Transcript Cryptography Training Day I

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
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Plain text
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Cipher Text
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Cryptanalysis
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Key
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Encryption
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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
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


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,
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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)
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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
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
Counts of the letters in the cryptogram show that:
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I is the most common single letter
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XL most common bigram, and XLI is the most common trigram
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e is the most common letter in the English language
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th is the most common bigram, and the the most common trigram.
This strongly suggests that
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
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
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
Using these initial guesses, Eve can
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spot patterns, such as "that".
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suggest other patterns for further guesses.
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"Rtate" might be "state", which would mean R~s.
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"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
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
A cryptosystem should be secure even if everything about the system, except the key, is public
knowledge.
Kerckhoffs’ Princible is counterintuitive.
History – Attack vectors
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Cryptoanalysis
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Classical cryptoanalysis
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Brute-force
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Analytic atacks
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Social Engineering
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Implementation atacks
Cryptography
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Symmetric
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Stream Ciphers
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Block Ciphers
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Asymmetric
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Protocols
Symmetric Encryption
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Symmetric encryption means same key is used to encrypt and decrypt


Many varieties (algorithms):
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
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
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“Strength” determined by key length in bits as well as algorithmic integrity
Symmetric Encryption
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
Symmetric encryption comes in two flavors:
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Stream ciphers transform the key as they progress, processing one chunk (bit, byte, whatever) at a time
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Block ciphers use fixed keys every block (blocksize=keysize)
Difference matters little in practice
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Stream generally faster, but requires more key complexity
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Many block ciphers have modes that effectively operate like stream ciphers
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Most data protection products use block ciphers
Stream Ciphers
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A stream cipher encrypts bits individually
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Both encryptrion and decryption is very simple
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Encryption
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Decryption
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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
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3 types of random number generators
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True Random Number Generators (TRNG)
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Pseudo Random Number Generators (PRNG)
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PRNGs are computed i.e they are deterministic
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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)
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CPRNGs are PRNG with in additional property, numbers are unpredictable.
Stream Ciphers - One Time Pad (OTP)
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Goal is to build a perfect cipher
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A cipher is unconditionally secure that it can not be broken even with infinite computing resources
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The One Time Pad (OTP) is a stream cipher where
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The key strem bits from TRNG
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Each key streams is used only once
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Key size is equal to plain text
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A Key can only be used once
Stream Ciphers - Linear Congruential Generator (LCG)
K
PRNG
K
Si
Xi
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S0 = seed
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Si+1 = A . S1 + B mod m
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Key K = (A, B)
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2 minuets to break
PRNG
Si
Yi
Xi
Stream Ciphers - LCG attack
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Eve knows X1, X2, X3
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Eve computes
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S1, S2, S3
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S2 = A . S1 + B mod m
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S3 = A . S2 + B mod m
Stream Ciphers - Linear Feedback Shift Register (LFSR)
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Goal is less and/or low power hardware
Block Ciphers – Data Encryption Standard (DES)
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Proposed by IBM at 1974
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With input from NSA
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From 1977 to 1998 it is used as US standard
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Insecure today (key too short)
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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
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Have X16 round
Advanced Encryption Standard (AES)
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1997 call for AES by NIST
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Aug 1998 15 algorithms submissions
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Aug 1999 5 finalist are selected
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October 2000 Algorithm called Rijndael choosen as AES
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Is now most important symmetric algorith in the world
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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
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Deterministic
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
ECB (Electronic Code Book)
Probabilistic
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Block cipher - CBC
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Stream cipher
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OFB (Output Feedback Block)
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CFB (Cipher Feedback Block)
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Counter mode
Electronic Code Book (ECB)
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simply repeats the AES encryption process
for each 128-bit block of data
For decryption, the process is reversed.
Electronic Code Book (ECB)
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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)
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
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)
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A close relative of CBC, makes a block cipher into a self-synchronizing stream cipher.
Output feedback (OFB)
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The output feedback (OFB) mode makes a block cipher into a synchronous stream cipher.
Counter (CTR)
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


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)
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
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
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The scheme was first published by Whitfield Diffie and Martin Hellman in 1976

Bases on discrete logaritm problem
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Easy to perform
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Hard to reverse
DH Key exchange
Eve
Alice
Bob
DH Key exchange
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p: prime modules

g: generator (should be prime)
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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