Module 4
Enhancing Cryptographic security & Modes Of Encryption
MModified by :Ahmad Al Ghoul
PPhiladelphia University
FFaculty Of Administrative & Financial Sciences
BBusiness Networking & System Management Department
RRoom Number 32406
EE-mail Address: ahmad4_2_69@hotmail.com
Network Security
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Ahmad Al-Ghoul 2010-2011
1
Objectives
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Key Escrow
Types of Ciphers
General Types of Ciphers
Some encryption Trends
Monoalphabetic Substitution Ciphers
Polyalphabetic Substitution Ciphers
Transposition Ciphers
DES
RSA
Error Prevention and Detection
Cipher Block Chain
One Way Encryption
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Encyption – can it be broken?
 Theoretically, it is possible to devise unbreakable
cryptosystems
 However, practical cryptosystems almost always
are breakable, given adequate time and computing
power
 The trick is to make breaking a cryptosystem hard
enough for the intruder
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Types of Ciphers

Ciphers can be broadly classified into the following two
categories depending upon whether
(i) a symbol of plaintext is immediately converted
into a symbol of ciphertext (Stream Ciphers)
(ii) or a group of plaintext symbols are converted as a
block into a group of ciphertext symbols (Block
Ciphers)
– Speed of Encryption
•
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stream symmetric > block symmetric > asymmetric
Ahmad Al-Ghoul 2010-2011
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Stream Ciphers
 A symbol of plaintext is immediately converted into a
symbol of ciphertext
 Advantages
– Speed of transformation
– Low error propagation
 Disadvantages
– Low diffusion (Change in the plaintext should affect many
parts of the ciphertext)
– Susceptible to malicious insertions and modifications
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Block Ciphers
 A group of plaintext symbols are converted as a block into
a group of ciphertext symbols
 Advantages
– Diffusion
– Immunity to insertions
 Disadvantages
– Slowness of encryption
– Error propagation
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Trends
 Block size: larger block sizes mean greater
security
 Key Size: larger key size means greater security
 Number of rounds: multiple rounds offer
increasing security
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DES
DES developed at IBM,
every five years re-certification is held,
it is a block cipher algorithm,
it maps 64-bit plaintext into 64 block of cipher text,
keys are 56 bit long, the procedures is repeated
several time, the brute force approach to decipher
requires 70 million billion trials (2 raised on 56)
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Overview of DES
DES is a careful combination of two fundamental
building blocks of encryption:
substitution and permutation (transposition)
Algorithm repeats these operation in 16 cycles
Algorithm uses only standard arithmetic and
logical operation on up to 64 numbers, although
complex, the algorithm is repetitive, making it
suitable for implementation on a single purpose
chip,
Several such chips are available on the market
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Rivest-Shamir-Adleman Encryption
RSA incorporates results from number theory, combined
with the difficulties of determining the prime factors of
a target
RSA operates with arithmetic mod n
Two keys d and e are used for encryption and decryption
They are interchangeable, the plain text is encrypted as
P(e)mod n
The decrypting key d is chosen, so that ((P(e)d) mod n=P
The underlying problem on which the RSA is based is that of
factoring large numbers
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RSA
Because of symmetry in modular arithmetic, encryption and
decryption are mutual inverse and commutative
The encryption key consists of a pair of integers (e,n) and
the decryption key is (d,n), e and d are used as:
P=C mod n = (P ) mod n = (P ) mod n
The value of n should be quite large, a product of two
primes p and q
Both should be large themselves, 100 digits each, and n is 200
digits long
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the RSA power
To give an intuitive feel what this means, suppose we have
to find the two factors of the number 437, which two numbers
multiplied together give 437. This can be solved easily by
a calculator, but numbers made sufficiently large, like
those requiring several hundreds or thousand of bits to
represent them make this task even difficult for computers
The state of art in factoring in 1994 was demonstrated by well
publicized event - the factoring of a 129 digit (429 bit) RSA modules.
The total processing power required was 4 600 MIPS years or
to a processing done by Pentium 100 running non stop for 46 year.
Today it is considered that 1024 bit modules provide enough
protection even for the computer power beyond year 2000
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ALGORITHM
 Key Generation
1.
2.
3.
4.
5.
Generate two large prime numbers, p and q
Let n = pq
Let m = (p-1)(q-1)
Choose a small number e, coprime to m
Find d, such that de % m = 1
 Publish e and n as the public key.
Keep d and n as the secret key.
 Encryption
 C = Pe % n
 Decryption
 P = Cd % n
 x % y means the remainder of x divided by y
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Key Generation
 1) Generate two large prime numbers, p and
q
 To make the example easy to follow I am
going to use small numbers, but this is not
secure. To find random primes, we start at a
random number and go up ascending odd
numbers until we find a prime. Lets have:
p = 7
q = 19
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Key Generation
 2) Let n = pq
 n = 7 * 19
= 133
 3) Let m = (p - 1)(q - 1)
 m = (7 - 1)(19 - 1)
= 6 * 18
= 108
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Key Generation
 4) Choose a small number, e coprime to m
 e coprime to m, means that the largest number that
can exactly divide both e and m (their greatest
common divisor, or gcd) is 1. Euclid's algorithm is
used to find the gcd of two numbers, but the
details are omitted here.
 e = 2 => gcd(e, 108) = 2 (no)
e = 3 => gcd(e, 108) = 3 (no)
e = 4 => gcd(e, 108) = 4 (no)
e = 5 => gcd(e, 108) = 1 (yes!)
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Key Generation
 5) Find d, such that de % m = 1
 This is equivalent to finding d which satisfies de
= 1 + nm where n is any integer. We can
rewrite this as d = (1 + nm) / e. Now we
work through values of n until an integer solution
for e is found:
 n = 0 => d = 1 / 5 (no)
n = 1 => d = 109 / 5 (no)
n = 2 => d = 217 / 5 (no)
n = 3 => d = 325 / 5
= 65 (yes!)
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Key Generation
 To do this with big numbers, a more
sophisticated algorithm called extended
Euclid must be used.
 Public Key
 n = 133
e = 5
 Secret Key
 n = 133
d = 65
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Communication
 Encryption
 The message must be a number less than the
smaller of p and q. However, at this point we don't
know p or q, so in practice a lower bound on p and
q must be published. This can be somewhat below
their true value and so isn't a major security
concern. For this example, lets use the message
"6."
 C = Pe % n
= 65 % 133
= 7776 % 133
= 62
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Decryption
 This works very much like encryption, but
involves a larger exponation, which is broken
down into several steps
 P = Cd % n
= 6265 % 133
= 62 * 6264 % 133
= 62 * (622)32 % 133
= 62 * 384432 % 133
= 62 * (3844 % 133)32 % 133
= 62 * 12032 % 133
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Decryption
 We now repeat the sequence of operations that
reduced 6265 to 12032 to reduce the exponent
down to 1.
 = 62 * 3616 % 133
= 62 * 998 % 133
= 62 * 924 % 133
= 62 * 852 % 133
= 62 * 43 % 133
= 2666 % 133
= 6
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Java RSA Code
 A Java implementation of RSA is just a transcription of the algorithm:
 import java.math.BigInteger;import
java.security.SecureRandom; class Rsa{ private BigInteger n,
d, e; public Rsa(int bitlen) { SecureRandom r = new
SecureRandom(); BigInteger p = new BigInteger(bitlen / 2,
100, r); BigInteger q = new BigInteger(bitlen / 2, 100, r); n =
p.multiply(q); BigInteger m = (p.subtract(BigInteger.ONE))
.multiply(q.subtract(BigInteger.ONE)); e = new BigInteger("3");
while(m.gcd(e).intValue() > 1) e = e.add(new BigInteger("2"));
d = e.modInverse(m); } public BigInteger encrypt(BigInteger
message) { return message.modPow(e, n); } public
BigInteger decrypt(BigInteger message) { return
message.modPow(d, n); }}
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Enhancing Cryptographic
Security
 Currently 3DES and RSA(1024) are
believed to be secure
– An intruder is unlikely to discover the content
of a message encrypted under one of them
 But some systems based on these
cryptosystem may not achieve their goals
– block replay
– operation mode dependent
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Error Prevention and Detection
 In the DES and any block Cipher each
block is an entity.
 An interceptor who understood the format
of a sender’s messages could modify
messages without needing to break the
encryption.
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Error Prevention and Detection
 Attack : Block Replay
Block 1 Block 2 Block 3 Block 4 Block 5
Encrypted
Name
Account Amount
– If ECB mode (each block encrypted separately) is used, then
intruder can replace the forth block arbitrarily using the
previously used data
 Solution
– Block Chaining
• Error propagation - cannot reconstruct the whole ciphertext
– Initial Chaining Value(Initial Vector)
• randomize the first block
• candidates : random number, date, time, etc.
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One-Way Functions
 One-way functions are relatively easy to compute, but
significantly harder to reverse. That is, given x it is easy to
compute f(x), but given f(x) it is hard to compute x. In this
context, “hard” is defined as something like: It would take
millions of years to compute x from f(x), even if all the
computers in the world were assigned to the problem.
 Breaking a plate is a good example of a one-way function.
It is easy to smash a plate into a thousand tiny pieces.
However, it’s not easy to put all of those tiny pieces back
together into a plate.
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One Way Encryption
 one-way encryption, allows for the encryption of
some plain text, but does not provide a way in
which to convert the cipher text back to its
original form.
 it is a widely used technique for ensuring the
integrity of system passwords.
 if the one-way encrypted passwords somehow fall
into the hands of a third-party, it isn't going to do
much good because they can never be converted
back to plain text.
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One Way Encryption
 The user enter his password, the input ( password ) is encrypted
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using the one-way algorithm.
The password that encrypted with one way encryption compared
with the stored encrypted password.
If they match, the input password must be correct.
The input parameter input_string is just the string that you
would like to encrypt.
The second, optional input parameter salt refers to a bit-string
that will influence the encryption outcome to further eliminate
the possibility of what are known as precomputation attacks
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