Cryptography cse,ru

Cryptography Introduction
Shimul Shakhawat
Computer Science & Engineering Dept.
University of Rajshahi

2
History
• 50 B.C. Julius Caesar uses cryptographic
technique
• 400 A.D. Kama Sutra in India mentions
cryptographic techniques
• 1250 British monk Roger Bacon
describes simple ciphers
• 1466 Leon Alberti develops a cipher
disk
• 1861 Union forces use a cipher during
Civil
War

3
History
• 1914 World War I – British, French, and
German forces use encryption
technology
• 1917 William Friedman, Father of U.S.
encryption efforts starts a school
for teaching cryptanalysis in
Illinois
• 1917 AT&T employee Gilbert Vernam
invents polyalphabetic cipher
• 1919 Germans develop the Engima machine
for encryption

4
History
• 1937 Japanese design the Purple
machine for encryption
• 1942 Navajo windtalkers help with secure
communication during World War II
• 1948 Claude Shannon develops statistical
methods for encryption/decryption
• 1976 IBM develops DES
• 1976 Diffie – Hellman develop public key /
private key cryptography
• 1977 Rivest – Shamir – Adleman develop the
RSA algorithm for public key / private key

Plaintext
• Plaintext is a text , in natural readable form.
• It is the message or data before it gets
encrypted.
• It is sometimes called cleartext
• Plaintext is denoted by M (message) or P
(plaintext).
• It can be a stream of bits , a text file , a bitmap,
a stream of digitized voice etc.
• It is simply binary data

Ciphertext
• An encrypted message is ciphertext
• It is denoted by C (ciphertext)
• It is also binary data
• Sometime it has the same size as M, sometimes
larger
• It is the results from plaintext by applying the
encryption key
• Message altered to be unreadable by anyone
except the intended recipients

Encryption
• The process of disguising a message in such a way to
hide its substance is called encryption.
• scrambling a message using a specialized
cryptographic algorithm to make it unreadable by
anyone except the intended recipients.
• The encryption function E, operates on M to produce
C. In mathematical notation
E(M)=C
Encryption Decryption
Plaintext
Ciphertext
Plaintext

Decryption
• The process of converting ciphertext back to the original
plaintext.
• In the reverse process, the decryption function D
operates on C to produce M:
D(C) = M
• Since the whole point of encrypting and then decrypting
a message is to recover the original plaintext, the
following identity must hold true:
D(E(M)) = M
Plaintext
Ciphertext
Plaintext

Cryptography
• The word cryptography comes from the two Greek
words: Krypto (secret) and graphein (write). So
cryptography means secret writing .
• The art and science of keeping messages secure is
called cryptography and it is practiced by
cryptographers
• The art of devising ciphers is called cryptography
• Cryptography deals with creating documents that can
be shared secretly over public communication channels
• Cryptographic documents are decrypted with the key
associated with encryption, with the knowledge of the
encryption

Cryptanalysis
• The art and science of breaking ciphertext is called
cryptanalysis.
• That is seeing through the disguise and it is
practiced by cryptanalysts.
• Cryptanalysis deals with finding the encryption key
for breaking cryptographic algorithms without the
knowledge of the encryption
• The art of breaking ciphers is called cryptanalysis
• Cryptanalyst: a person who breaks cryptographic
codes . Also referred to as “the attacker”.

Cryptology
• Cryptography and cryptanalysis is collectively
known as Cryptology.
• The branch of mathematics encompasses both
cryptography and cryptanalysis is called cryptology
and its practitioners are called cryptologists.
• Modern cryptologists are generally trained in
theoretical mathematics—they have to be.

Confidentiality
Three confidentiality or characteristics of cryptography
• Authentication: It should be possible for the
receiver of a message to ascertain its origin. An
intruder should not be able to masquerade as
someone else.
• Integrity: It should be possible for the receiver of a
message to verify that it has not been modified in
transit. An intruder should not be able to substitute
a false message for a legitimate one.
• Nonrepudiation: A sender should not be able to
falsely deny later that he sent a message.

Authentication
• Authentication is of ensuring that whoever
supplies or accesses the message is an
authorized party.
• Two solutions are:
– Passwords
– Digital signatures

Integrity
• This involves ensuring that when a message is
sent over a network, the data that arrives is the
same as the data that was originally sent. It is
important that the data has not been modified or
replaced .
• Technical solutions include:
– Encryption
– Hashing algorithms

Nonrepudiation
• Ensuring that the intended recipient actually
got the message.
• Ensuring that the alleged sender actually
sent the message.

Cryptographic Algorithm(Cipher)
• A cryptographic algorithm, also called a cipher, is
the mathematical function used for encryption and
decryption.
• Generally, there are two related functions: one for
encryption and the other for decryption.
• If the security of an algorithm is based on keeping
the way that algorithm works a secret, it is a
restricted algorithm.
• Restricted algorithms have historical interest, but
are woefully inadequate by today’s standards.

Restricted algorithm
• Drawbacks of restricted algorithm:
1. A large or changing group of users cannot use them,
because every time a user leaves the group everyone
else must switch to a different algorithm.
2. If someone accidentally reveals the secret,
everyone must change their algorithm.
3.Restricted algorithms allow no quality control or
standardization.

4. Every group of users must have their own unique
algorithm. Such a group can’t use off-the-shelf
hardware or software products; an eavesdropper
can buy the same product and learn the algorithm.
5. They have to write their own algorithms and
implementations. If no one in the group is a good
cryptographer, then they won’t know if they have
a secure algorithm.

Key and Key Space
• Key: Sequence that controls the operation and
behavior of the cryptographic algorithm
• rules used in algorithms to convert a document into a
secret document
• Keyspace : The range of possible values of the key is
called the keyspace.
• Now Ek(M)=C , Dk(C)=M then Dk (Ek(M))=M
Plaintext
Ciphertext
Plaintext
Key Key

20
• Keys are of two types:
– Symmetric
– Asymmetric
• A key is symmetric if the same key is used both for
encryption and decryption
• A key is asymmetric if different keys are used for encryption
and decryption
• Symmetric key methods
• DES 56-bit
• Triple DES 128-bit
• AES 128-bit and higher
• Blowfish 128-bit and higher
• Asymmetric key methods
• RSA (Rivest-Shamir-Adleman of MIT)
• PGP (Phil Zimmerman of MIT)

21
Cryptosystem
• Cryptosystem – The combination of algorithm,
plaintext, ciphertext, key, and key management
functions used to perform cryptographic operations
is called cryptosystem
• A cryptosystem is a 5-tuple (E,D,M,K,C), where
E: M x K  C —the set of encryption functions;
D: C x K  M —the set of decryption functions;
M —a set of plaintexts (some use P as symbol);
K —the set of keys;
C —the set of ciphertexts;

Cryptosystem Services
1. Authenticity
2. Integrity
3. Confidentiality
4. Nonrepudiation
5. Access Control
22

Symmetric Algorithms
• There are two general types of key-based algorithms:
symmetric and public-key.
• Symmetric algorithms , sometimes called conventional
algorithms, are algorithms where the same key is used
for both encryption and decryption.
• These algorithms, also called secret-key algorithms,
single key algorithms, or one-key algorithms
• It requires that the sender and receiver agree on a key
before they can communicate securely.
• This single key shared by two communicating parties.
• The shared key must remain secret to ensure the
confidentiality of the encrypted data

• The security of a symmetric algorithm rests in the
key; divulging the key means that anyone could
encrypt and decrypt messages. As long as the
communication needs to remain secret, the key
must remain secret.
• The shared key problem is the main technological
challenge for this kind of encryption.
• One method of distributing the key is using the sneaker-
net.
• Encryption and decryption with a symmetric algorithm
are denoted by: Ek(M)=C , Dk(C)=M

Types of Symmetric Algorithm
• Symmetric algorithms can be divided into two
categories:
1. Block ciphers
2. Stream ciphers
• Some operate on the plaintext a single bit(or
sometimes byte) at a time, these are called stream
algorithms or stream ciphers .
• Others operate on the plaintext in groups of bits.
The groups of bits are called blocks , and the
algorithms are called block algorithms or block
ciphers

Block Ciphers
• Most well-known and well-studied symmetric
algorithms use block ciphers.
• Block ciphers break up the message into constant-
size blocks and encrypt the code block by block.
• Typical block sizes are 64 bits or 128 bits.
• Messages are padded (with extra bits) to fit the
block size.
• The simplest type of block ciphers work in ECB
(Electronic Code Book) mode. In this mode, each
block is encrypted separately, independent of the
other blocks

Block Ciphers
• Two factors influence the security of a
symmetric block cipher:
– The quality of the algorithm (e.g., ECB mode
ciphers are less secure).
– The length of the key (e.g., 64 bit blocks are
questionable, but 128 bit blocks are considered
more than adequate).
• There is a classic trade-off between
efficiency and security.

Public-key algorithms
• Public-key algorithms (also called asymmetric algorithms)
are designed so that the key used for encryption is
different from the key used for decryption.
• Furthermore, the decryption key cannot (at least in any
reasonable amount of time) be calculated from the
encryption key. The algorithms are called "public-key"
because the encryption key can be made public.
• A complete stranger can use the encryption key to
encrypt a message, but only a specific person with the
corresponding decryption key can decrypt the message.
• In these systems, the encryption key is often called the
public key, and the decryption key is often called the
private key.

• The private key is sometimes also called the secret key,
but to avoid confusion with symmetric algorithms, that
tag won’t be used here.
• Encryption using public key K is denoted by:
Ek(M)=C
• Even though the public key and private key are different,
decryption with the corresponding private key is denoted
by:
Dk(C)=M
• Sometimes, messages will be encrypted with the private
key and decrypted with the public key; this is used in
digital signatures

Attack.
• An attempted cryptanalysis is called an attack.
• There are four general types of cryptanalytic attacks. Of
course, each of them assumes that the cryptanalyst has
complete knowledge of the encryption algorithm used:
1. Ciphertext-only attack
2. Known-plaintext attack
3. Chosen-plaintext attack
4. Adaptive-chosen-plaintext attack

Ciphertext-only attack
• Ciphertext-only attack : The cryptanalyst has the
ciphertext of several messages, all of which have been
encrypted using the same encryption algorithm.
• The cryptanalyst’s job is to recover the plaintext of as
many messages as possible, or better yet to deduce the
key (or keys) used to encrypt the messages, in order to
decrypt other messages encrypted with the same keys.

Known-plaintext attack
• Known-plaintext attack. The cryptanalyst has access not
only to the ciphertext of several messages, but also to
the plaintext of those messages.
• His job is to deduce the key (or keys) used to encrypt the
messages or an algorithm to decrypt any new messages
encrypted with the same key (or keys).

Chosen-plaintext attack
• Chosen-plaintext attack: The cryptanalyst not only has
access to the ciphertext and associated plaintext for
several messages, but he also chooses the plaintext that
gets encrypted.
• This is more powerful than a known-plaintext attack,
because the cryptanalyst can choose specific plaintext
blocks to encrypt, ones that might yield more information
about the key.
• His job is to deduce the key (or keys) used to encrypt the
messages or an algorithm to decrypt any new messages
encrypted with the same key (or keys).

Adaptive-chosen-plaintext attack
• Adaptive-chosen-plaintext attack : This is a special case of
a chosen-plaintext attack. The cryptanalyst not only can
choose the plaintext that is encrypted, but he can also
modify his choice based on the results of previous
encryption.
• In a chosen-plaintext attack, a cryptanalyst might just be
able to choose one large block of plaintext to be
encrypted.
• In an adaptive chosen-plaintext attack he can choose a
smaller block of plaintext and then choose another based
on the results of the first, and so forth.

Chosen-ciphertext attack
• There are at least three other types of cryptanalytic attack.
5 . Chosen-ciphertext attack: . The cryptanalyst can choose
different ciphertexts to be decrypted and has access to the
decrypted plaintext. For example, the cryptanalyst has
access to a tamperproof box that does automatic
decryption. His job is to deduce the key.
• This attack is primarily applicable to public-key algorithms .
A chosen-ciphertext attack is sometimes effective against a
symmetric algorithm as well.
• Sometimes a chosen-plaintext attack and a chosen-
ciphertext attack are together known as a chosen-text
attack .

6. Chosen-key attack : This attack doesn’t mean that the
cryptanalyst can choose the key. It means that he has
some knowledge about the relationship between
different keys . It’s strange and obscure, not very
practical
7. Rubber-hose cryptanalysis : The cryptanalyst threatens,
blackmails, or tortures someone until they give him the
key. Bribery is sometimes referred to as a purchase-key
attack

Security of Algorithms
• An algorithm is considered computationally secure
sometimes called strong if it cannot be broken with
available resources, either current or future.
• Different algorithms offer different degrees of
security . It depends on how hard they are to break.
1.If the cost required to break an algorithm is greater
than the value of the encrypted data, then it is
probably safe.
2. If the time required to break an algorithm is longer
than the time the encrypted data must remain secret,
then it is probably safe.

3. If the amount of data encrypted with a single key
is less than the amount of data necessary to break
the algorithm, then it is probably safe.
• Here the term "probably" is used because there is
always a chance of new breakthroughs in
cryptanalysis.
• On the other hand, the value of most data
decreases over time. It is important that the value
of the data always remain less than the cost to
break the security protecting it.

Categories of breaking an
algorithm
• Lars Knudsen classified different categories of breaking
an algorithm. In decreasing order of severity :
1. Total break : A cryptanalyst finds the key, K,
such that Dk(C)=M
2. Global deduction : A cryptanalyst finds an alternate
algorithm, A, equivalent to Dk(C)=M without knowing K.
3. Instance or local deduction : A cryptanalyst finds the
plaintext of an intercepted ciphertext.
4. Information deduction : A cryptanalyst gains some
information about the key or plaintext. This information
could be a few bits of the key, some information about the
form of the plaintext, and so forth.

Brute-force attack
• An algorithm is unconditionally secure , no matter
how much ciphertext a cryptanalyst has, if there is
not enough information to recover the plaintext.
• In point of fact, only a one-time pad is unbreakable
given infinite resources. All other cryptosystems are
breakable in a ciphertext only attack, simply by
trying every possible key one by one and checking
whether the resulting plaintext is meaningful. This
is called a brute-force attack

Complexity of an attack
• The complexity of an attack can be measured in three
different ways:
1. Data complexity : The amount of data needed(as
input) to perform the attack.
2. Processing or time complexity : The time needed to
perform the attack : This is often called the work
factor.
3.Storage requirements : The amount of memory needed
to perform the attack.

• Complexities are expressed as orders of magnitude.
If an algorithm has a processing complexity of 2128
then 2128
operations are required to break the
algorithm.
• If it is possible to perform a million operations every
second and a million parallel processors are set
against the task, it will still take over 1019
years to
recover the key. That’s a billion times the age of the
universe.

Types of Encryption Algorithms
• Two basic types
– Transposition ciphers
– Substitution ciphers
– Combinations are called product ciphers
• Substitution Ciphers
– Every letter or group of letters is replaced by
another letter or group of letters . Example:
Caesar cipher
– Easy to break by analyzing statistical
properties of written language

• Transposition Ciphers
– Instead of substituting letters in the plaintext,
we change their order
– Also easy to break by analyzing structure of
language
• Most actual encryption algorithms use a complex
combination of substitution and transposition
– Examples:
– Data Encryption Standard (DES)
– DES chaining

Substitution Ciphers
• A substitution cipher is one in which each character in
the plaintext is substituted for another character in
the ciphertext. The receiver inverts the substitution on
the ciphertext to recover the plaintext.
• In classical cryptography, there are four types of
substitution ciphers:
1. Simple substitution cipher or mono alphabetic
cipher
2. Homophonic substitution cipher
3. Polygram substitution cipher
4. poly alphabetic substitution cipher

Simple substitution cipher
• A simple substitution cipher, or mono alphabetic
cipher, is one in which each character of the
plaintext is replaced with a corresponding
character of ciphertext.
• The cryptograms in newspapers are simple
substitution ciphers.
• Caesar cipher is an example of a mono-
alphabetic cipher

Homophonic substitution cipher
• A homophonic substitution cipher is like a
simple substitution cryptosystem, except that a
single character of plaintext can map to one of
several characters of ciphertext.
• For example, "A" could correspond to either 5,
13, 25, or 56, "B" could correspond to either 7,
19, 31, or 4 2, and so on.

Polygram substitution cipher
• A polygram substitution cipher is one in which
blocks of characters are encrypted in groups.
• For example, "ABA" could correspond to "RTQ,"
"ABB" could correspond to "SLL, “ and so on.

Polyalphabetic substitution
cipher
• A polyalphabetic substitution cipher is made up
of multiple simple substitution ciphers.
• For example, there might be five different
simple substitution ciphers used; the particular
one used changes with the position of each
character of the plaintext.
• Vigenere cipher is an example of a poly-
alphabetic cipher

Caesar Cipher
• The famous Caesar Cipher, in which each plaintext
character is replaced by the character three to the
right modulo 26 ("A" is replaced by "D," "B" is replaced
by "E,"..., "W" is replaced by "Z," "X“ is replaced by "A,"
"Y" is replaced by "B," and "Z" is replaced by "C") is a
simple substitution cipher.
• It’s actually even simpler, because the ciphertext
alphabet is a rotation of the plaintext alphabet and not
an arbitrary permutation.

Transposition cipher
• In a transposition cipher the plaintext remains the
same, but the order of characters is shuffled
• around. In a simple columnar transposition cipher,
the plaintext is written horizontally onto a piece of
graph paper of fixed width and the ciphertext is
read off vertically (see Figure 1.4).
• Decryption is a matter of writing the ciphertext
vertically onto a piece of graph paper of identical
width and then reading the plaintext off
horizontally.

• Since the letters of the ciphertext are the same as
those of the plaintext, a frequency analysis on the
ciphertext would reveal that each letter has
approximately the same likelihood as in English.
• This gives a very good clue to a cryptanalyst, who
can then use a variety of techniques to determine
the right ordering of the letters to obtain the
plaintext. Putting the ciphertext through a second
transposition cipher greatly enhances security.

Columnar Transposition Ciphers
• A transposition cipher. Keyed by a phrase such as
“MEGABUCK”. The letter in the key indicated the order
of columns to be output. Plaintext horizontally read in,
ciphertext read out column by column.

One-time pad
• A one-time pad is the only (theoretically) 100% secure
method of encryption currently available today.
• The one-time pad's security comes from it's key; the key
(if chosen correctly) is EQUAL to the length of the
plaintext and is COMPLETELY random.
• When both conditions are simultaneously fulfilled, the
key is cryptographically secure.
• A one-time pad works as follows:
• Alice wants to send a message to Bob.
• Alice obtains a random key that is equal to the length of
the Plaintext. she wishes to send and transmits it to Bob
through an existing secure channel.

• She uses an algorithm to encrypt the Plaintext with the
key.
• The actual algorithm used doesn't matter, so long as it is
agreed upon by both Alice and Bob beforehand.
• After the encryption is completed, Alice DESTROYS the
key (so it can never be recovered or used again).
• Alice then sends the message to Bob who reverses the
encryption process and destroys his copy of the key.
• The key destruction ensures that the key will not be
reused. The cipher is called the one-time pad because
you have a "pad" of keys that are used only once and
thrown out

How it works
• The message is "THE BRITISH ARE COMING". So it
must have a random key of length 19. How the key is
obtained it is not important, but it has to be truly
random . And the key is “DKJFOISJOGIJPAPDIGN”
• Next procedure Cryptography Doc/One Time Pad
Tutorial.htm

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