Introduction to Cryptography --- Foundations of information and network security --- Lecture 3

Introduction to CryptographyIntroduction to Cryptography

--- Foundations of information and network --- Foundations of information and network security ---security ---

Lecture 3Lecture 3

Information and Network Security 2

OutlineOutline

Why study cryptologyWhy study cryptology?? Basic terms, notations and structure Basic terms, notations and structure

of cryptographyof cryptography Private & public key cryptography Private & public key cryptography

examplesexamples Modern secret key ciphers : usage and Modern secret key ciphers : usage and

methodologymethodology Encryption and possible attacksEncryption and possible attacks Secret key ciphers designSecret key ciphers design


Why Study cryptology(1)Why Study cryptology(1)

A B

Intruder

Communications security



Customer Merchant

TTP

Electronic Commerce Security



A B

LEA

Law enforcement


The Basic ProblemThe Basic Problem

We consider the We consider the confidentialityconfidentiality goal: goal:Alice and Bob are FriendsAlice and Bob are FriendsMarvin is a rivalMarvin is a rivalAlice wants to send secret messages (MAlice wants to send secret messages (M11,M,M22,…) to ,…) to

Bob over the InternetBob over the InternetRival Marvin wants to read the messages (MRival Marvin wants to read the messages (M11,M,M22,…) - ,…) -

Alice and Bob want to prevent this! Alice and Bob want to prevent this! Assumption:Assumption: The network is OPEN: Marvin is able to The network is OPEN: Marvin is able to

eavesdrop and read all data sent from Alice to Bob.eavesdrop and read all data sent from Alice to Bob.Consequence:Consequence: Alice must not send messages (M Alice must not send messages (M11,M,M22,,

…) directly – they must be “scrambled” or …) directly – they must be “scrambled” or encryptedencrypted using a ‘secret code’ unknown to Marvin but known using a ‘secret code’ unknown to Marvin but known to Bob.to Bob.


CryptographyCryptography

plaintext (data file or messages)

encryption

ciphertext (stored or transmitted safely)

decryption

plaintext (original data or messages)


ED

Message(cleartext, plaintext)

Encrypted message(ciphertext)

Encrypted message(ciphertext)

Encryption

Decryption

key

AliceBob

Private key cipherPrivate key cipher

Message(cleartext,plaintext

)


Basic termsBasic terms

Cryptology (to be very precise)Cryptology (to be very precise)Cryptography --- code designingCryptography --- code designingCryptanalysis --- code breakingCryptanalysis --- code breaking

Cryptologist: Cryptologist: Cryptographer & cryptanalystCryptographer & cryptanalyst

Encryption/enciphermentEncryption/enciphermentScrambling data into unintelligible to Scrambling data into unintelligible to

unauthorised partiesunauthorised parties Decryption/deciphermentDecryption/decipherment

Un-scramblingUn-scrambling


Types of ciphersTypes of ciphers

Private key cryptosystems/ciphersPrivate key cryptosystems/ciphersThe secret key is shared between two The secret key is shared between two

partiesparties Public key cryptosystems/ciphersPublic key cryptosystems/ciphers

The secret key is not shared and two The secret key is not shared and two parties can still communicate using their parties can still communicate using their public keyspublic keys


Examples of “Messages”Examples of “Messages”

Types of secret “Messages” Alice Types of secret “Messages” Alice might want to send Bob (in increasing might want to send Bob (in increasing length):length):Decision (yes/no),Decision (yes/no), eg. as answer to the eg. as answer to the

question “Are we meeting tomorrow?”question “Are we meeting tomorrow?”Numerical ValueNumerical Value, eg. as answer to the , eg. as answer to the

question “at what hour are we meeting?”question “at what hour are we meeting?”DocumentDocumentSoftwareSoftware, , ImagesImages etc. etc.


ConceptsConcepts

A private key cipher is composed of A private key cipher is composed of two algorithmstwo algorithmsencryption algorithm Eencryption algorithm Edecryption algorithm Ddecryption algorithm D

The same key K is used for encryption The same key K is used for encryption & decryption& decryption

K has to be distributed beforehandK has to be distributed beforehand


NotationsNotations

Encrypt a plaintext P using a key K & Encrypt a plaintext P using a key K & an encryption algorithm Ean encryption algorithm E

C = E(K,P)C = E(K,P) Decrypt a ciphertext C using the same Decrypt a ciphertext C using the same

key K and the matching decryption key K and the matching decryption algorithm Dalgorithm D

P = D(K,C)P = D(K,C)

Note: P = D(K,C) = D(K, E(K,P))Note: P = D(K,C) = D(K, E(K,P))


The Caesar cipher (e.g)The Caesar cipher (e.g)

The Caesar cipher is a substitution The Caesar cipher is a substitution cipher, named after Julius Caesar.cipher, named after Julius Caesar.

Operation principle:Operation principle:each letter is translated into the letter each letter is translated into the letter a fixed number of positionsa fixed number of positions after after it in the alphabet table.it in the alphabet table.

The fixed number of positions is a key The fixed number of positions is a key both for encryption and decryption.both for encryption and decryption.


The Caesar cipher (cnt’d)The Caesar cipher (cnt’d)

K=3

Inner: ciphertext

Outer: plaintext


An exampleAn example

For a key K=3,For a key K=3,plaintext letter:plaintext letter: ABCDEF...UVWXYZABCDEF...UVWXYZciphtertext letter: ciphtertext letter: DEF...UVWXYZABCDEF...UVWXYZABC

HenceHenceTREATY IMPOSSIBLETREATY IMPOSSIBLE

is translated intois translated intoWUHDWB LPSRVVLEOHWUHDWB LPSRVVLEOH


Breaking classic ciphersBreaking classic ciphers

With the help of fast computers, With the help of fast computers, 99.99% ciphers used before 1976 are 99.99% ciphers used before 1976 are breakable by using one of the 4 types breakable by using one of the 4 types of attacks (described later).of attacks (described later).

Modern cluster computers and future Modern cluster computers and future quantum computers can break several quantum computers can break several existing ciphers due to the power of existing ciphers due to the power of such computers.such computers.


Breaking the Caesar cipherBreaking the Caesar cipher

By trial-and errorBy trial-and error By using statistics on lettersBy using statistics on letters

frequency distributions of lettersfrequency distributions of lettersletterletter percentpercentAA 7.49%7.49%BB 1.29%1.29%CC 3.54%3.54%DD 3.62%3.62%EE 14.00%14.00%....................................................................


Toy example of private key Toy example of private key cryptography (TPC)cryptography (TPC)

Assume that a message is broken into 64-bit blocks and each Assume that a message is broken into 64-bit blocks and each 64-bit block of plaintext is encrypted separately:64-bit block of plaintext is encrypted separately:

Key space are combinations of numerical digits – max: 7 Key space are combinations of numerical digits – max: 7 digits- digits- (eg: key = [1]; or key = [1,3], or key = [1,4,2]).(eg: key = [1]; or key = [1,3], or key = [1,4,2]).

Assume that all 8 bits of a byte is used and key digits start Assume that all 8 bits of a byte is used and key digits start from left to right.from left to right.

Encryption: Each plaintext block is first shifted by the number Encryption: Each plaintext block is first shifted by the number of binary digits before the last non-zero digit of the key. It is of binary digits before the last non-zero digit of the key. It is then exclusive-ored with the key starting from the first byte of then exclusive-ored with the key starting from the first byte of the block, repeatedly to the end of the block (the key moves a the block, repeatedly to the end of the block (the key moves a distance of its size from left to right of the plaintext block).distance of its size from left to right of the plaintext block).

Decryption: do the reverse of encryption: the cipher-text is Decryption: do the reverse of encryption: the cipher-text is exclusive-ored and then shifted.exclusive-ored and then shifted.

0 0 0=1 1 0=0 1 1=1 0 1=

: exclusive : exclusive oror


Using TPCUsing TPC

Use TPC to encrypt the plaintext “12345”, key Use TPC to encrypt the plaintext “12345”, key = [1,4,2]= [1,4,2]Use TPC to encrypt the plaintext “TREATY Use TPC to encrypt the plaintext “TREATY IMPOSSIBLE”; key = [4];IMPOSSIBLE”; key = [4];Use TPC to encrypt the plaintext “100 Use TPC to encrypt the plaintext “100 dollars”, key = [2,4];dollars”, key = [2,4];


Principles of Private Key EncryptionPrinciples of Private Key Encryption

Devise cryptographic algorithms: Devise cryptographic algorithms: a set of fast functions (E1, E2, E3, ..En) that when in turn a set of fast functions (E1, E2, E3, ..En) that when in turn

applied to an input (initial or intermediate input) will applied to an input (initial or intermediate input) will produce a more potentially scrambled output.produce a more potentially scrambled output.

and a set of functions (D1,D2,D3, .. Dn) that when in turn and a set of functions (D1,D2,D3, .. Dn) that when in turn applied to the cipher text (final or intermediate) will applied to the cipher text (final or intermediate) will produce the original input text.produce the original input text.

Devise algorithms, tests and proofs to validate Devise algorithms, tests and proofs to validate your cryptographic algorithmsyour cryptographic algorithms Analysing algorithms.Analysing algorithms. Tests with powerful computers such as specialised, Tests with powerful computers such as specialised,

parallel, cluster, or quantum computers.parallel, cluster, or quantum computers. Mathematical proofs.Mathematical proofs.


Toy example of public key Toy example of public key cryptographycryptography

Definition: The multiplicative inverse of Definition: The multiplicative inverse of xx with modulo with modulo nn is is yy such that (such that (xx**yy) mod ) mod nn = 1 = 1

E.g:x=3; n=10, => y=7; since (3*7) mod 10 = 1 E.g:x=3; n=10, => y=7; since (3*7) mod 10 = 1

The above multiplicative inverse can be used to create a The above multiplicative inverse can be used to create a simple public key cipher: either simple public key cipher: either xx or or yy can be thought of as a can be thought of as a secret key and the other is the public key. Let secret key and the other is the public key. Let xx = 3, = 3, yy = 7, = 7, nn = = 10, and M be the message:10, and M be the message: M = 4 ;M = 4 ;

3*4 mod 10 = 2; (ciphertext) - encrypting 3*4 mod 10 = 2; (ciphertext) - encrypting 2*7 mod 10 = 4 = M ; (message) - decrypting2*7 mod 10 = 4 = M ; (message) - decrypting

M =6 ; M =6 ; 3*6 mod 10 = 8; 3*6 mod 10 = 8; 8*7 mod 10 = 6 = M (message)8*7 mod 10 = 6 = M (message)


What is PKE used for?What is PKE used for?

Private Key Encryption (PKE) can be Private Key Encryption (PKE) can be used:used:Transmitting data over an insecure Transmitting data over an insecure

channelchannelSecure stored data (encrypt & store)Secure stored data (encrypt & store)Provide integrity check:Provide integrity check:

(Key + Mes.) -> MAC (message authentication (Key + Mes.) -> MAC (message authentication code)code)


Morden Cryptography applicationsMorden Cryptography applications

Not just about confidentiality!Not just about confidentiality! IntegrityIntegrity

Digital signaturesDigital signatures Hash functionsHash functions

Fair exchangeFair exchange Contract signingContract signing

AnonymityAnonymity Electronic cashElectronic cash Electronic votingElectronic voting

Etc.Etc.


Modern private key ciphersModern private key ciphers

DES (US, 1977) (3DES)DES (US, 1977) (3DES) key -- 56 bits, plaintext/ciphertext -- 64 bitskey -- 56 bits, plaintext/ciphertext -- 64 bits

LOKI (ADFA, Australia, 1989)LOKI (ADFA, Australia, 1989) key, plaintext/ciphertext -- 64 bitskey, plaintext/ciphertext -- 64 bits

FEAL (NTT, Japan, 1990)FEAL (NTT, Japan, 1990) key -- 128 bits, plaintext/ciphertext -- 64 bitskey -- 128 bits, plaintext/ciphertext -- 64 bits

IDEA (Lai & Massey, Swiss, 1991) IDEA (Lai & Massey, Swiss, 1991) key -- 128 bits, plaintext/ciphertext -- 64 bitskey -- 128 bits, plaintext/ciphertext -- 64 bits

SPEED (Y Zheng in 1996)SPEED (Y Zheng in 1996) Key/(plaintext/ciphertext) -- 48,64,80,…,256 bitsKey/(plaintext/ciphertext) -- 48,64,80,…,256 bits

AES (Joan Daemen & Vincent Rijmen 2000)AES (Joan Daemen & Vincent Rijmen 2000) Key/(plaintext/ciphertext) -- 128, 192 and 256 bitsKey/(plaintext/ciphertext) -- 128, 192 and 256 bits


General approaches to CryptographyGeneral approaches to Cryptography

There are two general encryption methods: There are two general encryption methods: Block ciphers & Block ciphers & Stream ciphersStream ciphers

Block ciphersBlock ciphers Slice message M into (fixed size blocks) Slice message M into (fixed size blocks) mm11, …, , …, mmnn

Add padding to last block Add padding to last block Use EUse Ekk to produce (ciphertext blocks) to produce (ciphertext blocks) xx11, …, , …, xxnn

Use DUse Dkk to recover M from to recover M from mm11, …, , …, mmn n

E.g: DES, etc.E.g: DES, etc. Stream ciphersStream ciphers

Generate a long random string (or pseudo random)Generate a long random string (or pseudo random)called called one-time padone-time pad..

Message Message one-time pad one-time pad (exclusive or)(exclusive or) E.g: EC4E.g: EC4


Design of Private Key Ciphers(1)Design of Private Key Ciphers(1)

A Cryptographic algorithm should be efficient for A Cryptographic algorithm should be efficient for good usegood use It should be fast and key length should be of the right It should be fast and key length should be of the right

length – e.g.; not too shortlength – e.g.; not too short Cryptographic algorithms are not impossible to Cryptographic algorithms are not impossible to

break without a keybreak without a key If we try all the combinations, we can get the original If we try all the combinations, we can get the original

messagemessage The security of a cryptographic algorithm depends The security of a cryptographic algorithm depends

on how much work it takes for someone to break iton how much work it takes for someone to break it E.g If it takes 10 mil. years to break a cryptographic E.g If it takes 10 mil. years to break a cryptographic

algorithm X using all the computers of a state, X can be algorithm X using all the computers of a state, X can be thought of as a secure one – reason: cluster computers thought of as a secure one – reason: cluster computers and quantum computers are powerful enough to crack and quantum computers are powerful enough to crack many current cryptographic algorithms.many current cryptographic algorithms.


Design of Private Key Ciphers(2)Design of Private Key Ciphers(2)

Encryption Algorithm DesignEncryption Algorithm DesignShould the strength of the algorithm be Should the strength of the algorithm be

included in the implementation of the included in the implementation of the algorithm? Should we hide the algorithm?algorithm? Should we hide the algorithm?

Should the block size be small or large?Should the block size be small or large?Should the keyspace be large?Should the keyspace be large?Should we consider other search rather Should we consider other search rather

than brute-force search?than brute-force search?Should we consider the hardware Should we consider the hardware

technology?technology?


4 types of cryptanalysis4 types of cryptanalysis

Depending on what a cryptanalyst has Depending on what a cryptanalyst has to work with, attacks can be classified to work with, attacks can be classified intointociphertext only attackciphertext only attackknown plaintext attackknown plaintext attackchosen plaintext attackchosen plaintext attackchosen ciphertext attack (most severe)chosen ciphertext attack (most severe)


4 types of attacks 4 types of attacks

Ciphertext only attackCiphertext only attackthe only data available is a target the only data available is a target

ciphertextciphertext

Known plaintext attackKnown plaintext attacka target ciphertexta target ciphertextpairs of other ciphertext and plaintext pairs of other ciphertext and plaintext

(say, previously broken or guessing)(say, previously broken or guessing)


4 types of attacks 4 types of attacks

Chosen plaintext attacksChosen plaintext attacksa target ciphertexta target ciphertextcan feed encryption algorithm with can feed encryption algorithm with

plaintexts and obtain the matching plaintexts and obtain the matching ciphertextsciphertexts

Chosen ciphertext attackChosen ciphertext attacka target ciphertexta target ciphertextcan feed decryption algorithm with can feed decryption algorithm with

ciphertexts and obtain the matching ciphertexts and obtain the matching plaintextsplaintexts

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Introduction to Cryptography --- Foundations of information and network security --- Lecture 3