHA with hash value lengths of 256, 384, and 512 bits. Which were known as SHA-256, SHA-384, SHA NETWORK SECURITY By: Homera Durani

Comparison of SHA Parameters. 26NETWORK SECURITY By: Homera Durani

Message Digest Generation Using SHA append padding bits append length compression function output 27NETWORK SECURITY By: Homera Durani

Input is processed in 512-bit blocks Produces as output a 160-bit message digest Every bit of the hash code is a function of every bit of the input 28NETWORK SECURITY By: Homera Durani

29NETWORK SECURITY By: Homera Durani

Other Secure Hash Function Most follow basic structure of SHA-1 This is also called an iterated hash function – Ralph Merkle 1979 If the compression function is collision resistant, then so is the resultant iterated hash function 30NETWORK SECURITY By: Homera Durani

Other Secure Hash Function MD5 Whirlpool 31NETWORK SECURITY By: Homera Durani

MD5 Message Digest Algorithm (MD5) was developed by Ron Rivest. Ron Rivest RFC 1321 Input: arbitrary Output: 128-bit digest Most widely used secure hash algorithm – until recently Security of 128-bit hash code has become questionable (1996, 2004) 32NETWORK SECURITY By: Homera Durani

Whirlpool Developed by Vincent Rijmen who is co –inventor of Rijndael. Whirlpool is one of the two hash Function endorsed by NESSIE (New European Schemes for Signatures, Integrity, and Encryption ). Whirlpool is based on the use of a block cipher for the compression function. It is based on AES. Algorithm takes input less than bit Output a 512 – bit. 33NETWORK SECURITY By: Homera Durani

HMAC Effort to develop a MAC derived from a cryptographic hash code Executes faster in software No export restrictions Relies on a secret key RFC 2104 list design objectives Used in Ipsec Simultaneously verify integrity and authenticity 34NETWORK SECURITY By: Homera Durani

Motivations: Cryptographic hash functions executes faster in software than encryptoin algorithms such as DES Library code for cryptographic hash functions is widely available No export restrictions from the US HMAC has been issued as RFC 2104 and has been chosen as the mandatory – to – implement MAC for IP security, and used in other Internet Protocols such as TLS(Transport Layer Security ) to replace SSL(Secure Sockets Layer) and SET(Secure Electronic Transaction). 35NETWORK SECURITY By: Homera Durani

Objectives To use, without modifications, available in Hash Functions Easy Replace ability. Preserve original performance. Use and handle keys in a simple way. 36NETWORK SECURITY By: Homera Durani

Message, M secret key output 37NETWORK SECURITY By: Homera Durani

38NETWORK SECURITY By: Homera Durani

Public – key Encryption Structure The use of two keys has consequences in: key distribution, confidentiality and authentication. The scheme has six ingredients Plaintext Encryption algorithm Public and private key Ciphertext Decryption algorithm 39NETWORK SECURITY By: Homera Durani

Plaintext : Readable message. Encryption Algorithm : performs various transformation on the plaintext. Public and Private key : one is used for encryption and other is used for decryption. Cipher text : scrambled message (output). Decryption algorithm : accepts cipher text and match key and produce original plaintext. 40NETWORK SECURITY By: Homera Durani

Encryption using Public-Key system 41NETWORK SECURITY By: Homera Durani

Authentication using Public-Key System 42NETWORK SECURITY By: Homera Durani

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 exchange: Two sides cooperate two exhange a session key. 43NETWORK SECURITY By: Homera Durani

Requirements For Public Key Easy for party B to generate pairs: public key KU b ; private key KR b Easy for sender A to generate cipertext using public key: C = E KUb (M) Easy for receiver B to decrypt using the private key to recover original message M = D KRb (C) = D KRb [E KUb (M)] PUBLIC PRIVATE HINT: 44NETWORK SECURITY By: Homera Durani

It is computationally infeasible for an opponent, knowing the public key KUb to determine the private key KR b It is computationally infeasible for an opponent, knowing the public key KUb and a ciphertext, C, to recover the original message, M Either of the two related keys can be used for encryption, with the other used for decryption M = D KRb [E KUb (M)]= D KUb [E KRb (M)] 45NETWORK SECURITY By: Homera Durani

46NETWORK SECURITY By: Homera Durani

Public-Key Cryptographic Algorithms RSA and Diffie-Hellman RSA - Ron Rivest in 1977, Adi Shamir and Len Adleman at MIT, and published in RSA is a block cipher The most widely implemented Diffie-Hellman Echange a secret key securely Compute discrete logarithms 47NETWORK SECURITY By: Homera Durani

RSA Algorithm Most widely accepted and implemented approach to public key encryption Block cipher where M and C are integers between 0 and n-1 for some n Following form: C = M e mod n M = C d mod n = (M e ) d mod n = M ed mod n 48NETWORK SECURITY By: Homera Durani

Sender and receiver know the values of n and e, but only the receiver knows the value of d Public key: KU = {e,n} Private key: KR = {d,n} 49NETWORK SECURITY By: Homera Durani

RSA Requirements It is possible to find values of e, d, n such that M ed = M mod n for all M<n It is relatively easy to calculate M e and C for all values of M<n It is infeasible to determine d given e and n Here is the magic! 50NETWORK SECURITY By: Homera Durani

51NETWORK SECURITY By: Homera Durani

52NETWORK SECURITY By: Homera Durani

RSA Example Select two prime numbers, p=7 and q=11 Calculate n = pq = 7 x 11 = 187 Calculate  (n) = (p-1)(q-1) = 16 * 10 = 160 Select e such that e is relatively prime to  (n) = 160 and less than  (n) ; in this case, e= 7 Determine d such that de = 1 mod 160 and d<160. The correct value is d = 23, because 23 x 7 = 161 = 10 x NETWORK SECURITY By: Homera Durani

Plain text 88 Cipher text 11 and output plaintext 88 Pu = 7, 187 pr = 23, 187 EncryptionDecryption 88 7 mod 187 = mod 187 = 88 54NETWORK SECURITY By: Homera Durani

RSA Encryption Plaintext:M<n Ciphertext:C = M e (mod n) 55NETWORK SECURITY By: Homera Durani

RSA Decryption Cipher text:C Plaintext:M = C d (mod n) 56NETWORK SECURITY By: Homera Durani

RSA Strength Brute force attack: try all possible keys – the larger e and d the more secure The larger the key, the slower the system For large n with large prime factors, factoring is a hard problem Cracked in 1994 a 428 bit key; $100 Currently 1024 key size is considered strong enough 57NETWORK SECURITY By: Homera Durani

Diffie- Hellman key Exchange 58NETWORK SECURITY By: Homera Durani

Diffie – Hellman Key Exchange 59NETWORK SECURITY By: Homera Durani

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 60NETWORK SECURITY By: Homera Durani