1. Cryptography and Key Management
Unit - 3

2. Outline Basics of cryptography
Symmetric Cryptography (DES, Triple DES, AES, Key distribution)
Asymmetric cryptography
Public and private keys
RSA
Elliptic curve
Hash function
Digital signatures
PKI
Applied cryptography

3. Why Cryptography? Cryptography is a component of many security systems
It applies to numerous aspects of the security models ( Confidentiality, Authentication, Integrity, Authorization, Non- repudiation)
Desired Property
Threat
Solution
Confidentiality
Disclosure
Encryption for secrecy
Disguising traffic
patterns
Authentication
Spoofing
Digital signature
Integrity
Modification,
replay
Message digests, hashing,
time stamps
Non-repudiation
Denial

4. Cryptosystem Where A cryptosystem is a 5-tuples consisting of
(E,D,M,K,C)
Where
E : Encryption Algorithm
D: Decryption Algorithm
M: Set of planetext
K: Set of Keys
C: Set of Ciphers
E: M X K -> C, D: C X K -> M

5. Encryption Terms and Operations
Plaintext – an original message
Ciphertext – an encrypted message
Encryption – the process of transforming plaintext into ciphertext (also encipher)
Decryption – the process of transforming ciphertext into plaintext (also decipher)
Encryption key – the text value required to encrypt and decrypt data

6. Key
A key is an input to a cryptographic algorithm used to obtain confidentiality, integrity, Authenticity or other property over some data
The security of the cryptosystem often depends on keeping the key secret to some set of parties
The keyspace is the set of all possible keys
Entropy is a measure of the variance in keys (typically measured in bits)
Keys are often stored in some secure place: passwords, disk keyrings, smartcards, certificates…

7. What Is Cryptography
Cryptography is the science of hiding information in plain sight, in order to conceal it from unauthorized parties.
Substitution cipher first used by Caesar for battlefield communications

8. Secure Communications
Encryption Key
Decryption Key
Alice
plaintext
Encrypt
ciphertext
Decrypt
Bob
Mallory/ Oscar
Eve
Enemy or Adversary
Fig. Basic Communication Scenario

9. Eve’s Goals Read the message
Figure out the key Alice is using and read all the messages encrypted with that key
Modify the content of the message in such a way that Bob will think Alice sent the altered message.
Impersonate(imitate) Alice and communicate with Bob who thinks: he is communicating with Alice.
Oscar is a passive observer who is trying to perform (1) and (2).
Mallory is more active and evil who is trying to perform
(3) And (4).

10. Attack Methods Ciphertext only: Alice has only a copy of ciphertext
Known Plaintext: Eve has a copy of ciphertext and the corresponding plaintext and tries to deduce the key.
Chosen Plaintext: Eve has a copy of ciphertext corresponding to a copy of plaintext selected by Alice who believes it is useful to deduce the key.
Chosen Ciphertext: Eve has a copy of plaintext corresponding to a copy of ciphertext selected by Alice who believes it is useful to deduce the key.

11. Encryption Methodologies

12. Types of Encryption Block cipher Stream cipher
Encrypts blocks of data, often 128 bits
Stream cipher
Operates on a continuous stream of data

13. Block Ciphers Encrypt and decrypt a block of data at a time
Typically 128 bits
Typical uses for block ciphers
Files, messages, text communications, web
Well known encryption algorithms
DES, 3DES, AES, CAST, Twofish, Blowfish, Serpent

14. Decryption: simple XOR with the same key
Stream Ciphers
Used to encrypt a continuous stream of data, such as an audio or video transmission
A stream cipher is a substitution cipher that typically uses an exclusive-or (XOR) operation that can be performed very quickly by a computer.
Plaintext 1
Key
Ciphertext
Encryption: simple XOR with key
Ciphertext 1
Key
Plaintext
Decryption: simple XOR with the same key

15. Encryption Algorithm
Algorithm used to make content unreadable by all but the intended receivers
E(key, plaintext) = ciphertext
D(key, ciphertext) = plaintext
Block vs. Stream Ciphers
Block: input is fixed blocks of same length
Stream: stream of input

16. Substitution Cipher
Plaintext characters are substituted to form ciphertext
“A” becomes “R”, “B” becomes “G”, etc.
Character rotation
Caesar rotated three to the right (A > D, B > E, C > F, etc.)
A table or formula is used
ROT13 is a Caesar cipher
Subject to frequency analysis attack

17. Caesar Cipher Substitution cipher
Every character is replaced with the character three slots to the right

18. Transposition Cipher
Plaintext messages are transposed into ciphertext, Scrambles the symbols to produce output
The key is the permutation of symbols
Plaintext:
Write into columns going down
Read from columns to the right
Ciphertext:
AKCNBTAEORTTVRIAOITDCNAHG
Subject to frequency analysis attack A K C N B T E O R V I D H G

19. Mono-alphabetic Cipher
One alphabetic character is substituted or another
Caesar right-three shift:
Or a more random scheme:
Subject to frequency analysis attack A B C D E F G H I J … Z K L M A B C D E F G H I J … Z W R T N P Q U X

20. Polyalphabetic Cipher
Two or more substitution alphabets
CAGED becomes RRADB
Not subject to frequency attack
Plaintext A B C D E F G H I … Z
Alpha 1 W R T N P Q X
Alpha 2 K U
Alpha 3 V
Alpha 4 M O
Alpha 5 Y J

21. Running-key Cipher
Plaintext letters converted to numeric (A=0, B=1, etc.)
Plaintext values “added” to key values giving ciphertext
Modulo arithmetic is used to keep results in range 0-26
Add 26 if results < 0; subtract 26 if results > 26
Plaintext A T C K O N E V I
Key S R 19 2 10 14 13 4 21 8 18 17
Sum 23 6 3 16 7 11 12
Ciphertext X G D Q H L M

22. One-time Pad
Assume you have a secret bit string s of length n known only to two parties, Alice and Bob
Alice sends a message m of length of n to bob
Alice uses the following encryption function to generate ciphertext c forall i=1 to n : ci = mi ⊕ si
XOR the data with the secret bit string
Plaintext A T C K O N E V I
Key X G J R Q W P F 19 2 10 14 13 4 21 8 23 6 9 3 17 16 22 15 5
Sum 25 1 7 11 18
Ciphertext Z B H L U

23. Cryptography-Types

24. Symmetric key A common secret that all parties must know
Difficult to distribute key securely
Used by DES, 3DES, AES, Twofish, Blowfish, IDEA, RC5
Fig. Symmetric cryptography

25. Asymmetric key Public / private key Keys mathematically tied together
Openly distribute public key to all parties
Keep private key secret
Anyone can use your public key to send you a message
Used by RSA. El Gamal, Elliptic Curve
Fig. Asymmetric cryptography

26. Asymmetric Encryption Uses
Encrypt message with recipient's public key
Only recipient can read it, using his or her private key
Provides confidentiality
Sign message
Hash message, encrypt hash with your private key
Anyone can verify the signature using your public key
Provides integrity and non-repudiation (sender cannot deny authorship)
Sign and encrypt
Both of the above

27. Adding Authenticity Digital signatures
used to verify authenticity of origin
Originator’s
Signed Message
Cleartext
Message
Private Key
Originator
Public Key
Recipient
Sign
Verify

28. Using Symmetric and Asymmetric Together
Key exchange using asymmetric cryptography
Uses asymmetric keys to distribute bulk encryption keys
Allows rapid distribution of short-term keys

29. Symmetric Cryptography

30. Data Encryption Standard (DES)
The Data Encryption Standard (DES) is a symmetric-key block cipher published by the National Institute of Standards and Technology (NIST).
Signaled the beginning of the modern area of cryptography
In 1973, NIST published a request for proposals for a national symmetric-key cryptosystem.
Block cipher - Fixed sized input
8-byte input and a 8-byte key (56-bits+8 parity bits)

31. DES Overview
Figure Encryption and decryption with DES

32. DES Structure
The encryption process is made of two permutations (P-boxes), which we call initial and final permutations, and sixteen rounds of complex key dependent calculation.

33. DES - Basics
Fundamentally DES performs only two operations on its input, bit shifting (permutation), and bit substitution.
The key controls exactly how this process works.
By doing these operations repeatedly and in a non- linear manner you end up with a result which can not be used to retrieve the original without the key.
By applying relatively simple operations repeatedly a system can achieve a state of near total randomness.

34. DES Initial round permutes input, then 16 rounds
Each round key (ki) is 48 bits of input key
Function f is a substitution table (s-boxes)

35. DES Key Processing
The key is usually stored as a 64-bit number, where every eighth bit is a parity bit.
The parity bits are pitched during the algorithm, and the 56-bit key is used to create 16 different 48-bit subkeys - one for each round.
Subkeys Generation
First, the key is loaded according to the PC-1 and then halved.
Then each half is rotated by 2 bits in every round except the first, second, 9th and last rounds.
The reason for this is that it makes it secure against related-key cryptanalysis.
Then 48 of the 56 bits are chosen according to a compression permutation.

36. The Key Schedule
The subkeys used by the 16 rounds are formed by the key schedule which consists of:
An initial permutation of the key (PC1) which selects 56- bits in two 28-bit halves
16 stages consisting of
selecting 24-bits from each half and permuting them by PC2 for use in function f,
rotating each half either 1 or 2 places depending on the key rotation schedule KS

37. Security of DES
DES, as the first important block cipher, has gone through much scrutiny. Among the attempted attacks, three are of interest: brute-force, differential cryptanalysis, and linear cryptanalysis.
Brute-Force Attack
Differential Cryptanalysis
Linear Cryptanalysis

38. DES- Current State
Currently DES is no longer certified for US federal use.
The availability of faster hardware, and access to large distributed systems meant that 56-bit DES keys could be recovered by brute force searches in an unreasonably short time (days or even hours).
DES should almost certainly not be used in any new product, and should not be used in existing products to protect information with a lifetime of more than a few minutes.

39. 3DES or Triple-DES
Triple-DES is a block cipher, which applies the Data Encryption Standard (DES) cipher algorithm three times to each data block.
DES used a single 56-bit key.
3DES uses three 56-bit keys (often just referred to as a 3DES key), and performs three rounds of DES operations on the data.
The result is that DES technology could be used until long term solution (the Advanced Encryption Standard) is found.

40. 3DES
A typical process of 3DES is known as EDE (Encrypt- Decrypt-Encrypt).
In this case, the first and third keys are equal, so the effective key length is 112-bits.
In the first operation, the plaintext is encrypted with the first DES key, K1.

41. 3DES
In the second step, the results of the first step, C1, is decrypted using the second key, K2
Since K2 ≠ K1, this does not result in the original plaintext message.

42. 3DES
In the final step, the results of the second step, C2, is encrypted using the third key, K3
The output ciphertext C3 is the final encrypted message.
Recall that K3 = K1 in this case, so even though there are three 56-bit keys, the effective key length is only bits.

43. 3DES or Triple-DES
Decryption in this case follows the reverse of the encryption process, as shown below.

44. 3DES or Triple-DES
Although the length of the key has doubled, there are 256 (= 72,057,594,037,927,936) times as many keys.
Therefore a brute force search for a 3DES-EDE key would take 256 times longer on the same hardware than a brute force search for a DES key.
3DES is still an acceptable encryption method.

45. AES DES is near end of useful life
NIST has begun process to look for successor to DES
The Advanced Encryption Standard (AES) was the result of an open international search organized by NIST for a replacement for DES.
AES Process:
Proposals submitted 3/98
AES Workshop - 8/98
15 proposals selected
Key sizes of 128, 192, and 256 bits

46. AES Features The features of AES are as follows
Symmetric key symmetric block cipher
128-bit data, 128/192/256-bit keys
Stronger and faster than Triple-DES
Provide full specification and design details
Software implementable in C and Java

47. AES Algorithm – High Level
KeyExpansion—round keys are derived from the cipher key using Rijndael's key schedule
Initial Round
AddRoundKey—each byte of the state is combined with the round key using bitwise xor
Each consists of 4-subprocess
SubBytes: The 16 input bytes are substituted by looking up a fixed table (S-box) given in design. The result is in a matrix of four rows and four columns.
ShiftRows—a transposition step where each row of the state is shifted cyclically a certain number of steps.
MixColumns—a mixing operation which operates on the columns of the state, combining the four bytes in each column.
AddRoundKey: The 16 bytes of the matrix are now considered as 128 bits and are XORed to the 128 bits of the round key.
Final Round (no MixColumns)
SubBytes
ShiftRows
AddRoundKey

48. The State and Key Schedule
Input is a 128 bit block (16 bytes) that is placed in the state array
The key is entered in a block and divided into key schedule words of 4 bytes/word.
The key schedule is an expansion of the key—eg, a bit key is expanded into 44 key schedule words.
A square matrix of bytes is used by the standard to describe the state.

49. Rounds and Transformation Stages
The encryption process executes a round function, Nr times, with the number of rounds (Nr) being dependent on key size.
The round function consists of four transformation stages.
SubBytes()
ShiftRows()
MixColumns()
AddRoundKey()

50. Rounds and Transformation Stages
The cipher begins with an AddRoundKey().
All rounds then execute each of the transformations except the last round.
The MixColumns( ) transformation is not executed in the final round.
For a 128 bit key, there are 10 rounds.
12 and 14 rounds are used with keys of 192 and 256.

51. AES Decryption
AES decryption is accomplished using inverses of the transformations, in the appropriate order.
The AddRoundKey( ) is its own inverse when (since A  B  B = A).

52. The Key Exchange Problem
Although symmetric encryption is commonly used due to its historical position in the cryptography and its speed, it suffers from a serious problem of how to safely and secretly deliver a secret key from the sender to the recipient. This problem forms the basis for the key exchange problem.
The key exchange problem involves:
ensuring that keys are exchanged so that the sender and receiver can perform encryption and decryption,
ensuring that an eavesdropper or outside party cannot break the code,
ensuring the receiver that a message was encrypted by the sender.

53. Manual Key Distribution
Manually distributed symmetric keys should be either encrypted or use split knowledge
The distribution mechanism should assure
The authorized distribution of keys
That the entity distributing the keys is trusted by both the transmitter and recipient
The keys are protected according to relevant standards (e.g. FIPS=>Federal Information Processing Standard)
The keys are received by the authorized recipient

54. Electronic Key Distribution/Transport of Symmetric Keys
Requires other secret or public keys to have been previously distributed
Mechanism should insure that
The distributed key is not disclosed or modified
The key is protected in accordance with industry standards ( e.g. FIPS)
The recipient has received the correct key
Keys in this category are the secret authentication key, long and short term data encryption keys, key encrypting key for wrapping, master key for key derivation, and secret authorization key.

55. Thank You ! References: http://www.garykessler.net/library/crypto.html
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