Types of Cryptosystems: Block vs. Stream, Symmetric vs. Asymmetric - Prof. Krzysztof Gaj, Study notes of Cryptography and System Security

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Types of Cryptosystems

ECE 646 - Lecture 3

Implementation of

Security Services

Block vs. stream ciphers

Types of Cryptosystems (1)

Cryptosystem (Cipher)

message

ciphertext

cryptographic

key

n bits m bits k bits

Block vs. stream ciphers

Stream

cipher

Internal state - IS

Block

cipher

K K

M 1 , M 2 , …, Mn m 1 , m 2 , …, mn C 1 , C 2 , …, Cn c 1 , c 2 , …, cn

Ci=fK(Mi) ci = fK(mi, ISi) ISi+1=gK(mi, ISi)

Every block of ciphertext is a function of only one corresponding block of plaintext Every block of ciphertext is a function of the current block of plaintext and the current internal state of the cipher

Typical stream cipher

Sender Receiver

P seudorandom K ey G enerator mi plaintext ci ciphertext ki keystream key initialization vector (seed) P seudorandom K ey G enerator mi plaintext ci ciphertext ki keystream key (^) vector (seed)initialization

Secret-key vs. public-key ciphers

Types of Cryptosystems (2)

Public Key (Asymmetric) Cryptosystems

Public key of Bob - KB Private key of Bob^ -^ kB

Alice Bob

Network Encryption Decryption Classification of cryptosystems Terminology secret-key symmetric symmetric-key classical conventional public key asymmetric One-way function

X f(X) Y

f-^1 (Y)

EXAMPLE:

f: Y=f(X) = AX^ mod P

where P and A are constants, P is a large prime, A is an integer smaller than P Number of bits of P Average number of multiplications necessary to compute f f -^1 1000 1500 1030

Trap-door one-way function

X f(X) Y

f-^1 (Y)

Whitfield Diffie and Martin Hellman

“ New directions in cryptography ,” 1976

PUBLIC KEY

PRIVATE KEY

Key Distribution

Alice Bob

message ciphertext message ciphertext Bob’s public key Bob’s private key Bob’s public key message ciphertext Bob’s public key

Intruder

Digital Signature

Alice Bob

signature message signature message Alice’s public key Alice’s private key Alice’s public key signature message Alice’s public key

Intruder

signature message Alice’s public key

Judge

Hash functions Basic requirements

1. Public description, NO key
2. Compression arbitrary length input  fixed length output
3. Ease of computation Hash functions Security requirements

It is computationally infeasible

Given To Find

h(m) m

m and h(m)

m ’  m , such that

h(m’) = h(m)

m ’  m , such that

h(m’) = h(m)

Message Hash function Public key cipher

Alice

Signature Alice’s private key

Bob

Hash function Alice’s public key Non-repudiation Hash value 1 Hash value 2 Hash value Public key cipher yes/no Message Signature

Message Hash function Public key cipher

Alice

Signature Alice’s private key

Bob

Hash function Alice’s public key Non-repudiation Hash value 1 Hash value 2 Hash value Public key cipher yes/no Message Signature Signature generation function Signature verification function Message Secret key algorithm

Alice

MAC Secret key of Alice and Bob

Bob

Secret key algorithm Authentication MAC’ MAC yes (^) no Message MAC Secret key of Alice and Bob

KAB KAB

MAC - Message Autentication Codes (keyed hash functions) arbitrary length message MAC function MAC m fixed length

secret key

K

Relations among security services INTEGRITY

AUTHENTICATION

NON-REPUDIATION

CONFIDENTIALITY

Message Hash function Public key cipher

Alice

Signature Alice’s private key

Bob

Hash function Alice’s public key Non-repudiation Hash value 1 Hash value 2 Hash value Public key cipher yes no Message Signature Message Secret key algorithm

Alice

MAC Secret key of Alice and Bob

Bob

Secret key algorithm Authentication MAC’ MAC yes no Message MAC Secret key of Alice and Bob

KAB KAB

Hybrid Systems Features required from today’s ciphers

STRENGTH

FUNCTIONALITY

• easy key distribution
• digital signatures

PERFORMANCE

Features of secret-key ciphers

STRENGTH

FUNCTIONALITY

• easy key distribution
• digital signatures

PERFORMANCE

Permutation C order of wires P Software Hardware ASM sequence of instructions <<, |, & sequence of instructions ROL, OR, AND n n x 1 x 2 x 3 x n - 1 x n

... y 1 y 2 y 3 y n - 1 y n

Basic operations of secret key ciphers - P-box P-box n x n Basic Operations of the Public Key Cryptosystem RSA Encryption Decryption ciphertext (^) = plaintext^ mod public key modulus public key exponent plaintext = ciphertext mod private key modulus private key exponent k - bits k - bits^ k - bits k - bits k - bits k - bits

Alice Bob

session key ( random secret-key ) Bob’s public key Hybrid Systems Bob’s private key

Network

Session key encrypted using Bob’s public key Message encrypted using session key

Hybrid Systems - Sender’s Side (2)

Alice

session key random Bob’s public key message Secret key cipher Public key cipher

Session key encrypted using Bob’s public key Message encrypted using session key Hybrid Systems - Receiver’s Side (2)

Bob

session key random Bob’s private key message Secret key cipher Public key cipher

Session key encrypted using Bob’s public key Message encrypted using session key Evaluating the security of secret-key ciphers

Classification of attacks (4) Chosen ciphertext attack

Given:

Looked for:

key

Encryption module (^) key

Capability to decipher

an arbitrarily chosen

fragment of the ciphertext