Chapter3

Public-Key Cryptography and Public-Key Cryptography and Message AuthenticationMessage 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 One-way HASH functionfunction

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 size2. H produces a fixed length output3. 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) = h5. 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)xy

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 functionsSHA-1 MD5 RIPEMD-

160

Digest length 160 bits 128 bits 160 bits

Basic unit of processing

512 bits 512 bits 512 bits

Number of steps

80 (4 rounds of 20)

64 (4 rounds of 16)

160 (5 paired rounds of 16)

Maximum message size

264-1 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 KUb, private key KRb)

2. Easy for sender to generate ciphertext:

3. Easy for the receiver to decrypt ciphertect using private key: )(MEC KUb

)]([)( MEDCDM KUbKRbKRb

Requirements for Public-Key Cryptography

4. Computationally infeasible to determine private key (KRb) knowing public key (KUb)

5. Computationally infeasible to recover message M, knowing KUb and ciphertext C

6. Either of the two keys can be used for encryption, with the other used for decryption:

)]([)]([ MEDMEDM KRbKUbKUbKRb

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 Key KU = {e,n}

7. Private key KR = {d,n}

)1)(1()( qpn)(1;1)),(gcd( neen

)(mod1 ned

Example of RSA Algorithm

The RSA Algorithm - Encryption

Plaintext: M<n

Ciphertext: C = Me (mod n)

The RSA Algorithm - Decryption

Ciphertext: C

Plaintext: M = Cd (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): xA < q

compute their public key: yA = axA mod q

each user makes public that key yA

Diffie-Hellman Key Exchange

shared session key for users A & B is KAB: KAB = a

xA.xB mod q

= yA

xB mod q (which B can compute)

= yB

xA mod q (which A can compute) KAB 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 xA=97, B chooses xB=233 compute respective public keys:

yA=397 mod 353 = 40 (Alice)

yB=3233 mod 353 = 248 (Bob)

compute shared session key as: KAB= yB

xA mod 353 = 24897 = 160 (Alice)

KAB= yA

xB mod 353 = 40233 = 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 ManagementPublic-Key Certificate Use