CRYPTOGRAPHY I
Hakan Tolgay
[email protected]
Introduction

Cryptography

Where security engineering meets mathematics.

A word from Greek κρυπτός kryptós, "hidden, secret"

The practice and study of techniques for securing information.

Modern form of cryptography aims

Confidentiality

Data integrity

Authentication

Non-repudiation
Introduction

Basic terminology

Plain text

Cipher Text

Cryptanalysis

Key

Encryption

Decryption
History – Caesar – Shift cipher


Julius Caesar enciphered his dispatches by writing D for A, E for B and so on
When Augustus Caesar ascended the throne, he changed the imperial cipher system so that C was now written for
A, D for B, and so on.

we would say that he changed the key from D to C.
Ceasar’s Alphabet
abcdefghijklmnopqrstuvwxtz
defghijklmnopqrstuvwxyzabc
Ceasar’s message
Plain text: defend the east wall of the castle
Cipher text: ghihqg wkh hdvw zdoo ri wkh fdvwoh
History - Monoalphabetic Substitution

The Arabs generalized this idea to the monoalphabetic substitution, in which a keyword is used to permute the
cipher alphabet.
Example MonoAlphabet
Plaintext alphabet: abcdefghijklmnopqrstuvwxyz
Ciphertext alphabet:SOMERDINGXHBVLTUJWKYZFACPQ
Secret message
Plain text: security
Cipher text: KRMZWGYP
History – Frequency Analysis




In cryptanalysis, frequency analysis is the study of the frequency of letters or groups of letters in a
ciphertext.
The method is used as an aid to breaking classical ciphers.
There is a characteristic distribution of letters that is roughly the same for almost all samples of that
language
For instance, given a section of English language,

E, T, A and O are the most common

Z, Q and X are rare

TH, ER, ON, and AN are the most common pairs of letters (termed bigrams or digraphs)

SS, EE, TT, and FF are the most common repeats.
History – Frequency Analysis

Common percentages in standard English are:
e
t
12.7 9.1
a
o
i
n
s
h
r
d
l
u
c
8.2
7.5
7.0
6.7
6.3
6.1
6.0
4.3
4.0
2.8
2.8
m
w
f
y
g
p
b
v
k
x
j
q
z
2.4
2.4
2.2
2.0
2.0
1.9
1.5
1.0
0.8
0.2
0.2
0.1
0.1
History – Frequency Analysis

Suppose Eve has intercepted the cryptogram below
LIVITCSWPIYVEWHEVSRIQMXLEYVEOIEWHRXEXIPFEMVEWHKVSTYLXZIXLIKIIXPIJVSZEYPERRGERIM
WQLMGLMXQERIWGPSRIHMXQEREKIETXMJTPRGEVEKEITREWHEXXLEXXMZITWAWSQWXSWEXTVEPMRXRSJ
GSTVRIEYVIEXCVMUIMWERGMIWXMJMGCSMWXSJOMIQXLIVIQIVIXQSVSTWHKPEGARCSXRWIEVSWIIBXV
IZMXFSJXLIKEGAEWHEPSWYSWIWIEVXLISXLIVXLIRGEPIRQIVIIBGIIHMWYPFLEVHEWHYPSRRFQMXLE
PPXLIECCIEVEWGISJKTVWMRLIHYSPHXLIQIMYLXSJXLIMWRIGXQEROIVFVIZEVAEKPIEWHXEAMWYEPP
XLMWYRMWXSGSWRMHIVEXMSWMGSTPHLEVHPFKPEZINTCMXIVJSVLMRSCMWMSWVIRCIGXMWYMX


Counts of the letters in the cryptogram show that:

I is the most common single letter

XL most common bigram, and XLI is the most common trigram

e is the most common letter in the English language

th is the most common bigram, and the the most common trigram.
This strongly suggests that


X~t, L~h and I~e.
The second most common letter in the cryptogram is E; since the first and second most frequent letters in the
English language, e and t are accounted for, Eve guesses that E~a, the third most frequent letter.
History – Frequency Analysis

Tentatively making these assumptions, the following partial decrypted message is obtained.
heVeTCSWPeYVaWHaVSReQMthaYVaOeaWHRtatePFaMVaWHKVSTYhtZetheKeetPeJVSZaYPaRRGaReM
WQhMGhMtQaReWGPSReHMtQaRaKeaTtMJTPRGaVaKaeTRaWHatthattMZeTWAWSQWtSWatTVaPMRtRSJ
GSTVReaYVeatCVMUeMWaRGMeWtMJMGCSMWtSJOMeQtheVeQeVetQSVSTWHKPaGARCStRWeaVSWeeBtV
eZMtFSJtheKaGAaWHaPSWYSWeWeaVtheStheVtheRGaPeRQeVeeBGeeHMWYPFhaVHaWHYPSRRFQMtha
PPtheaCCeaVaWGeSJKTVWMRheHYSPHtheQeMYhtSJtheMWReGtQaROeVFVeZaVAaKPeaWHtaAMWYaPP
thMWYRMWtSGSWRMHeVatMSWMGSTPHhaVHPFKPaZeNTCMteVJSVhMRSCMWMSWVeRCeGtMWYMt


Using these initial guesses, Eve can

spot patterns, such as "that".

suggest other patterns for further guesses.

"Rtate" might be "state", which would mean R~s.

"atthattMZe" could be guessed as "atthattime", yielding M~i and Z~m.

"heVe" might be "here", giving V~r.
Filling in these guesses, Eve gets:
hereuponlegrandarosewithagraveandstatelyairandbroughtmethebeetlefromaglasscasei
nwhichitwasencloseditwasabeautifulscarabaeusandatthattimeunknowntonaturalistsof
courseagreatprizeinascientificpointofviewthereweretworoundblackspotsnearoneextr
emityofthebackandalongoneneartheotherthescaleswereexceedinglyhardandglossywitha
lltheappearanceofburnishedgoldtheweightoftheinsectwasveryremarkableandtakingall
thingsintoconsiderationicouldhardlyblamejupiterforhisopinionrespectingit
History – Kerckhoffs’ Princible


A cryptosystem should be secure even if everything about the system, except the key, is public
knowledge.
Kerckhoffs’ Princible is counterintuitive.
History – Attack vectors

Cryptoanalysis

Classical cryptoanalysis

Brute-force

Analytic atacks

Social Engineering

Implementation atacks
Cryptography

Symmetric

Stream Ciphers

Block Ciphers

Asymmetric

Protocols
Symmetric Encryption

Symmetric encryption means same key is used to encrypt and decrypt


Many varieties (algorithms):


Means both parties need access to the same keys
DES, TDES, AES, Twofish, RC4, CAST5, IDEA, Blowfish…
Can be strong and also fairly high-performance

“Strength” determined by key length in bits as well as algorithmic integrity
Symmetric Encryption


Symmetric encryption comes in two flavors:

Stream ciphers transform the key as they progress, processing one chunk (bit, byte, whatever) at a time

Block ciphers use fixed keys every block (blocksize=keysize)
Difference matters little in practice

Stream generally faster, but requires more key complexity

Many block ciphers have modes that effectively operate like stream ciphers

Most data protection products use block ciphers
Stream Ciphers

A stream cipher encrypts bits individually

Both encryptrion and decryption is very simple

Encryption


Decryption



Yi = e(Xi) = Xi + Si mod2
Xi = d(Yi) = Yi + Si mod2
Which is actually XOR
00
0
01
1
10
1
11
0
How do we generate key stream bits?
Stream Ciphers - Random numbers

3 types of random number generators

True Random Number Generators (TRNG)


Pseudo Random Number Generators (PRNG)

PRNGs are computed i.e they are deterministic


True random numbers stem from random physical processes. E.g coin flipping, key stroke timing, mouse move
Ex: rand () in C
Cryptographically Secure PRNG (CPRNG)

CPRNGs are PRNG with in additional property, numbers are unpredictable.
Stream Ciphers - One Time Pad (OTP)

Goal is to build a perfect cipher

A cipher is unconditionally secure that it can not be broken even with infinite computing resources

The One Time Pad (OTP) is a stream cipher where

The key strem bits from TRNG

Each key streams is used only once

Key size is equal to plain text

A Key can only be used once
Stream Ciphers - Linear Congruential Generator (LCG)
K
PRNG
K
Si
Xi

S0 = seed

Si+1 = A . S1 + B mod m

Key K = (A, B)

2 minuets to break
PRNG
Si
Yi
Xi
Stream Ciphers - LCG attack

Eve knows X1, X2, X3

Eve computes

S1, S2, S3

S2 = A . S1 + B mod m

S3 = A . S2 + B mod m
Stream Ciphers - Linear Feedback Shift Register (LFSR)

Goal is less and/or low power hardware
Block Ciphers – Data Encryption Standard (DES)

Proposed by IBM at 1974

With input from NSA

From 1977 to 1998 it is used as US standard

Insecure today (key too short)

3DES is secure
X
64 bits
DES
56 bits
K
64 bits
Y
DES – Inside DES
X
64 bits
T
T
56 bits
K
 Transposition shuffles the input (permutation)
64 bits
Y
DES – Inside DES

Have X16 round
Advanced Encryption Standard (AES)

1997 call for AES by NIST

Aug 1998 15 algorithms submissions

Aug 1999 5 finalist are selected

October 2000 Algorithm called Rijndael choosen as AES

Is now most important symmetric algorith in the world

Number of rounds depends on the key
Key
Rounds
128
10
192
12
256
14
X
128bits
AES
128bits
128/192/256 bits
K
Y
Modes of Operation for Block Ciphers

Deterministic


ECB (Electronic Code Book)
Probabilistic

Block cipher - CBC

Stream cipher

OFB (Output Feedback Block)

CFB (Cipher Feedback Block)

Counter mode
Electronic Code Book (ECB)


simply repeats the AES encryption process
for each 128-bit block of data
For decryption, the process is reversed.
Electronic Code Book (ECB)

identical blocks of unencrypted data, referred to as plain text, are encrypted the same way and
will yield identical blocks of encrypted data
Cipher Block Chaining (CBC)


Invented by IBM at 1976
Goal is to achieve an encryption method that encrypts
each block using the same encryption key, while resulting
in different cipher text
Cipher feedback (CFB)

A close relative of CBC, makes a block cipher into a self-synchronizing stream cipher.
Output feedback (OFB)

The output feedback (OFB) mode makes a block cipher into a synchronous stream cipher.
Counter (CTR)




counter mode turns a block cipher into a
stream cipher.
It generates the next keystream block by
encrypting successive values of a
"counter".
The counter can be any function which
produces a sequence which is
guaranteed not to repeat for a long
time,
An actual increment-by-one counter is
the simplest and most popular.
Asymmetric Cryptography

Also know as Public-key cryptography

How could to people never met share a key?
Diffie–Hellman (DH)


is a specific method of securely exchanging cryptographic keys over a public channel
allows two parties that have no prior knowledge of each other to jointly establish a shared secret
key over an insecure communication channel

The scheme was first published by Whitfield Diffie and Martin Hellman in 1976

Bases on discrete logaritm problem

Easy to perform

Hard to reverse
DH Key exchange
Eve
Alice
Bob
DH Key exchange

p: prime modules

g: generator (should be prime)

x: private number

r: result

g^x mod p = r

Let g=3 and p=17 and x=4

3^4 mod 17 = 9

3 ^ x mod 17 = 9
DH Key exchange
Eve
Alice
g=3 p=17
Select random private number: x=15
3^15 mod 17 = 6
g=3 p=17
6 12
Bob
g=3 p=17
6
Select random private number: x=13
12
12^15 mod 17 = 10
3^13 mod 17 = 12
6^13 mod 17 = 10
Thank you