JRRG PRUQLQJ, PB QDPH LV UREHUW...
Transcript of JRRG PRUQLQJ, PB QDPH LV UREHUW...
5/12/2014 1
JRRG PRUQLQJ, PB QDPH LV UREHUW FDPSEHOO
5/12/2014 2
Cryptology: Past & Present
Robert Campbell
Aka Two Millenia in 60 Minutes
5/12/2014 3
Caesar Cipher
Choose a key between 0 and 25
“Add” the key to each letter
DOO JDXO LV GLYLGHG - FDHVDU
ABCDEFGHIJKLMNOPQRSTUVWXYZ
key=3 ALL GAUL IS DIVIDED - CAESAR
Attacks:
- Exhaust – only 26 key choices
- Crib – Guess signature
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Monoalphabetic Subst
Create a mixed alphabet:
Encrypt:
ABCDEFGHIJKLMNOPQRSTUVWXYZ
WASHINGTOBCDEFJKLMPQRUVXYZ
THIS MESSAGE IS ENCRYPTED
QTOP EIPPWGI OP IFSMYKQIH
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Monoalphabetic (cont)
Key Size = 26! = 26*25*...*3*2*1 =
403,291,461,126,605,635,584,000,000
Attacks:
Crib – Guess a word
Statistics – ETNORIAS
Guess and fill out N OZET TFXIACSTU SONV GTVVZPT RVNFP Z ITETIVTU
ZHCOZYTS ZFU SOT JTAKDIU KZHJTIVENHHT
I OZET TFXIACSTU SONV GTVVZPT RVNFP A ITETIVTU
ZHCOZYTS ZFU SOT JTAKDIU KZHJTIVENHHT
I OAET TFXIACSTU SOIV GTVVAPT RVIFP A ITETIVTU
AHCOZYTS AFU SOT JTAKDIU KAHJTIVEIHHT
I OAET TNXIACSTD SOIV GTVVAPT RVINP A ITETIVTD
AHCOZYTS AND SOT JTAKDID KAHJTIVEIHHT
I OAEE ENXIACSED SOIV GEVVAPT RVINP A IEEEIVED
AHCOZYES AND SOE JEAKDID KAHJEIVEIHHE
ABCDEFGHIJKLMNOPQRSTUVWXYZ
Z UT N F
I HAVE ENCRYPTED THIS MESSAGE USING A REVERSED
ALPHABET AND THE KEYWORD WALKERSVILLE
ABCDEFGHIJKLMNOPQRSTUVWXYZ
ZYXUTQPONMJHGFDCBIVSREKLAW
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Solving Monoalphabetic
Al-Kindi, 801-873 AD, Iraq
“A Manuscript on Deciphering
Cryptographic Messages”
Frequency Analysis
Black Chambers
France – Rossignol (1600’s)
England – Wallis (1600’s)
Austria – 1700’s
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Letter Counts
Gettysburg Address
FOURXSCOREXANDXSEVENXYEARS
XAGOXOURXFOREFATHERS…
ETNORIAS
Letter Frequencies
Ciphers & Frequencies
Caesar
Monalphabetic
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Breaking the Pattern I
Encrypt each letter differently
Polyalphabetic ciphers
Vigenere Cipher
Stream & Machine Ciphers
ENIGMA
SSL/RC4
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Polyalphabetic - Vigenère
Vigenere – Simple Polyalphabetic
Choose a key word
“Add” the key word to the plain
THISXSIMPLEXMESSAGEXISXENCRYPTEDXWITHXVIGENERE
CATCATCATCATCATCATCATCATCATCATCATCATCATCATCATC
VHBUXLKMINEQOELUAZGXBUXXPCKAPMGDQYIMJXOKGXPEKG
A+C=C
B+C=D
A+A=A
B+A=B
A+T=T
B+T=U
Add mod 26
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Vigenère (cont)
Key size = 26*26*...*26=26len
Attacks:
Recover keyword length
Statistical
Crib
Guess and fill out
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Vigenere w/ Keyword DO Vigenere w/ Keyword DONUT
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Babbage/Kasiski Attack I ZAWOKSXGONMXLDNYQPARTQSJPXRDPRJQKEGNQHDRDOWCRTXFAKIBDDRXQLSUO
ESTGNXFAKGKSTIKKMTSKPLHRZMSNKLKSMHKGQUKVKCLRXMWAFDTGTNDPVKYKQ
KAKYXSTGNXGAKVKCLRXMWAFDPVAADMVAKIBDDRXQWOKVNHTBTQOTJOWHDKUYL
BVBXLWFDMVAKQXMSBXWLDNYQTEIKQZAGZXFO
ZAWOKSXGONMXLDNYQPARTQSJPXRDPRJQKEGNQHDRDOWCRTXFAKIBDDRXQLSUO
ESTGNXFAKGKSTIKKMTSKPLHRZMSNKLKSMHKGQUKVKCLRXMWAFDTGTNDPVKYKQ
KAKYXSTGNXGAKVKCLRXMWAFDPVAADMVAKIBDDRXQWOKVNHTBTQOTJOWHDKUYL
BVBXLWFDMVAKQXMSBXWLDNYQTEIKQZAGZXFO
LDNY 190
XFAK 20
IBDD 105
STGN 65
KVKC 35
DMVA 40
GCD = 5
So key is 5 chars (probably)
ZAWOKSXGONMXLDNYQPARTQSJPXRDPRJQKEGNQHDRDOWCRTXFAKIBDDRXQLSUO
ESTGNXFAKGKSTIKKMTSKPLHRZMSNKLKSMHKGQUKVKCLRXMWAFDTGTNDPVKYKQ
KAKYXSTGNXGAKVKCLRXMWAFDPVAADMVAKIBDDRXQWOKVNHTBTQOTJOWHDKUYL
BVBXLWFDMVAKQXMSBXWLDNYQTEIKQZAGZXFO
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Babbage/Kasiski Attack II ZAWOKSXGONMXLDNYQPARTQSJPXRDPRJQKEGNQHDRDOWCRTXFAKIBDDRXQLSUO
ESTGNXFAKGKSTIKKMTSKPLHRZMSNKLKSMHKGQUKVKCLRXMWAFDTGTNDPVKYKQ
KAKYXSTGNXGAKVKCLRXMWAFDPVAADMVAKIBDDRXQWOKVNHTBTQOTJOWHDKUYL
BVBXLWFDMVAKQXMSBXWLDNYQTEIKQZAGZXFO
K 11%
D,X 7%
A 6%
Q,T 5.6%
Alpha 1
D,X 14%
K 12%
Alpha 2
Q 23%
X 19%
K,M 12%
Alpha 3
L,S 14%
W 12%
V 9%
Alpha 4
A 26%
T 16%
D 14%
Alpha 5
K 26%
R 21%
N,G 9%
ZHBLXSELLAMEQAAYXUXETXXGCXYIMEJXPBTNXMAEDVBZETEKXXIIIAEXXQPHO
LXQTNEKXXGRXQVKRRQFKWQEEZTXKXLRXJUKNVRXVRHIEXTBXSDALQADWAHLKX
PXXYEXQTNELXXVRHIEXTBXSDWAXNDTAXXIIIAEXXBLXVUMQOTXTQWODMAXUFQ
YIBEQTSDTAXXQERPOXDQAAYXYBVKXEXTZEKL
Guess #1:
Spacers (X) are: X, Q, S, A, K
Keyword is ATVDN
Guess #2:
Spacers (X) are: D, Q, L, A, K
Keyword is GTODN
THILXMESLAGEXAASXBXENXEGCRYPMEDXWBTHXTAEXVIZENERXXCIPAERXXPHI
LEQTHERXXAREQVERYQFEWXEETTEKXFREJUENCRXPROIERTIXSXASQAXWHHLEX
WXXSEEQTHESXXPROIERTIXSXWHXNXTHXXCIPAERXILXPUTQONXAQWIDTAXOFX
YIVEXTSXTHXXKEYPORDXAASXFBVEXLXTTERL
THIL_MESLAGE_AAS_BXEN_EGCRYPMED_WBTH_TAE_VIZENERX_CIPAER__PHI
LEQTHERX_AREQVERYQFEW_EETTEK_FREJUENCR_PROIERTIXS_ASQA_WHHLE_
WX_SEEQTHESX_PROIERTIXS_WHXN_THX_CIPAER_IL_PUTQON_AQWIDTA_OF_
YIVE_TS_THX_KEYPORD_AAS_FBVE_LXTTERL
THIS_MESSAGE_HAS_BEEN_ENCRYPTED_WITH_THE_VIGENERE_CIPHER__WHI
LE_THERE_ARE_VERY_FEW_LETTER_FREQUENCY_PROPERTIES_AS_A_WHOLE_
WE_SEE_THESE_PROPERTIES_WHEN_THE_CIPHER_IS_PUT_ON_A_WIDTH_OF_
FIVE_AS_THE_KEYWORD_HAS_FIVE_LETTERS
Solution:
Spacers (X) are: D, Q, L, T, K
Keyword is GTOWN
Alpha 1
D,X X,R
K E
Alpha 2
Q X
X E
K,M R,T
Alpha 3
L,S X,E
W I
V H
Alpha 4
A E
T X
D H
Alpha 5
K X
R E
N,G A,T
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Breaking the Pattern II
Use several letters per encryption
Digraphic
Hill’s Cipher
Playfair Cipher
Codebooks
DES, AES, et al
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Playfair
Digraphic cipher
2-letter blocks encrypt to 2-letter blocks
Confuses letter counts (monographics)
To Encrypt:
Both letters on same row - move right
Both in same column - move down
Otherwise - Opposite corners, same row
Example:
WH EA TS TO NE DE SI GN ED IT
AQ HP NT NQ UN IM NC EO MI DN
P L A Y F
I R B C D
E G H K M
N O Q S T
U V W X Z
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Polyalphabetic (alt view)
Another way of looking at it:
SAGEXISXENCRYPTEDXWITHXVIGENERE
+
CATCATCATCATCATCATCATCATCATCATC
VHBUXLKMINEQOEL
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Machine Ciphers
A Vigenere cipher with a long keyword
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Enigma
German military & police, 1930-45
Daily Key = 15896255521782636000 ~ 264
Total Key ~ (112 digits) ~ 2372
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Enigma: Basic Design
A
S
D
F
A
S
D
F
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Enigma - Key Space
Rotor Choice & Order: 6, 60, 1680
Rotor Wiring: 26! = 288.4 (27 digits)
Ring Settings: 263 = 17576 = 214.1
Plug/Stecker Settings: 150738274937250 = 247.1 (14 digits)
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Enigma: Attacks
Polish Work - 1930’s
Recovered wheel wiring from cipher
Bombe
British Work - 1940’s
Turing-Welchman bombe
Production scale recoveries
Rotor wiring - captures
Settings - bombe
Pluggings - crib loops &
diagonal board
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Codebooks, Playfair & Electronic Codebooks
P L A Y F
I R B C D
E G H K M
N O Q S T
U V W X Z
EA
HP
DES
This_is_
T@3a*bA1
AES
Now_is_the_time_
A#$0an^a]ci21+Ea
Codebook
X
Retreat
AB2236
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DES: Data Encrypt Standard
Developed by IBM
Adopted by NIST for Govt
Released 1976
64 bit (8 char) blocks
56 bit key space ~ 72057594037927936
1000 years on 1 GHz Pentium (very roughly)
3 days on EFF “Deep Crack” (1998)
No other (known) effective attacks
5/12/2014 24
AES: Advanced Encryption
Rijndael developed by Daemen & Rijmen
Catholic Univ of Leuven, Belgium
Adopted as AES by US Govt (2000)
128 bit (16 char) blocks
128 bit key space ~ 340282366920938463463374607431768211456
4722366482869645213696000 years on 1GHz Pentium
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Public-Private Keys
Key has two parts: Public & Private
Anyone can encrypt with the Public Key
Only owner has Private key to decrypt
RSA (1977) - Factoring
El Gamal (1985) – Discrete Logarithm
(1973)
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Diffie-Hellman
Key Agreement
Developed 1976 by Diffie, Hellman & Merkle
Based on “Discrete Logarithm” problem:
Computing gx(mod p) is easy
Given y, finding x so that y= gx(mod p) is hard
Developed by Malcolm Williamson, GCHQ, 1975
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Diffie-Hellman (cont)
Agree (openly) on g, p Say g=2, p=101
Choose secret xA, say xA = 37
Compute yA=gxA=237=55 (mod 101)
Alice Bob
Charlie
Choose secret xB, say xB = 15
Compute yB=gxB=215=44 (mod 101)
yA=55 yB=44
Compute yBxA=4437=69 (mod 101) Compute yA
xB=5515=69 (mod 101)
So the shared secret is 69
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WWW – An example
Go to an SSL-encrypted site
e.g. https://www.fortify.net/sslcheck.html
Little lock appears in browser
What Happened?
Server sent its public keys (certificate)
You used them to send key to server
Communicate, encrypted w/ shared key
Alice
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References (Selected)
- The Code Book, S. Singh, 1999
- The Codebreakers, D. Kahn, 1967 (2nd Ed, 1996)
- Codes and Ciphers, Churchhouse, 2001
- Elementary Cryptanalysis: A Mathematical Approach, A. Sinkov, 1966
- Making, Breaking Codes: An Introduction to Cryptology, P. Garrett
- Basic Cryptanalysis, http://www.fas.org/irp/doddir/army/fm34-40-2/
- Handbook of Applied Cryptography, Menezes, van Oorschot & Vanstone, 1996 http://www.cacr.math.uwaterloo.ca/hac/
- Wikipedia, http://en.wikipedia.org/wiki/Cryptography
- These Slides, http://www.umbc.edu/~rcampbel/MEPP/Cryptology
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Backup Slides
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Is E more common than T?
20 chars 100 chars
1000 chars
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Overview
Past
Substitution Ciphers
Permutations
Machine Ciphers
Present
Codebooks: DES & AES
Public Key
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Depth Reading
What if a very long keyword is used?
Book cipher
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Conclusions
Modern Cryptography can be used by
anyone, but…
Without some understanding, it can be
abused by anyone
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Permutation Ciphers
Rail-fence: TIIAALECCPEHSSRIFNEIHR
Used together with ciphers
Codes
Navajo code:
Ship = TOH-DINEH-IH
September = GHAW-JIH
JN-25 (Japanese Navy) Code:
SUBMARINE = 97850
Other Classical Crypto
TIIAALECCPE
HSSRIFNEIHR
T I I A A L E C C P E
H S S R I F N E I H R THISISARAILFENCECIPHER
5/12/2014 36
Enigma Details
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Cycles in Permutations ABCDEFGHIJKLMNOPQRSTUVWXYZ
WASHINGTOBCDEFJKLMPQRUVXYZ PWASH =
ABCDEFGHIJKLMNOPQRSTUVWXYZ
VWXYZBURLINGTOACDEFHJKMPQS PB5 =
GG and FNF and CSPKC
(AWVURMEIOJB)(DHTQL)(CSPK)(FN)(G)(X)(Y)(Z)
(BWMTHREZSF)(AVKNO)(GUJIL)(CXP)(DYQ)
G
G
F
N
N
F
C
S
S
P
P
K
K
C
Cycles of length 11, 5, 4, 2, 1, 1, 1 and 1
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Cycles in Permutations ABCDEFGHIJKLMNOPQRSTUVWXYZ
WASHINGTOBCDEFJKLMPQRUVXYZ PWASH =
(AWVURMEIOJB)(DHTQL)(CSPK)(FN)(G)(X)(Y)(Z)
ABCDEFGHIJKLMNOPQRSTUVWXYZ
VWXYZBURLINGTOACDEFHJKMPQS PB5 =
(BWMTHREZSF)(AVKNO)(GUJIL)(CXP)(DYQ)
ABCDEFGHIJKLMNOPQRSTUVWXYZ
MVFRLOUHAWXYZBINGTCDEJKPQS PB5 PWASH =
(AMZSCFOI)(BVJWKXPN)(ELYQGU)(DRT)(H)
P-1WASH PB5 PWASH =
ABCDEFGHIJKLMNOPQRSTUVWXYZ
RWNUQIVDBAXYZJEFGHKLMOPSTC (ARHDUMZCNJ)(BWPFI)(EQGVO)(LYT)(KXS)
5/12/2014 39
Cycles in Enigma
Given cycle type of Enigma permutation
Try all the 6*26*26*26 wheel settings
Check the cycle type
If it matches, we found wheel setting
Then pluggings are just monoalphabetic
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Indicators & Cycles
Message Indicators:
Start with a fixed daily setting
Choose random “indicator”: (i1i2i3) AQP
Encrypt it: AQPAQP YALSWY
See many examples over day:
p1: i1Y and p4: i1S, so p4 p1: YS
Also p5 p2: AW and p6 p3: LY
From SJEZSX get p4 p1: SZ, etc
Eventually, get p4 p1: [7,5,5,3,3,2,1]
5/12/2014 41
Enigma: Crib Loops
Encryption: P*W(t)*P
Guess a crib
Find a “loop”: ABCA
P*W(1)*P*P*W(2)*P*P*W(3)*P = Id
W(1)*W(2)*W(3) = Id
Example:
ZMGERFEWMLKMTAWXTSW - cipher
OBERKOMMANDODERWEHR - crib
AMEA (in W(9)*W(7)*W(14))
5/12/2014 42
References - Enigma
Enigma, W. Kozaczuk, 1984 – Technical
details in appendices
Seizing the Enigma, D. Kahn, 1991 – History
of Naval Enigma
http://www.codesandciphers.org.uk/enigma/
http://en.wikipedia.org/wiki/Enigma_machine
Enigma Notes, A. Biryukov
[http://www.wisdom.weizmann.ac.il/~albi/cryptanalysis/lectures.htm]
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Public Key
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Public Key aka Non-Secret Encryption
The Key Management Problem
Agree on a secret key without meeting
The digital signature problem
How do I know this is from him?
Generally based on “hard” problem
Factoring Problem
Discrete Logarithm Problem
5/12/2014 45
Public-Key Developing the Concepts
Diffie & Hellman - New Directions in
Cryptography, Nov 1976
Merkle - Secure Communications over
Insecure Channels, 1975-78
Ellis – The Possibility of Non-Secret
Encryption, Jan 1970
Bell Labs - Final Report on Project C43,
October 1944
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Public-Key Concepts One-Way Functions
One-Way Function:
Computing y=F(x) is “hard”
Computing x=F-1(y) is “easy”
Trap-Door Function:
Computing y=F(x) is “hard”
Unless, you know some secret S, in which case
computing y=F (x) is “easy”
Example: Table lookup is easy, reverse lookup
is hard
Need good definition of “easy” and “hard”
5/12/2014 47
RSA Choose secret primes p, q
Compute public modulus N= pq
Choose public encrypt exponent e
Compute secret decrypt exponent:
d=e-1(mod (p-1)(q-1))
Secret Key = {d}
Alice Bob Charlie
Choose secret (plaintext) message, P
Encrypt message: C = Pe (mod N)
Public Key = {N,e}
Encrypted Message = C
Compute Cd (mod N)
Note that the result is P
So the secret message, P, has
been passed from Bob to Alice
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RSA Worked Example Choose secret primes p=17 q=23
Compute modulus N= pq=391
Choose encrypt exponent e=3
Compute secret decrypt exponent:
d =e-1(mod (p-1)(q-1)) = 3-1 (mod
(17-1)(23-1)) =3-1(mod 351) = 235
Secret Key = {d=235}
Alice Bob Charlie
Choose secret message, 10
Encrypt message: C = Pe (mod N) =
103 (mod 391) = 218
Public Key = {391,3}
Encrypted Message = 218
Compute Cd (mod N) = 218235 (mod 391)
Note that the result is P = 10
So the secret message, P=10, has
been passed from Bob to Alice
5/12/2014 49
Modular Arithmetic
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Modular Arithmetic I
Binary Arithmetic (mod 2)
Addition:
Even + Even = Even [0 + 0 = 0 (mod 2)]
Even + Odd = Odd [0 + 1 = 1 (mod 2)]
Odd + Odd = Even [1 + 1 = 0 (mod 2)]
Multiplication:
Odd * Odd = Odd [1 * 1 = 1 (mod 2)]
Even * Odd = Even [0 * 1 = 0 (mod 2)]
Even * Even = Even [0 * 0 = 0 (mod 2)]
Division:
Odd/Odd = Odd [1/1 = 1 (mod 2)]
Even/Odd = Even [0/1 = 0 (mod 2)]
Anything/Even = ??? [X/0 = ? (mod 2)]
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Modular Arithmetic II
Arithmetic mod 101 (Note: 101 is prime) Addition:
35 – 56 = -21 = 80 (mod 101)
Multiplication: 23 * 52 = 1196 = 85 + (11 * 101) = 85 (mod 101)
Division: 85/23 = 52 (mod 101) (as 23*52 = 85)
(Extended Euclidean Algorithm)
Exponentiation: 534 = 88 (mod 101)
Russian Peasant Algorithm: • 52 = 25
• 54 = (52)2 = (25)2 = 625 = 19
• 58 = (54)2 = (19)2 = 361 = 58
• 516 = (58)2 = (58)2 = 3364 = 31
• 532 = (516)2 = (31)2 = 961 = 52
• So 534 = (52+32) = (52)(532) = (25)(52) = 1300 = 88 (mod 101)
5/12/2014 52
Modular Arithmetic III
Arithmetic mod 26 (Note: 26 = 2*13) Addition:
25 + 5 = 30 = 4 (mod 26)
10 – 22 = -12 = 14 (mod 26)
Multiplication: 5 * 12 = 60 = 8 + (2 * 26) = 8 (mod 26)
6 * 13 = 78 = 0 + (3 * 26) = 0 (mod 26)
(Product of non-zeros can be zero)
Division: 12/5 = 18 (mod 26) (as 5*18 = 12)
21/2 = ?? (mod 26)
(Can’t divide by any multiple of 2 or 13)
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Fast Exponentiation I
Compute 232(mod 41) Hard Way:
Compute 232, then reduce mod 41
232 = 2*...*2= 4294967296 = 37 (mod 41)
Better:
Reduce at each step
2*2*2*2*2*2 = 64 = 23 (mod 41)
23*2 = 46 = 5 (mod 41) … etc
Best (almost):
232(mod 41) = (((((22)2)2)2)2) (mod 41)
5/12/2014 54
Fast Exponentiation II Russian Peasant Arithmetic
Compute 337 (mod 51) Note: 37 = 1001012
37 = ((((((1)2+0)2+0)2+1)2+0)2+1)
So 337 = 3(((((2)2)2+1)2)2+1)
= (((((3)2)2)2)*3)2)2*3)
So ….
(3)2 = 9, then ((3)2)2 = 92 = 81 = 30
((((3)2)2)2) = 302 = 900 = 33 ((((3)2)2)2)*3 = 33*3 = 99 = 48
(((((3)2)2)2)*3)2 = 482 = 2304 = 9
((((((3)2)2)2)*3)2)2 = 92 = 81 = 30
((((((3)2)2)2)*3)2)2*3) = 30*3 = 90 = 39
5/12/2014 55
Hill Cipher
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Hill’s Cipher
Matrix Multiply: C = P*M (mod 26)
21
32M
Example:
HI LL CI PH ER
(7,8)(11,11)(2,8)(15,7)(4,17)
(22,37)(33,55)(12,22)(37,59)(25,46)
(22,11)(7,3)(12,22)(11,7)(25,20)
WL HD MW LH ZU
26mod
225
2321
-M
5/12/2014 57
A Toy Hill
C = aP + b (mod 26)
Example: a = 3; b = 2
AXHILLXCIPHERXTOY
CTXAJJTIAVXOBTHSW
e.g. X23
so (3)(23)+2=71-(2)(26)=19 (mod 26)
And 19T
Problems?
If a=6; b=5 then AF and NF
If a=13; b=3 then AD, CD, ED, …
Why?
5/12/2014 58
Breaking Hill Given a Crib …
Cipher: WL HD = (22,11)(7,3)
Plaintext guessed: HI LL = (7,8)(11,11)
wz
yxM
26mod1111
87
37
1122
wz
yx
PMC
Get Equations:
22 = 7x + 8z (mod 26)
11 = 7y + 8w (mod 26)
7 = 11x + 11z (mod 26)
3 = 11y + 11w (mod 26)
Solve: x=2; y=3; z=1; w=2
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Vigenere w/ Keyword DONUT
Hill Cipher
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Topics in Crypto & Math
Combinatorics
Statistics
Group Theory
Algebra
Number Theory
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Combinatorics
Keyspace of a scrambled alphabet
How many ways can I scramble a 26-letter alphabet?
26! = (26)(25)(24)…(3)(2)(1) = 403,291,461,126,605,635,584,000,000
Keyspace of the Enigma
Choosing Wheels
Example: 3 Wheels out of 5 – (5)(4)(3) = 60
Steckerboard Keyspace
Example: 5 Cables – (26)(25)(24)(23)(22)(21)(20)(19)(18)(17)/((25)(5!)) = 6425074656
5/12/2014 62
Statistics
Language Statistics
Monographic: ETNORIAS
Digraphic: QU, ED, etc
Statistical Tests
f-Test – Test for Monoalphabetic
2-Test
IC (Index of Coincidence) Test
5/12/2014 63
Group Theory
Permutation Groups
Enigma
Bombe Cribs & Loops – Cycle structure
is constant in a conjugacy class.
5/12/2014 64
Algebra
Cribs
Cipher = Plain + Key
If we see Cipher and can guess Plain
Then we recover Key = Cipher - Plain
Diffie-Hellman Public Key
(ga)b = (gb)a
Hill Cipher
C = MP
Given a crib, solve as a linear system
5/12/2014 65
Number Theory
Diffie-Hellman
RSA Public Key
Fermat’s Little Thm & the f-Function
Finite Fields
Used in AES construction