1. Cryptography Kρύπτω (kryptos)– Hidden Secret writing
The message is not hidden
Encrypt
Change information from one form to another to hide its meaning
It is the conerstone of security

2. Threats
to a
message

3. Message
Message
Alice
Bob

4. Eavesdropping
Message
Alice
Bob
Eve

5. Interception
Message
Alice
Mallory
Bob

6. Modification
Message
Message
Alice
Mallory
Bob

7. Fabrication
Alice
Bob
Message
“Alice”

8. Basic Idea Encryption Plaintext Ciphertext Decryption Ciphertext
This the
Infromation
Security class in
Monterrey Tech
Encryption
Esta es la clase
De Seguridad
Informática en
El Tecnológico
De Monterrey
Plaintext
Ciphertext
Esta es la clase
De Seguridad
Informática en
El Tecnológico
De Monterrey
Decryption
This the
Infromation
Security class in
Monterrey Tech
Ciphertext
Plaintext

9. Consistency equation (symmetric ciphers)
E(k,m)
m=D(k,E(k,m))
D(k,E(k,m)) m

10. Basic principles of security
Confidentiality
Privacy, secret messages
Integrity
Message does not change in transit
Availabilty
Authentication
Validate identity of
Non-repudiation
Sender cannot deny sending the message
Receiver cannot deny receiving the message

11. Scytale (700 A de C)

12. Cesar (ROT 3)
n = 3
50 AC

13. ROT 13
n = 13

14. PigPen cipher (18th century)

15. Frequency analysis English Spanish
Problema con cifradores de sustitución monoalfabéticos

16. Mary Queen of Scots

17. Frequency analysis

18. Polyalphabetic cipher
Leon Alberti 1460s
Proposed the use of multiple alphabets to cipher a single message
Blaise de Vigenère 1586
He is credited with the implementation of the ideas of Alberti

19. Example ABCDEFGHIJKLMNOPQRSTUVWXYZ DEFGHIJKLMNOPQRSTUVWXYZABC
Original alphabet
DEFGHIJKLMNOPQRSTUVWXYZABC
Cipher alphabet 1
NOPQRSTUVWXYZABCDEFGHIJKLM
Cipher alfabet 2
JAVAXJALA
Plain text:
MDYDAMDOD
Cipher text with alpahbet 1
MNYNAWDYD
Cipher text with the two alpahbets

20. Vigenère cipher

21. “One-time Pad” Te perfect cipher
The key is a random sequence of numbers
Key and message haver the same length
Use to fight the frequency analysis
Two problems
Absolute synchronization between sender and receiver
Number of keys is limited (distribution)

22. Enigma

23. Ciphers
Private
key
Public
key

24. General ci = E(pi,n) = pi + n mod 26 Substitution Ciphers
Each character is changed (substituted) by another character or symbol
A → C, B → D,
Cesar ci = E(pi) = pi + 3
General
ci = E(pi,n) = pi + n mod 26

25. Monoalphabetic Cipher
Each letter in the plaintext is changed by the the same letter in the ciphertext
Using 3 as the key
ABCDEFGHIJKLMNOPQRSTUVWWXYZ
defghijklmnopqrstuvwwxyzabc
using “palabra” as the key
palbrcdefghijkmnoqstuvwwxyz

26. Polialphabetic Cipher
A letter in the plantext can be replaced by a different letter in the ciphertext
Vigenère:
C = P + K mod 26
Usando “secreto” como llave
Plaintext: ESTEMENSAJEESFACIL
Key: secretosecretosecr
Ciphertext: wwvvqxbkelviltsgkc

27. Transposition Cipher
The symbols do not change they are just rearrenged
SECURITY → ITRUCYES
PERMUTATIONS
Transposition by columns
ESTEM
ENSAJ
EESMA
SDIFI
CILDE
DESCI
FRARA
EEESC DFSNE DIERT
SSILS AEAMF DCRMJ
AIEIA

28. Stream and block ciphers

29. A secure encryption algorithm
Based in solid mathematical principles
Cryptographers
Analized by competent people
Cryptoanalists
It has endured through time
Basic principles:
Confusion
Diffusion

30. Principles
Confusion
Non evident relationship between plaintext/key/ciphertext
What happens if I change one symbol in the plaintext. The change in the ciphertext cannot be predicted
Avoid clear patterns
Diffusion
Spread the information of the plaintext over the entire ciphertext
The interceptor requires access to much of the ciphertext to deduce the algorithm

31. Stream and block ciphers
(+) Good speed of transformations
(+) Loe error propagation
(-) Low diffusion
(-) Susceptible to malicious insertions
Bloques
(+) High diffusion
(+) Inmunity to malicious insertions
(-) Slow in the process of encryption
(-) High proagation of errors

32. The cryptographer's dilemma
“An encryption algorithm must be regular for it to be algorithmic and for cryptographers to be able to remember it. Unfortunately, the regularity gives clues to the cryptoanalyst”

33. Crytographic algorithms
The majority uses binary arithmetic
Easier to handle
Fast to process
Everything is digital anyways!

34. DES (Data Encryption Standard)
1973: NBS (now NIST) calls for the design of a commercial algorithm
Public use
NSA was involved.....discretely
“Intentional weaknesses” (?)
Small keys (56 bits) y blocks of 64 bits
IBM gets in with Lucifer
Horst Feistel algorithm, developed in the early 70s in IBM
Block cipher with private key (symmetric)
Originally the keys and the bolcks were 128 bits
German inmigrate, 1934
1976: NBS adopts IBM cipher as the industry standard
1997: It is successfully attacked (brute force)
2000: NIST changes to AES

35. DES Block cipher Operates on 64 bits blocks of data 64 bits key
But the “real” length is 56 bits
8 bits are used as parity bits
16 rounds of subtstitutions and permutations determined by S-Boxes and P-Boxes
The same algorithm for decrytion

36. DES general structure IP: Initial Permutation FP: Final Permutation
IP y FP are inverse
Operates over 64 bits blocks
F: Feistel function

38. Initial Permutation (IP)

39. Feistel Function Expansion and Permutation S box (Substitution)
One (different) for each
Round. “key schedule”
48 bits
S box (Substitution)
6 bits input
4 bits output
32 bits

40. Feistel Function

41. Expansion Function (E)

42. S-Boxes (substitution)

43. S1
Input:
Row: 1yyyy Column: x0110x
Output: 0010 (2)

44. Permutation (P)

45. Key schedule PC1 (Permuted Choice 1) 64 bits to 56 bits Permutation
2 halves of 28 bits
Independently rotated
1 or 2 positions
PC2 (Permuted Choice 2)
56 bits input
48 bits output

46. 64 bits 56 bits 28 bits 28 bits 1 or 2 positions 1 or 2 positions

47. Permutated Choice 1 (PC-1)

48. Rotations in the Key schedule

49. Permutated Choice 2 (PC-2)

50. Final Permutation (FP)

51. FP = IP-1

53. Double DES
E(k2, E(k1,m))
Encrypt the message twice with two different keys
Key of 112 bits (?)
It does not give more security
257 = 2*256 brute force attack
“meet in the middle” attack

54. Triple DES C = E(k3,D(k2, E(k1,m))) Keys of 168 bits (?)
Equivalent to 118 bits keys.
Variation of triple DES
C = E(k1,D(k2, E(k1,m)))
Equivalent 80 bits keys
90 bits keys are good enough now

55. DES security under scrutiny
The design criteria were never made public
Many thought NSA “installed” a “backdoor”
NSA modified the S-boxes
Walter Tuchman working for IBM in a modified version of Lucifer. Then NSA brought him to work with them
The size of the key was small. Rumor has it NSA influenced in this
NSA wanted a 48 bits key

56. DES security under scrutiny
Up to this day. An intentional weakness has not been discovered. And it has been test a lot!
In 1990 Eli Biham and Adi Shamir published a method to break block ciphers (differential cryptanalysis).
The S-Boxes of DES were very resistance to the attack
"It took the academic community two decades to figure out that the NSA 'tweaks' actually improved the security of DES." Bruce Schneier
The biggest threat is brute force attacks

57. DES survival 1977: Diffie and Hellman
Proposed a machine which could break DES in a day
$20,000,000 US
1993: Wiener
Proposed a machine to find the key in 7 hours
$1,000,000
None of them were implemented
At leas publicly

58. DES survival 1997: RSA Security offer $10,000 to the first place
Project DESCHALL won using Internet in 3 months
“DESCHALL Project”. Wikipedia
1998: “Deep Crack” machine from EFF
$250,000 US machine broke DES in 56 hours
"There are many people who will not believe a truth until they can see it with their own eyes. Showing them a physical machine that can crack DES in a few days is the only way to convince some people that they really cannot trust their security to DES."
“EFF DES cracker”. Wikipedia
2006: COPACOBONA
Two universities from Germany, $10,000 US machine
120 FPGAs
7 days
In 2008 they reduced the time to less than one day

59. AES (Advanced Encryption Standard)
1997: NIST published RFP
1999: 5 finalists
2001: They chose Rijndael
Invented by Vincent Rijmen y Joan Daemen, originaly called Rijndael (“raindel”)
Official government standar since may of 2002
Private key algorithm (symmetric)
128 bits blocks and keys of 128, 192 ó 256 bits
9, 11 ó 13 rounds of substitutions, rotations and mixing of bits, depending on the size of the key

60. AES in action

61. Keys distribution
DES and AES solved the problem of standardization and allowed businesses (banks) to use cryptography
The problem is:
How do I send the key before starting a ciphered communication
Having an adequate scheme requires resources (money)
A bank has thousands of clients, a different key for each one of them
And renew the key periodically
COMSEC distributes keys in USA

62. Keys handling C1 C2
K12
K13
K23
K14
K23 C3 C4
K34
Each user n-1 keys

63. A better solution C1 C2 K1 K2 TTP (Trusted Third Party) K4 K3 C3 C4
E(K1, “1,2”||K12)
E(K2, “1,2”||K12)
Ticket
Each user needs only ONE key

64. Key distribution Might seem a trivial problem
But soon became an unmanageable situation
Later on it was claimed an unsolvable problem
Typical “Catch 22” situation
… until mid 70s

65. God rewards fools
Ralph Merkle, Martin Hellman and Whitfield Diffie

66. Whitfield Diffie
Born in 1944, 1995 MIT Math graduate
Martin Hellman
Born in 1945, 1969 Stanford PhD
Ralph Merkle
1977 Stanford PhD

67. Sending a secret message
¿Y la llave?
Alice
Bob

68. Sending a secret message without previous key exchange
Alice
Bob
Alice
Bob
Alice
Bob

69. Sending a secret message without previous key exchange
It works in theory, but not in cryptography
The one which gets encrypted last is the first to get decrypted
In cryptography the order is vital
It did not work!!!!
But......
It fed the inspiration.....

70. Merkle puzzles Problems that can be solved with some effort
Find the key of a symmetric cipher (ej. 32 bits)
Puzzle(p) = E(p, “message”)
Brute force attack
232 attempts at the most

71. Merkle puzzles Alice Bob prepare 232 puzzles
For each puzzle she chooses a random key pi (i= )
Puzzle i = E(pi, “Puzzle # ri” || ki)
Keeps the 232 mappings (ri, ki)
Sends all 232 puzzles to Bob
Bob
Chooses one puzzle at random an solves it (brute force)
Get (rj, kj)
Send rj to Alice
Uses kj as a common key
Alice: Prepare n puzzles 232 O(n)
Bob: Solve one puzzle 232 O(n)
Attacker: O(n2)

72. Functions Bidirectional Y = 2*X X = 2/Y Unidirectional
One way function
Easy to do, but really hard to undo (impossible)
Paint color mixing, break an egg, Lock
Modular arithmetic

73. Modular and exponential arithmetic
We can solve it by trial and error
If the results grows so does the x
If the result is 81 and we test x=5 → 243, x is too big
With normal arithmetic we can say if we are getting closer or not
With modular arithmetic we CAN NOT
3x mod 7 x 3x
3xmod

74. Hellman-Diffie-Merckle
gx mod p
p and g known by both
ga mod p
gb mod p
(gb mod p)a mod p
(ga mod p)b mod p
gba mod p
gab mod p
In practice g is 2, 5 or 7. a, b y p need to be big

75. Hellman-Diffie-Merckle?
ga mod p
gb mod p
(gb mod p)a mod p
(ga mod p)b mod p
gba mod p
gab mod p

76. Key exchange It was a giant step But it had some drawbacks
Alice y Bob have to be “on-line” simultaneously in order to exchange messages
They kept on working
In 1975 Diffie conceived a cypher with asymmetric key → two keys
One to encrypt and a different to decrypt

77. Public key Two keys One of them has to be made public
The other, private. Only known by the owner
A secure channel is not needed
More computer power is needed
10,000 times slower than private key

78. Public key Both keys belong to the same “person”
Private
Este es el
texto original
del mensaje
en claro
#$”%/&%
*?¿[])(&”#
[]=()/&%¡
Este es el
texto original
del mensaje
en claro
Encrypt
Decrypt
Both keys belong to the same “person”
The process can be made backwards

79. Confidentiality
Alice
Bob

80. Authentication
Bob
Alice

81. Public key Diffie y Hellman
Private key is impractical for actual applications. Too many keys
P = D(KPRIV, E(KPUB, P))
Anyone can send a message but only the intended recipient will be able to read it
P = D(KPUB, E(KPRIV, P))
Anyone can read the message but the recipient will know for sure it is from the intended sender
It does not need so many keys as private key
Based in hard problems

82. A lot more locks....... only one KEY!
Public
Key
Private
Key

83. A lot more locks....... only one KEY!

84. A lot more locks....... only one KEY!
Private
Key

85. A lot more locks....... only one KEY!

86. They invented the concept …..
The concept of the asymmetric key was revolutionary
Diffie published the idea in 1975 and many scientists joined the cause ....
But after a year nobody had found the elusive “one way function”
Easy in one direction but almost impossible in the other (backwards)
But easy backwards if someone has secret information (key)

87. Rivest-Shamir-Adleman
Rivest, Shamir y Adleman
Shamir, Rivest y Adleman

88. RSA Invented by Ron Rivest, Adi Shamir and Leonard Adleman
Made public in 1978
It is the most used public key algorithm
Uses the concept of “one way function”
Easy to do in one direction but almos impossible to do in the other
Select two very big primer numbers p y q
Calculate N = p*q
If N is 100 figures operations will be needed to factorize N
p and q are the private key
N is the public key

89. ¿p and q given N?
“Confía en el tiempo, que suele dar dulces salidas a muchas amargas dificultades”
Miguel de Cervantes Saavedra
N is at least 10308
1995. Pentium 100MHz 8MB RAM
50 to factorize 10130
With 100,000,000 computers
15 seconds
Quantum processors
Reading: “15 = 3*5 in half the time”

90. RSA Select two very big prime numbers p y q Public key N = pq
Private key d
d*e = 1 mod (p-1)(q-1)
Linear Congruence Equation
d is calculated by means of Euclidean Algorithm
C = Pe mod n
P = Cd mod n

91. Linear Congruence Equation
ax ≡ b mod n
It is solvable iif x ↔ b is divisible
by the Greater Common Divisor
gcd(a,n)
Solvable by the Euclidean algorithm to find relative prime numbers

92. RSA example Alice choses two big and secret prime numbers p = 17
q = 11
Alice generates N = pq = 187 y chooses another number e
N = 187
e = 7
e y (p-1)*(q-1) must be relative prime numbers
Alice publishes N and e (her public key)
C = Pe mod n

93. RSA example Bob wants to send a message ('x', ascii 88) P = 88
C = 887 mod 187 = 11
887 mod 187 = (884 mod 187)(882 mod 187)(881 mod 187)
One way function, exponential with modular arithmetic
Ciphertext (11) is sent through unsecure channel
Alice receives 11

94. RSA example Alice receives 11 Calculate d using Euclidean algorithm
e*d = 1 mod (p-1)(q-1)
7*d = 1 mod 16*10
7*d = 1 mod 160
7*d = 161
d = 23
P = Cd mod n
P = 1123 mod 187
P = 88 → 'x'

95. Comparison PRIVATE KEY 1 key Key must be kept secret
The most used to keep confifentiality and integrity of data
The distribution of the key has to be made by other channel
Fast
PUBLIC KEY
2 keys
One secret, the other has to be ade public
Applied in key exchange and authentication
Distribution is open
Slow (10,000 times slower than private key)
WHY????

96. Key exchange K is key to exchange S Sender, R Receiver
S sends CS = E(KPRIV-S, K) to R
In R
D(KPUB-S, CS) and it gets K
Anyone hearing and has KPUB-S can obtain K
S sends E(KPUB-R, K) to R
Only R can decrypt and obtain K
D(KPRIV-R, K)
Problem: R cannot be sure the comes from S

97. Key exchange

98. “Digest” Hashing algorithms SHA-1, SHA-2, SHA-3 Secure Hash Algorithm
Developed by NIST
Any length input (file)
160 bits output
MD2, MD4, MD5
MD5 developed by Ronald Rivest
Released in 1991
128 bits output

99. Digital signatures Sender Generates a digest of the message
Encrypt the digest using sender private key
Send the original message in plaintext and the encrypted cipher
Receiver
Decrypt the digest with the sender public key
Generates another digest with the plaintext
Compares both digests to see if the message is valid

100. Digital signature
Wikipedia

101. Digital Signatures Authenticates the source of the message
The message did not change in transit
Non repudiation and integrity
It does not assure confidenciality
Types
HMAC (Hashed Message Authentication Code)
DSA (Digital Signature Algorithm)
DSS (Digital Signature Standard)
Used by the USA government

102. Digital Certificates
SELF STUDY!!!