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Chapter 1.

Overview of Cryptography

Jeong H. Yi

jhyi@ics.uci.edu

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Information security and cryptography

Cryptography is the study of mathematical techniques relatedto aspects of information security

Cryptographic goals

Confidentiality Data integrity

Authentication

Non-repudiation

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Taxonomy of cryptographic primitives.Arbitrary length hash functions

One-way permutations

Random sequences

Symmetric-key ciphers

Arbitrary length hash functions(MACs)

Signatures

Pseudorandom sequences

Identification primitives

Public-key ciphers

Signatures

Identification primitives

UnkeyedPrimitives

Symmetric-keyPrimitives

Public-keyPrimitives

SecurityPrimitives

Blockciphers

Stream

ciphers

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Background on Functions

Function f : X Y is called a function f from set X to set Y.

X: domain

Y: codomain.

for y = f(x) where x X and y Y y: image of x

x: preimage of y Im(f), image of f

the set that all y Y have at least one preimage

1 1 function if each element in Y is the image of at most one element in X.

onto function if Im(f) =Y

bijection function if f is 11 and onto.

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Background on Functions (ctd)

one-way function if f(x) is easy to compute for all x X, but

it is computationally infeasible to find any x X such that f(x) =y.

trapdoor one-way function if given trapdoor information, it becomes feasible to find an x X

such that f(x) =y.

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Symmetric-key ciphers

Block cipher breaks up the plaintext into blocks of a fixed length, and then

encrypts one block at a time.

Stream cipher

takes the plaintext string and produces a ciphertext string usingkeystream

specific case of block cipher with the size of 1

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Digital signatures

Nomenclature M: messages

S: signatures

SA: signing transformation for A

VA: verification transformation for A

Definition

SAand VAprovide a digital signature scheme (or mechanism) for A.

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Authentication

Entity authentication (Identification) corroboration of the identity of an entity (e.g., a person, a

computer terminal, a credit card, etc.).

Message authentication (Data origin authentication)

corroborating the source of information

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Symmetric-key cryptography

Advantages high data throughput

relatively short size

primitives to construct various cryptographic mechanisms

Disadvantages

the key must remain secret at both ends.

O(n2) keys to be managed.

relatively short lifetime of the key

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Public-key cryptography

Advantages Only the private key must be kept secret

relatively long life time of the key

relatively efficient digital signature mechanisms

smaller verification key

O(n) keys to be managed

Disadvantages

low data throughput

much larger key sizes

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Summary of comparison

public-key cryptography signatures (particularly, non-repudiation) and key management

symmetric-key cryptography

encryption and some data integrity applications

Key sizes

Private keys must be larger (e.g., 1024 bits for RSA) than secretkeys (e.g., 64 or 128 bits)

most attack on symmetric-key systems is an exhaustive key search public-key systems are subject to short-cut attacks (e.g., factoring)

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Key establishment and management

Key establishment process to establish a shared secret key available to two or more

parties

subdivided into key agreement and key transport.

Key management the set of processes and mechanisms which support key

establishment and

the maintenance of ongoing keying relationships between parties

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Key management through symmetric-key tech.

Advantages easy to add and remove entities

needs to store only one long-term secret key.

Disadvantages

initial interaction with the TTP.

n long-term secret keys maintained by TTP

TTP can read all messages.

If TTP is compromised, all communications are insecure

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Key management through public-key tech.

Advantages No TTP is required.

Only n public keys need to be stored

Disadvantages

Active adversary can compromise the key management scheme(e.g. man-in-the-middle attack)

Need TTP (e.g., CA) to certify the public key of each entity.

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Public-key certification

Advantages

prevents an active adversary from impersonation

TTP cannot monitor communications.

Disadvantages

If the signing key of the TTP is compromised, all communicationsbecome insecure.

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Attacks on encryption schemes

Ciphertext-only attack

deduce the decryption key or plaintext by only observing ciphertext.

Known-plaintext attack

using a quantity of plaintext and corresponding ciphertext.

Chosen-plaintext attack

chooses plaintext and is then given corresponding ciphertext.

Adaptive chosen-plaintext attack

chosen-plaintext attack where the choice of plaintext may depend on theciphertext received from previous requests.

Chosen-ciphertext attack

selects the ciphertext and is then given the corresponding plaintext.Adaptive chosen-ciphertext attack

chosen-ciphertext attack where the choice of ciphertext may depend onthe plaintext received from previous requests.

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Attacks on protocols

known-key attack uses previously used keys to determine new keys

replay attack records a communication session and replays that session

impersonation attack deceives the identity of one of the legitimate parties

dictionary attack using code book

forward search attack

if message space is small or predictableinterleaving attack impersonation or other deception involving selective combination of

information from parallel sessions

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Models for evaluating security

Unconditional security (perfect secrecy) Adversaries have unlimited computational resources

Observation of the ciphertext provides no information to anadversary

Complexity-theoretic security Adversaries have polynomial computational power.

Asymptotic analysis and usually also worst-case analysis is used

Provable security provably secure if the difficulty of defeating crypto system can be

shown to be as difficult as solving a well-known number-theoreticproblem

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Models for evaluating security (ctd)

Computational security (Practical security)

computationally secure if the level of computation to defeat cryptosystem exceeds the computational resources of the adversary

Most of the known public-key and symmetric-key schemes

Ad hoc security (heuristic security)

any variety of convincing computational security

unforeseen attacks may remain