CS_Chapter_2Security concerns of different types of devices.pptx

Computer Security
(CoSc-2041 – 5 ECTS)
Sem. II - 2016/2024
Chapter 2
Cryptography and Encryption Techniques
Department of Computer Science
Haymanot.T

Security Techniques: Cryptography
Terminology
Cryptography: Schemes for encryption and decryption
Encryption: The process by which plaintext is
converted into ciphertext.
Decryption: Recovering plaintext from the ciphertext
Secret key: Used to set some or all of the various
parameters used by the encryption algorithm. In a
classical (symmetric key) cryptography, the same
secret key is used for encryption and decryption
 Cryptanalysis: The study of “breaking the code”.
 Cryptology: Cryptography and cryptanalysis together constitute
the area of cryptology.

Cryptography
Cryptography has five ingredients:
• Plaintext
• Encryption algorithm
• Secret Key
• Ciphertext
• Decryption algorithm
Security depends on the secrecy of the key, not
the secrecy of the algorithm

Cryptography
Simplified Encryption Model:

Cryptography
A sender S wanting to transmit message M to a
receiver R
To protect the message M, the sender first
encrypts it into an unintelligible message M’
After receipt of M’, R decrypts the message to
obtain M
M is called the plaintext
 What we want to encrypt
M’ is called the ciphertext
 The encrypted output
Description:

Cryptography
Given
P=Plaintext
C=CipherText
C = EK (P) Encryption
P = DK ( C) Decryption
Notation:

Cryptography
Caesar Cipher - early example:
Caesar Cipher: The earliest known example
of a substitution cipher in which each
character of a message is replaced by a
character three position down in the
alphabet.
Plaintext: are you ready
Ciphertext: duh brx uhdgb

Cryptography
If we represent each letter of the alphabet
by an integer that corresponds to its
position in the alphabet:
The formula for replacing each character ‘p’ of
the plaintext with a character ‘c’ of the
ciphertext can be expressed as:
c = E3(p ) = (p + 3) mod 26

Cryptography
A more general version of this cipher that
allows for any degree of shift:
c = Ek(p ) = (p + k) mod 26
The formula for decryption would be
p = Dk(c ) = (c - k) mod 26
In these formulas
 ‘k’ is the secret key. The symbols ’E’ and ’D’ stand
for Encryption and Decryption respectively, and p
and c are characters in the plain and cipher text
respectively.

Cryptography
Properties of encryption function
It is computationally infeasible to find the key
K when given the plaintext P and associated
ciphertext C= EK (p)
It should also be computationally infeasible to
find another key k’ such as EK(p) = EK’(p).
Uniqueness.

Cryptography
Types of attacks
The attacker has only the ciphertext and his
goal is to find the corresponding plaintext
The attacker has a ciphertext and the
corresponding plaintext and his goal is to
find the key
A good cryptosystem protects against all types
of attacks
Attackers use both Mathematics and Statistics

Cryptography
Intruders
Eavesdropping (listening/spying the message)
An intruder may try to read the message
If it is well encrypted the intruder will not know the
content
However, just the fact the intruder knows that there
is communication may be a threat (Traffic analysis)
Modification
Modifying a plaintext is easy, but modifying
encrypted messages is more difficult
Insertion of messages
Inserting new message into a ciphertext is difficult

Cryptography
There are two fundamentally different
cryptographic systems
Symmetric cryptosystem/ Private key
Asymmetric cryptosystem/ Public key

Symmetric cryptosystem/ Private key
A symmetric cryptosystem, also known as a secret key or private key cryptosystem, is
an encryption system that uses the same key for both encryption and decryption
processes. In this system, the sender and receiver of a message use a shared secret
key to encrypt and decrypt the information.
Here's an overview of how a symmetric cryptosystem works:
1.Key Generation: A secret key is generated by a trusted entity or algorithm. This
key should be kept confidential and known only to the sender and the intended
recipient.
1.Encryption: The sender uses the secret key to encrypt the plaintext message into
ciphertext. This process scrambles the message in a way that it becomes
unreadable without the corresponding key.

Cont.…
3. Transmission: The encrypted ciphertext is transmitted over an insecure
channel, such as the internet or a network.
4. Decryption: The recipient uses the same secret key to decrypt the ciphertext
back into the original plaintext message. By applying the key in reverse, the
recipient can reverse the encryption process and recover the original message.
It's important to note that both the sender and the receiver must have access to
the same secret key. Therefore, the key needs to be securely shared between
them before any communication takes place. This requirement for key
distribution is a significant challenge in symmetric cryptosystems.

Cont.…
Common examples of symmetric cryptosystems include the Data
Encryption Standard (DES), Advanced Encryption Standard (AES), and
the Triple Data Encryption Algorithm (3DES). These algorithms are
widely used for secure communication, data protection, and
confidentiality in various applications.

Asymmetric cryptosystem/ Public key
An asymmetric cryptosystem, also known as a public key cryptosystem, is an
encryption system that uses a pair of mathematically related keys: a public key
and a private key. Unlike symmetric cryptosystems, where the same key is used
for encryption and decryption, in asymmetric cryptography, these keys have
different functions.
Here's how an asymmetric cryptosystem works:
1.Key Generation: The receiver generates a key pair consisting of a public key
and a private key. The private key is kept secret, while the public key is made
available to anyone who wants to send encrypted messages to the receiver.

Cryptography
Symmetric Cryptosystem
Also called secret-key/private-key cryptosystem
The same key is used to encrypt and decrypt a
message
 P = DK [EK (P) ]
Have been used for centuries in a variety of forms
The key has to be kept secret
The key has to be communicated using a secure
channel
They are still in use in combination with public key
cryptosystems due to some of their advantages

Cryptography
Asymmetric Cryptosystem
Also called public-key cryptosystem
 keys for encryption and decryption are different but form a unique pair
 P = DKD [EKE (P) ]
 Only one of the keys need to be private while the other can be public
Invented by Diffie and Hellman in 1976
Uses Mathematical functions whose inverse is not known by
Mathematicians of the day
It is a revolutionary concept since it avoids the need of using a
secure channel to communicate the key
It has made cryptography available for the general public and made
many of today’s on-line application feasible

Cryptography
Public-key Cryptosystem
Which one of the encryption or decryption key is
made public depends on the use of the key
If Hana wants to send a confidential message to
Ahmed
 She encrypts the message using Ahmed’s public key
 Send the message
 Ahmed will then decode it using his own private key
On the other hand, if Ahmed needs to make sure that
a message sent by Hana really comes from her, how
can he make that?

Cryptography
Using digital signature
Hana has to first encrypt a digital signature using her
private key
Then encrypt the message (signature included) with
Ahmed’s public key
Sends the encrypted message to Ahmed
Ahmed decrypts the message using his private key
Ahmed then decrypts the signature using Hana’s
public key
If successful, he insures that it comes from Hana

Cryptography
Public-key Cryptosystem: Example RSA
RSA is from R. Rivesh, A. Shamir and L. Aldermen
Principle: No mathematical method is yet known to efficiently
find the prime factors of large numbers
In RSA, the private and public keys are constructed from very
large prime numbers (consisting of hundred of decimal digits)
One of the keys can be made public
Breaking RSA is equivalent to finding the prime factors: this is
know to be computationally infeasible
It is only the person who has produced the keys from the prime
number who can easily decrypt the messages

Cryptography
Public-key Cryptosystem: Average time required
for exhaustive key search
Key Size
(bits)
Number of
Alternative Keys
Time required at
106 Decryption/µs
32 232 = 4.3 x 109 2.15 milliseconds
56 256 = 7.2 x 1016 10 hours
128 2128 = 3.4 x 1038 5.4 x 1018 years
168 2168 = 3.7 x 1050 5.9 x 1030 years

Cryptography
Summary
 A pair of keys (private, public)
 If you have the private key, you can easily
decrypt what is encrypted by the public key
 Otherwise, it is computationally infeasible to
decrypt what has been encrypted by the
public key

Cryptography
Hash functions
One application of cryptography in distributed systems is
the use of hash functions
A hash function H takes a message m of arbitrary length
and produces a bit string h, h= H (m)
When the hash value h is sent with the message m, it
enables to determine whether m has been modified or not
It is similar to cyclic-redundancy check (CRC) and Check
sum

Cryptography
Hash functions
Properties of hash functions
 One-way function: It is computationally infeasible to
find m that corresponds to a known output of h
 Collision resistance
 Weak-collision resistance: It is computationally infeasible,
given m and H, to find m’ ≠ m such that H(m) = H(m’)
 Strong-collision resistance: Given H, it is computationally
infeasible to find any two different input values m and m’,
such that H(m) = H(m’)

Cryptography
DES - Popular Example of Symmetric Cryptosystem
In 1973, the NBS (National Bureau of Standards, now called NIST -
National Institute of Standards and Technology) published a request for
an encryption algorithm that would meet the following criteria:
have a high security level
be easily understood
not depend on the algorithm's confidentiality
be adaptable and economical
be efficient and exportable
In late 1974, IBM proposed "Lucifer", which was then modified by NSA
(National Security Agency) in 1976 to become the DES (Data Encryption
Standard). The DES was approved by the NBS in 1978. The DES was
standardized by the ANSI under the name of ANSI X3.92, also known as
DEA (Data Encryption Algorithm).

Cryptography
DES- Example of Symmetric Cryptosystem …
DES Utilizes block cipher, which means that during the
encryption process, the plaintext is broken into fixed length blocks
of 64 bits.
The key is 56 bits wide. 8-bit out of the total 64-bit block key is
used for parity check (for example, each byte has an odd number
of bits set to 1).
56-bit key gives 256 ( 7.2*1016) possible key variations
DES algorithm involves carrying out combinations, substitutions
and permutations between the text to be encrypted and the key,
while making sure the operations can be performed in both
directions (for decryption).
The combination of substitutions and permutations is called a
product cipher.

Cryptography
DES was best suited for implementation in hardware,
probably to discourage implementations in software, which
tend to be slow by comparison during that time.
Modern computers are so fast that satisfactory software
implementations for DES are possible.
DES is the most widely used symmetric algorithm despite
claims whether 56 bits is long enough to guarantee security.
Using current technology, 56-bit key size is vulnerable to a
brute force attack.

Cryptography
DES Encryption starts with an initial permutation (IP) of the 64
input bits. These bits are then divided into two 32-bit halves
called L and R. The encryption then proceeds through 16 rounds,
each using the L and R parts, and a subkey.
The R and subkeys are processed in the so called f-function, and
exclusive-or of the output of the f-function with the existing L
part to create the new R part. The new L part is simply a copy of
the incoming R part.
In the final round, the L and R parts are swapped once more
before the final permutation (FP) producing the output block.
Decryption is identical to encryption, except that the subkeys are
used in the opposite order. That is, subkey 16 is used in round 1,
subkey 15 is used in round 2, etc., ending with subkey 1 being
used in round 16.

Cryptography
The
S-Box
If S1 is the function defined in this table and B is a block of 6 bits, then S1(B) is determined as
follows: The first and last bits of B represent in base 2 a number in the decimal range 0 to 3 (or
binary 00 to 11). Let that number be i. The middle 4 bits of B represent in base 2 a number in the
decimal range 0 to 15 (binary 0000 to 1111). Let that number be j. Look up in the table the number in
the i-th row and j-th column. It is a number in the range 0 to 15 and is uniquely represented by a 4
bit block. That block is the output S1(B) of S1 for the input B. For example, for input block B =
011011 the first bit is "0" and the last bit "1" giving 01 as the row. This is row 1. The middle four bits
are "1101". This is the binary equivalent of decimal 13, so the column is column number 13. In row
1, column 13 appears 5. This determines the output; 5 is binary 0101, so that the output is 0101.
Hence S1(011011) = 0101.

Cryptography
Cracking: The most basic method of attack for any cypher is
brute force - trying every possible key in turn.
The length of the key determines the number of possible
keys, and hence the feasibility of the approach.
DES is not adequate with this regard due to its key size
In academia, various proposals for a DES-cracking machine
were advanced.
In 1977, Diffie and Hellman proposed a machine costing an
estimated US$20 million which could find a DES key in a single day.
By 1993, Wiener had proposed a key-search machine costing US$1
million which would find a key within 7 hours.
However, none of these early proposals were ever
implemented.

Cryptography
The EFF's US$250,000 DES
cracking machine
contained 1,856 custom
chips and could brute force
a DES key in a matter of
days - the photo shows a
DES Cracker circuit board
fitted with several Deep
Crack chips.

Cryptography
A variant of DES, Triple DES (3-DES), provides enhanced security by executing
the core algorithm three times in a row.
With triple length key of three 56-bit keys K1, K2 & K3, encryption is:
 Encrypt with K1
 Decrypt with K2
 Encrypt with K3
Decryption is the reverse process:
 Decrypt with K3
 Encrypt with K2
 Decrypt with K1
Setting K3 equal to K1 in these processes gives us a double length key K1, K2.
Setting K1, K2 and K3 all equal to K has the same effect as using a single-length
(56-bit key).
Thus it is possible for a system using triple-DES to be compatible with a system
using single-DES.

Cryptography
RSA- Example of Asymmetric/Public-Key Cryptosystem
The RSA algorithm
 Used for both public key encryption and digital
signatures.
 Security is based on the difficulty of factoring large
integers.
Major Activities
 Key Generation (Algorithm)
 Encryption
 Digital signing
 Decryption
 Signature verification

Cryptography
RSA- Key Generating Algorithm
1. Generate two large random primes, p and q
2. Compute n = pq and (φ) phi = (p-1)(q-1)
3. Choose an integer e, 1 < e < φ, such that gcd(e, phi) = 1
4. Compute the secret exponent d, 1 < d < φ, such that
d = e-1 mod φ , i.e. φ divides (ed-1)
5. The public key is (n, e) and the private key is (n, d).
 Keep all the values d, p, q and φ secret
 n is known as the modulus
 e is known as the public exponent or encryption exponent
 d is known as the secret exponent or decryption exponent.

Cryptography
RSA- Encryption
Sender A does the following
 Obtains the recipient B's public key (n, e)
 Represents the plaintext message as a positive integer m
 Computes the ciphertext c = me mod n
 Sends the ciphertext c to B
RSA- Decryption
Recipient B does the following
 Uses his private key (n, d) to compute m = cd mod n
 Extracts the plaintext from the message representative
m

Cryptography
RSA- Digital signing
Recipient B does the following
 Uses sender A's public key (n, e) to compute integer v = se mod n
 Extracts the message digest from this integer
 Independently computes the message digest of the information that has
been signed
 If both message digests are identical, the signature is valid
RSA- Signature verification
Sender A does the following
 Creates a message digest of the information to be sent
 Represents this digest as an integer m between 0 and n-1
 Uses her private key (n, d) to compute the signature
s = md mod n.
 Sends this signature s to the recipient, B.

Cryptography
RSA- Key Generation Simple Example
1. Select primes p=11, q=3.
2. n = pq = 11*3 = 33
phi = (p-1)(q-1) = 10*2 = 20
3. Choose e=3
Check gcd(e, p-1) = gcd(3, 10) = 1 (i.e. 3 and 10 are relatively prime -
have no common factors except 1) and check gcd(e, q-1) = gcd(3, 2) = 1,
therefore gcd(e, phi) = gcd(e, (p-1)(q-1)) = gcd(3, 20) = 1
4. Compute d (1<d<phi) such that d = e-1 mod phi = 3-1 mod 20
i.e. find a value for d such that phi divides ed-1 (20 divides 3d-1.)
Simple testing (d = 2, 3 ...) gives d = 7
Check: ed-1 = 3*7 - 1 = 20, which is divisible by phi (20).
5. Public key = (n, e) = (33, 3)
Private key = (n, d) = (33, 7).

Cryptography
RSA- Encryption Example
Now say we want to encrypt the message m = 7
 c = me mod n = 73 mod 33 = 343 mod 33 = 13
 Hence the ciphertext c = 13
To check decryption we compute
 m = cd mod n = 137 mod 33 = 7
RSA- Decryption Example
Given
Public key = (n, e) = (33, 3)
Private key = (n, d) = (33, 7)

Cryptography
RSA- More Meaningful Example
Message: ATTACKxATxSEVEN
Grouping the characters into blocks of three and computing a
message representative integer for each block:
 ATT ACK XAT XSE VEN
 In the same way that a decimal number can be represented as the sum
of powers of ten, e.g. 135 = 1 x 102 + 3 x 101 + 5, we could represent our
blocks of three characters in base 26 using A=0, B=1, C=2, ..., Z=25
ATT = 0 x 262 + 19 x 261 + 19 = 513
ACK = 0 x 262 + 2 x 261 + 10 = 62
XAT = 23 x 262 + 0 x 261 + 19 = 15567
XSE = 23 x 262 + 18 x 261 + 4 = 16020
VEN = 21 x 262 + 4 x 261 + 13 = 14313

Cryptography
RSA- More Meaningful Example – Key Generation
1. We "generate" primes p=137 and q=131 (we cheat by
looking for suitable primes around √n)
2. n = pq = 137*131 = 17,947
phi = (p-1)(q-1) = 136*130 = 17680
3. Select e = 3
check gcd(e, p-1) = gcd(3, 136) = 1, OK and
check gcd(e, q-1) = gcd(3, 130) = 1, OK.
4. Compute d = e-1 mod phi = 3-1 mod 17680 = 11787.
 d = e-1 mod phi , i.e. phi divides (ed-1)
5. Hence
 public key, (n, e) = (17947, 3) and
 private key (n, d) = (17947, 11787).

Cryptography
RSA- More Meaningful Example – Encryption/Decryption
To encrypt the first integer that represents "ATT“ (513),
we have
 c = me mod n = 5133 mod 17947 = 8363
We can verify that our private key is valid by decrypting
 m = cd mod n = 836311787 mod 17947 = 513
Given
Public key = (n, e) = (17947, 3)
Private key = (n, d) = (17947, 11787)
Overall, our plaintext is represented by the set of integers m
 (513, 62, 15567, 16020, 14313)
 We compute corresponding cipher text integers c = me mod n
 (8363, 5017, 11884, 9546, 13366)

Cryptography
Digital Signature

Cryptography
Digital Signature for Message Integrity and Confidentiality
Confidentiality insures that messages cannot be
intercepted and read by eavesdroppers
Message integrity insures that messages are protected
against modification
Principles of Digital Signature
 User A signs digitally a message m using “backward”
cryptographic hash of the message m with the private
key of A and attach it to the message m.
 Anybody can then decrypt A’s digital signature using
A’s public key and compare it with the cryptographic
hash of the message m to verify that m was signed by
A and m was not altered.

Cryptography
Digital Signature for Assurance
Consider the situation where Bob has just sold Alice something for
500 Birr through a deal that is made by E-mail
Alice sends an E-mail accepting to pay 500 Birr
Two issues need to be taken care of in addition to
authentication
 Alice needs to be assured that Bob will not modify the amount and
show that Alice promised to pay more than 500 Birr
 Bob needs to be assured that Alice will not deny that she sends the
message
If Alice signs the message digitally, the two issues will be solved
There are several ways to place digital signatures
One popular way is to use public-key cryptosystem such as RSA

Cryptography
Digital Signature Using Message Digest
H = H (m) is sent along m, where H is a cryptographic
hash function
KA
-(H(m)) (or KB
+(m, KA
-(H(m)))) is sent so that Bob
knows that it comes from Alice by decrypting it
Bob hashes the message m and compares it with H that
he has received from Alice
Hash/Message Digest: Short “signature” of the
message, 128–512 bits, that depend on entire message
It is extremely improbable that unequal messages have
same hash
Example: MD5 (Message Digest version 5)

Cryptography
Key Distribution: Verifying Someone’s Public Key
Even with public-key cryptosystems and digital
signatures, we still have the problem of authentication:
binding users to keys.
Early days articles envisioned phonebook-like database
with Name and Public Key entries.
Attacker can put in his own key for someone else, and
start signing fake contracts (and even checks!).
Maybe we can secure the phonebook, but then it kills the
idea of keys widely and easily available (publicly) .
Problem: How secure is that database itself?

Cryptography
Key Distribution: Problems
Distribution of a key is a difficult matter!
Solution: Certification/Certificate Authority (CA)
that signs (certifies) the public key
For public key, we need a body that certifies the
public key is that of the party we need to
communicate with
For a symmetric cryptosystem, the initial key must
be communicated along a secured channel(?)

Cryptography
Certification
A certificate is a public key and some naming “stuff”, digitally signed
by someone you trust (third party) - Certification Authority (CA).
Remark: Just because they are CAs doesn’t mean you should trust them.
The critical thing is that the name in the certificate must match the
alleged name.
Common solution to public key distribution today is to have trusted
third party to sign the user’s public encryption key.
Resulting certificate will contain information like user’s name/ID,
user’s public key, name of CA, start date of certificate, and length of
time it is valid.
User publishes certificate with the X.509 standard (for formatting
certificates).

Cryptography
Certification - Associated Overheads
An important issue is the longevity of certificates
Lifelong certificates are not feasible
Therefore, we need a way to revoke certificates
 Certificate Revocation List (CRL) published regularly
 Problems
 Vulnerability between the publishing and the request for
revocation
 Restricting the lifetime of a certificate
 A client contacts the certification authority for each public key,
checks whether it is valid or not

Cryptography
Applications – Electronic Payment
Payment systems - based on direct payment
a) Paying in cash.
b) Using a check.
c) Using a credit card.

Cryptography
Applications – Electronic Payment …
Payment systems based on money transfer between banks.
a) Payment by money order.
b) Payment through debit order.

Cryptography
Applications – Security in Electronic Payment
General requirements
 In cash based systems (using ATM), the main issue is
authentication
 Use of magnetic card
 PIN
 Digital money
 Protection against fraud
 It should not be possible to use the money more than once
 It should not be possible to use forged money
 Credit card or check based system
 No tampering/alteration
 Protection against repudiation (the buyer denies having made
the order)

Cryptography
Applications – Electronic Cash (E-Cash)
There are a number of electronic payment
systems based on the concept of digital coins
E-cash is one of the most famous
 Achieves anonymity in the payment system
 When Alice wants to buy some goods from Bob she
contacts her bank and requests for withdrawal
 The Bank hands out the digital money in the form of
signed notes representing some value with each
having a uniquely associated signature

Cryptography
Applications – Electronic Cash (E-Cash) …
To prevent the notes to be copied each note has a
serial number
Bob can check that it is not a forged money by
looking at the bank’s signature
Bob can check that the money has not already
been spent by contacting the bank
The drawback of this system is that the bank has
to remember the serial numbers that have been
spent or not

Cryptography
Applications – Secure Electronic Transaction (SET)
SET is the result of efforts by VISA, Mastercard, etc.
to develop a standard way of purchasing goods over a
network using a credit card
SET is an open standard: entire protocol is published
Dual signature is used in order to avoid
 The merchant from knowing the detail of the payment
information
 The Bank from knowing about the order information

Cryptography
The concept of session keys after authentication
During the establishment of a secure channel, after the
authentication phase, the communicating parties use
session/temporary keys
Benefits
 The session key is safely discarded when the channel is no longer
used
 When a key is used very often it becomes vulnerable. Thus by
using the main key less often, we make them vulnerable
 Replay attacks can be avoided
Authentication keys are often expensive to replace
Such a combination of long-lasting and cheaper/more
temporary session keys is a good choice

Cryptography
Summary
Advantage of private/secret key cryptography is that
it provides better secrecy but needs prearranged key
exchange.
Advantage of public-key cryptography is that it
allows for secrecy between two parties who have not
arranged in advance to have a shared key (or trusted
some third party to give it to them) and the
disadvantage is overhead and speed.
Therefore, in practice, hybrid systems use public-key
to establish session key for private key !!

Thank you
End of Chapter 2
any?, comment?

CS_Chapter_2Security concerns of different types of devices.pptx

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