# Chapter3 Public-Key Cryptography and Message Authentication.

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Chapter3 Public-Key Cryptography and Message Authentication

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 : 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)

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 SHA-1MD5RIPEMD- 160 Digest length160 bits128 bits160 bits Basic unit of processing 512 bits Number of steps 80 (4 rounds of 20) 64 (4 rounds of 16) 160 (5 paired rounds of 16) Maximum message size 2 64 -1 bits

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

HMAC Structure

Public-Key Cryptography Principles The use of two keys has consequences in: key 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 1. Computationally easy for a party B to generate a pair (public key KU b, private key KR b ) 2. Easy for sender to generate ciphertext: 3. Easy for the receiver to decrypt ciphertect using private key:

Requirements for Public-Key Cryptography 4. Computationally infeasible to determine private key (KR b ) knowing public key (KU b ) 5. Computationally infeasible to recover message M, knowing KU b and ciphertext C 6. 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 1. Select p,q p and q both prime 2. Calculate n = p x q 3. Calculate 4. Select integer e 5. Calculate d 6. Public KeyKU = {e,n} 7. Private keyKR = {d,n}

Example of RSA Algorithm

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 encryption helps address key distribution problems have two aspects of this: distribution of public keys use of public-key encryption to distribute secret keys

Distribution of Public Keys can be considered as using one of: public announcement publicly available directory public-key authority public-key certificates

Public Announcement users distribute public keys to recipients or broadcast to community at large eg. append PGP keys to email messages or post to news groups or email list major weakness is forgery anyone can create a key claiming to be someone else and broadcast it until forgery is discovered can masquerade as claimed user

Publicly Available Directory can obtain greater security by registering keys with a public directory directory must be trusted with properties: contains {name,public-key} entries participants register securely with directory participants can replace key at any time directory is periodically published directory can be accessed electronically still vulnerable to tampering or forgery

Public-Key Authority improve security by tightening control over distribution of keys from directory has properties of directory and requires users to know public key for the directory then users interact with directory to obtain any desired public key securely does require real-time access to directory when keys are needed

Public-Key Authority

Public-Key Certificates certificates allow key exchange without real-time access to public-key authority a certificate binds identity to public key usually with other info such as period of validity, rights of use etc with all contents signed by a trusted Public-Key or Certificate Authority (CA) can be verified by anyone who knows the public- key authorities public-key

Public-Key Certificates

Public-Key Distribution of Secret Keys use previous methods to obtain public-key can use for secrecy or authentication but public-key algorithms are slow so usually want to use private-key encryption to protect message contents hence need a session key have several alternatives for negotiating a suitable session

Simple Secret Key Distribution proposed by Merkle in 1979 A generates a new temporary public key pair A sends B the public key and their identity B generates a session key K sends it to A encrypted using the supplied public key A decrypts the session key and both use problem is that an opponent can intercept and impersonate both halves of protocol

Public-Key Distribution of Secret Keys if have securely exchanged public-keys:

Hybrid Key Distribution retain use of private-key KDC shares secret master key with each user distributes session key using master key public-key used to distribute master keys especially useful with widely distributed users rationale performance backward compatibility

Diffie-Hellman Key Exchange first public-key type scheme proposed by Diffie & Hellman in 1976 along with the exposition of public key concepts note: now know that Williamson (UK CESG) secretly proposed the concept in 1970 is a practical method for public exchange of a secret key used in a number of commercial products

Diffie-Hellman Key Exchange a public-key distribution scheme cannot be used to exchange an arbitrary message rather it can establish a common key known only to the two participants value of key depends on the participants (and their private and public key information) based on exponentiation in a finite (Galois) field (modulo a prime or a polynomial) - easy security relies on the difficulty of computing discrete logarithms (similar to factoring) – hard

Diffie-Hellman Setup all users agree on global parameters: large prime integer or polynomial q a being a primitive root mod q each user (eg. A) generates their key chooses a secret key (number): x A < q compute their public key: y A = a x A mod q each user makes public that key y A

Diffie-Hellman Key Exchange shared session key for users A & B is K AB : K AB = a x A. x B mod q = y A x B mod q (which B can compute) = y B x A mod q (which A can compute) K AB is used as session key in private-key encryption scheme between Alice and Bob if Alice and Bob subsequently communicate, they will have the same key as before, unless they choose new public-keys attacker needs an x, must solve discrete log

Diffie-Hellman Example users Alice & Bob who wish to swap keys: agree on prime q=353 and a=3 select random secret keys: A chooses x A =97, B chooses x B =233 compute respective public keys: y A = 3 97 mod 353 = 40 (Alice) y B = 3 233 mod 353 = 248 (Bob) compute shared session key as: K AB = y B x A mod 353 = 248 97 = 160 (Alice) K AB = y A x B mod 353 = 40 233 = 160 (Bob)

Key Exchange Protocols users could create random private/public D-H keys each time they communicate users could create a known private/public D- H key and publish in a directory, then consulted and used to securely communicate with them both of these are vulnerable to a meet-in-the- Middle Attack authentication of the keys is needed

Diffie-Hellman Key Echange

Key Management Public-Key Certificate Use

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