Cryptography and Message Authentication NS3

Chapter3 Public-Key Cryptography and Message Authentication Henric Johnson Blekinge Institute of Technology, Sweden http://www.its.bth.se/staff/hjo/ [email_address]

OUTLINE Approaches to Message Authentication Secure Hash Functions and HMAC Public-Key Cryptography Principles Public-Key Cryptography Algorithms Digital Signatures Key Management

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)

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)

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

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)

Simple Hash Function One-bit circular shift on the hash value after each block is processed would improve

Message Digest Generation Using SHA-1

SHA-1 Processing of single 512-Bit Block

Other Secure HASH functions 160 (5 paired rounds of 16) 64 (4 rounds of 16) 80 (4 rounds of 20) Number of steps 2 64 -1 bits Maximum message size 512 bits 512 bits 512 bits Basic unit of processing 160 bits 128 bits 160 bits Digest length RIPEMD-160 MD5 SHA-1

HMAC Use a MAC derived from a cryptographic hash code, such as SHA-1. 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

Public-Key Cryptography Principles The use of t wo keys has consequences in: k ey distribution, confidentiality and authentication . The scheme has six ingredients (see Figure 3.7) Plaintext Encryption algorithm Public and private key Ciphertext Decryption algorithm

Encryption using Public-Key system

Authentication using Public-Key System

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.

Requirements for Public-Key Cryptography Computationally easy for a party B to generate a pair (public key K U b , private key KR b ) Easy for sender to generate ciphertext: Easy for the receiver to decrypt ciphertect using private key:

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

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

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}

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

The RSA Algorithm - Decryption Ciphertext: C Plaintext: M = C d (mod n)

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

Key Management Public-Key Certificate Use

Cryptography and Message Authentication NS3

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Cryptography and Message Authentication NS3