A

Project Report

on

Seminar Topic

RSA Cryptography

in partial fulfillment

for the award of the Degree of

Bachelors of Technology

in Department of Computer Science

Submitted To: Submitted By:

Mohit Khandelwal Charchit Taneja

Project In-charge 11EIACS026

CSE Department CSE

IET Alwar

Department of Computer Science

Institute of Engineering and Technology, Alwar

January, 2015

i

Candidates Declaration

I hereby declare that the work, which is being presented in this report, entitled RSA

Cryptography in partial fulfillment for the award of Degree of Bachelor of Technology in

department of Computer Science, Institute of Engineering and Technology affiliated to,

Rajasthan Technical University is a record of my own investigations carried under the Guidance

of Mr. Mohit Khandelwal, Department of Computer Science Engineering, IET Alwar.

I have not submitted the matter presented in this report anywhere for the award of any other

Degree.

Charchit Taneja

11EIACS026

Computer Science

Counter Signed by:

Mohit Khandelwal

ii

Preface

This paper introduces Cryptography Techniques. Cryptography is The science of protecting data &

Network Security keeping information private and Secure from unauthorized Users.

This paper gives the Fundamental Requirements for the Data Transmission, the security attacks like

Interruption, Interception and Modification of the data Transmission.

The Cryptographic Process explaining through a generalized function is discussed through which

encryption and decryption is done by the various algorithms like RSA algorithm, Hash Functions and many

cryptographic algorithms. The Cryptanalysis is the process of attempting to discover the plain text and/ or

the key.

Applications of Various Cryptographic Technologies. Why & How to Provide Network Security in the

Certificates issuing, The Validity & Trust for Certificate Services, Certificate Revocation in the Internet,

Intranet and other Network Communications, the Applications of Network Security to the various Data

Transfer techniques and protocols. From the dawn of civilization, to the highly networked societies that we

live in Today communication has always been an integral part of our existence.

iii

Acknowledgement

It is a matter of great pleasure and privilege for me to present this seminar report, RSA

Cryptography that I had developed for fulfillment of my Bachelor of Technology in Computer

Science and Engineering. I have received enormous help, guidance and advice from many people

and I feel that it will be not be right to mention a line about at least some of them. The author

would like to express their utmost gratitude to the Institute of Engineering and Technology,

Alwar for providing opportunity to author to pursue for the degree of Bachelor of Technology.

I am grateful to our chairman Dr. V.K. Agarwal for providing me the opportunity to study in this

institution as well as providing us with all the necessary facilities.

Our principal Dr. Anil Kumar Sharma has been source of inspiration to us in our work sincerely.

I am also thankful to Prof (Dr.) S.K.Singh (H.O.D., CSE) and Mr. Mohit Khandelwal (Project

In-charge) for their encouragement and guidance. Their words of encouragement led us to finish

our work successfully.

I am also thankful to all faculty members of Computer Science & Engineering and Information

Technology Department and all other for help given to us directly or indirectly for the success of

this seminar.

Charchit Taneja

11EIACS026

CSE

iv

Table of Contents Candidates Declaration ............................................................................................................................... i

Preface .......................................................................................................................................................... ii

Acknowledgement ....................................................................................................................................... iii

Chapter 1 ....................................................................................................................................................... 1

1.1 Introduction ........................................................................................................................................ 1

1.2 HISTORY .............................................................................................................................................. 3

1.2.1 CLASSIC CRYPTOGRAPHY: ............................................................................................................ 3

1.3 THE COMPUTER ERA: .......................................................................................................................... 6

1.4 Cryptography Terminology ................................................................................................................. 8

Chapter 2 ..................................................................................................................................................... 10

2.1 Cryptography Services ...................................................................................................................... 10

2.2 Fundamental Requirements ............................................................................................................. 11

2.3 Attacks ............................................................................................................................................... 12

2.3.1 Passive Attacks: .......................................................................................................................... 12

2.3.2 Active Attacks: ............................................................................................................................ 13

2.3.3 Cipher Text Only Attack: ............................................................................................................ 13

2.3.4 Known Plaintext Attack .............................................................................................................. 14

2.3.5 Chosen Plaintext Attack: ............................................................................................................ 14

2.4 Security Attacks ................................................................................................................................. 14

2.5 Common Security Threats ................................................................................................................. 15

Chapter 3 ..................................................................................................................................................... 16

3.1 CIPHER ............................................................................................................................................... 16

3.2 CLASSICAL CIPHER ............................................................................................................................. 16

3.3 MODERN CIPHER ............................................................................................................................... 18

3.3.1 INPUT BASED CIPHERS: .............................................................................................................. 18

3.3.2 KEY BASED CIPHER: .................................................................................................................... 20

3.4 HASH FUNCTIONS: ............................................................................................................................ 23

Chapter 4 ..................................................................................................................................................... 25

4.1 ENCRYPTION MODES ........................................................................................................................ 25

4.1.1 ELECTRONIC CODEBOOK (EBC): ................................................................................................. 25

4.1.2 CIPHER BLOCK CHAINING: .......................................................................................................... 25

4.1.3 CIPHER FEEDBACK (CFB): ........................................................................................................... 25

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4.1.4 OUTPUT FEEDBACK (OFB): ......................................................................................................... 25

4.1.5 LRW Encryption Mode ............................................................................................................... 26

4.1.6 XTS Encryption Mode ................................................................................................................. 26

Chapter 5 ..................................................................................................................................................... 28

5.1 APPLICATIONS ................................................................................................................................... 28

5.2 Public-Key Encryption for Digital Signatures ..................................................................................... 30

5.3 Public-Key Encryption for Digital Certificates ................................................................................... 30

5.4 Digital Certificate .............................................................................................................................. 30

5.4.1 Cryptographic Technologies ....................................................................................................... 31

5.4.2 Based on Algorithms .................................................................................................................. 32

Chapter 6 ..................................................................................................................................................... 34

6.1 RSA (cryptosystem) ........................................................................................................................... 34

6.2 History ............................................................................................................................................... 34

6.3 Operation .......................................................................................................................................... 35

6.3.1 Key generation ........................................................................................................................... 35

6.3.2 Encryption .................................................................................................................................. 36

6.3.3 Decryption .................................................................................................................................. 37

Chapter 7 ..................................................................................................................................................... 38

CONCLUSION ........................................................................................................................................... 38

Chapter 8 ..................................................................................................................................................... 39

Reference ................................................................................................................................................ 39

1

Chapter 1

1.1 Introduction

Cryptography comes from Greek word kryptos, meaning "hidden or secret"; and

grphin means "writing". Cryptography is the practice and study of hiding information. Modern

cryptography intersects the disciplines of mathematics, computer science, and electrical

engineering. Applications of cryptography include ATM cards, computer passwords, and

electronic commerce.

Cryptology prior to the modern age was almost synonymous with encryption, the

conversion of information from a readable state to apparent gibberish. The sender retained the

ability to decrypt the information and therefore avoid unwanted persons being able to read it. Since

First World War and the advent of the computer, the methods used to carry out cryptology have

become increasingly complex and its application more widespread.

Modern cryptography follows a strongly scientific approach, and designs cryptographic

algorithms around computational hardness assumptions that are assumed hard to break by an

adversary. Such systems are not unbreakable in theory but it is infeasible to do so for any practical

adversary. Information-theoretically secure schemes that provably cannot be broken exist but they

are less practical than computationally-secure mechanisms. An example of such systems is the

one-time pad. Alongside the advancement in cryptology-related technology, the practice has raised

a number of legal issues, some of which remain unresolved.

Until modern times cryptography referred almost exclusively to encryption, which is the

process of converting ordinary information (called plaintext) into unintelligible gibberish (called

cipher text). Decryption is the reverse, in other words, moving from the unintelligible cipher text

back to plaintext. A cipher (or cypher) is a pair of algorithms that create the encryption and the

reversing decryption. The detailed operation of a cipher is controlled both by the algorithm and in

each instance by a key. This is a secret parameter (ideally known only to the communicants) for a

specific message exchange context.

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A "cryptosystem" is the ordered list of elements of finite possible plaintexts, finite possible

cypher texts, finite possible keys, and the encryption and decryption algorithms which correspond

to each key. Keys are important, as ciphers without variable keys can be trivially broken with only

the knowledge of the cipher used and are therefore useless (or even counter-productive) for most

purposes. Historically, ciphers were often used directly for encryption or decryption without

additional procedures such as authentication or integrity checks.

In colloquial use, the term "code" is often used to mean any method of encryption or

concealment of meaning. However, in cryptography, code has a more specific meaning. It means

the replacement of a unit of plaintext (i.e., a meaningful word or phrase) with a code word (for

example, wallaby replaces attack at dawn). Codes are no longer used in serious cryptography

except incidentally for such things as unit designations (e.g., Bronco Flight or Operation

Overlord)since properly chosen ciphers are both more practical and more secure than even the

best codes and also are better adapted to computers.

Cryptanalysis is the term used for the study of methods for obtaining the meaning of

encrypted information without access to the key normally required to do so; i.e., it is the study of

how to crack encryption algorithms or their implementations.

Some use the terms cryptography and cryptology interchangeably in English, while others

(including US military practice generally) use cryptography to refer specifically to the use and

practice of cryptographic techniques and cryptology to refer to the combined study of cryptography

3

and cryptanalysis. English is more flexible than several other languages in which cryptology (done

by cryptologists) is always used in the second sense above.

The study of characteristics of languages which have some application in cryptography (or

cryptology), i.e. frequency data, letter combinations, universal patterns, etc., is called crypto

linguistics.

1.2 HISTORY

Before the modern era, cryptography was concerned solely with message confidentiality

(i.e., encryption)conversion of messages from a comprehensible form into an incomprehensible

one and back again at the other end, rendering it unreadable by interceptors or eavesdroppers

without secret knowledge (namely the key needed for decryption of that message). Encryption was

used to (attempt to) ensure secrecy in communications, such as those of spies, military leaders,

and diplomats. In recent decades, the field has expanded beyond confidentiality concerns to

include techniques for message integrity checking, sender/receiver identity authentication, digital

signatures, interactive proofs and secure computation, among others.

1.2.1 CLASSIC CRYPTOGRAPHY:

The earliest forms of secret writing required little more than local pen and paper analogs,

as most people could not read. More literacy, or literate opponents, required actual cryptography.

The main classical cipher types are transposition ciphers, which rearrange the order of letters in a

message (e.g., 'hello world' becomes 'ehlol owrdl' in a trivially simple rearrangement scheme),

and substitution ciphers, which systematically replace letters or groups of letters with other letters

or groups of letters (e.g., 'fly at once' becomes 'gmz bu podf' by replacing each letter with the

one following it in the Latin alphabet). Simple versions of either have never offered much

confidentiality from enterprising opponents.

An early substitution cipher was the Caesar cipher, in which each letter in the plaintext was

replaced by a letter some fixed number of positions further down the alphabet. It was named after

4

Julius Caesar who is reported to have used it, with a shift of 3, to communicate with his generals

during his military campaigns, just like EXCESS-3 code in boolean algebra. There is record of

several early Hebrew ciphers as well. The earliest known use of cryptography is some carved

ciphertext on stone in Egypt (ca 1900 BC), but this may have been done for the amusement of

literate observers. The next oldest is bakery recipes from Mesopotamia. Cryptography is

recommended in the books as a way for lovers to communicate without inconvenient discovery.

The Greeks of Classical times are said to have known of ciphers (e.g., the scytale

transposition cipher claimed to have been used by the Spartan military). Steganography (i.e.,

hiding even the existence of a message so as to keep it confidential) was also first developed in

ancient times. An early example, from Herodotus, concealed a messagea tattoo on a slave's

shaved headunder the regrown hair. Another Greek method was developed by Polybius (now

called the "Polybius Square"). More modern examples of steganography include the use of

invisible ink, microdots, and digital watermarks to conceal information.

Cipher texts produced by a classical cipher (and some modern ciphers) always reveal

statistical information about the plaintext, which can often be used to break them. After the

discovery of frequency analysis perhaps by the Arab mathematician and polymath, Al-Kindi (also

known as Alkindus), in the 9th century, nearly all such ciphers became more or less readily

breakable by any informed attacker. Such classical ciphers still enjoy popularity today, though

mostly as puzzles (see cryptogram). Al-Kindi wrote a book on cryptography entitled Risalah fi

Istikhraj al-Mu'amma (Manuscript for the Deciphering Cryptographic Messages), in which

described the first cryptanalysis techniques.

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Essentially all ciphers remained vulnerable to cryptanalysis using the frequency analysis

technique until the development of the polyalphabetic cipher, most clearly by Leon Battista Alberti

around the year 1467, though there is some indication that it was already known to Al-Kindi.

Alberti's innovation was to use different ciphers (i.e., substitution alphabets) for various parts of a

message (perhaps for each successive plaintext letter at the limit). He also invented what was

probably the first automatic cipher device, a wheel which implemented a partial realization of his

invention. In the polyalphabetic Vigenre cipher, encryption uses a key word, which controls letter

substitution depending on which letter of the key word is used. In the mid-19th century Charles

Babbage showed that polyalphabetic ciphers of this type remained partially vulnerable to extended

frequency analysis techniques.

Although frequency analysis is a powerful and general technique against many ciphers,

encryption has still been often effective in practice; many a would-be cryptanalyst was unaware of

the technique. Breaking a message without using frequency analysis essentially required

knowledge of the cipher used and perhaps of the key involved, thus making espionage, bribery,

burglary, defection, etc., more attractive approaches to the cryptanalytically uninformed. It was

finally explicitly recognized in the 19th century that secrecy of a cipher's algorithm is not a sensible

or practical safeguard of message security; in fact, it was further realized that any adequate

cryptographic scheme (including ciphers) should remain secure even if the adversary fully

understands the cipher algorithm itself. Security of the key used should alone be sufficient for a

good cipher to maintain confidentiality under an attack. This fundamental principle was first

explicitly stated in 1883 by Auguste Kerckhoffs and is generally called Kerckhoffs' principle;

alternatively and more bluntly, it was restated by Claude Shannon, the inventor of information

theory and the fundamentals of theoretical cryptography, as Shannon's Maxim'the enemy

knows the system'.

Different physical devices and aids have been used to assist with ciphers. One of the earliest

may have been the scytale of ancient Greece, a rod supposedly used by the Spartans as an aid for

a transposition cipher. In medieval times, other aids were invented such as the cipher grille, which

was also used for a kind of steganography. With the invention of polyalphabetic ciphers came

more sophisticated aids such as Alberti's own cipher disk, Johannes Trithemius' tabula recta

scheme, and Thomas Jefferson's multi-cylinder. Many mechanical encryption/decryption devices

6

were invented early in the 20th century, and several patented, among them rotor machines

famously including the Enigma machine used by the German government and military from the

late '20s and during World War II. The ciphers implemented by better quality examples of these

machine designs brought about a substantial increase cryptanalytic difficulty after WWI.

Fig: Enigma Machine

1.3 THE COMPUTER ERA:

The development of digital computers and electronics after World War II made possible

much more complex ciphers. Furthermore, computers allowed for the encryption of any kind of

data representable in any binary format, unlike classical ciphers which only encrypted written

language texts; this was new and significant. Computer use has thus supplanted linguistic

cryptography, both for cipher design and cryptanalysis. Many computer ciphers can be

characterized by their operation on binary bit sequences (sometimes in groups or blocks), unlike

classical and mechanical schemes, which generally manipulate traditional characters (i.e., letters

and digits) directly.

However, computers have also assisted cryptanalysis, which has compensated to some

extent for increased cipher complexity. Nonetheless, good modern ciphers have stayed ahead of

cryptanalysis; it is typically the case that use of a quality cipher is very efficient (i.e., fast and

requiring few resources, such as memory or CPU capability), while breaking it requires an effort

many orders of magnitude larger, and vastly larger than that required for any classical cipher,

7

making cryptanalysis so inefficient and impractical as to be effectively impossible. Alternate

methods of attack (bribery, burglary, threat, torture,) have become more attractive in consequence.

Credit card with smart-card capabilities. The 3-by-5-mm chip embedded in the card is

shown, enlarged. Smart cards combine low cost and portability with the power to compute

cryptographic algorithms.

Extensive open academic research into cryptography is relatively recent; it began only in

the mid-1970s. In recent times, IBM personnel designed the algorithm that became the Federal

(i.e., US) Data Encryption Standard; Whitfield Diffie and Martin Hellman published their key

agreement algorithm known as Diffie-Hellman algorithm; and the RSA algorithm was published

in Martin Gardner's Scientific American column. Since then, cryptography has become a widely

used tool in communications, computer networks, and computer security generally. Some modern

cryptographic techniques can only keep their keys secret if certain mathematical problems are

intractable, such as the integer factorization or the discrete logarithm problems, so there are deep

connections with abstract mathematics. There are no absolute proofs that a cryptographic

technique is secure (but see one-time pad); at best, there are proofs that some techniques are secure

if some computational problem is difficult to solve, or this or that assumption about

implementation or practical use is met.

As well as being aware of cryptographic history, cryptographic algorithm and system

designers must also sensibly consider probable future developments while working on their

designs. For instance, continuous improvements in computer processing power have increased the

scope of brute-force attacks, thus when specifying key lengths, the required key lengths are

similarly advancing. The potential effects of quantum computing are already being considered by

8

some cryptographic system designers; the announced imminence of small implementations of

these machines may be making the need for this preemptive caution rather more than merely

speculative.

Essentially, prior to the early 20th century, cryptography was chiefly concerned with

linguistic and lexicographic patterns. Since then the emphasis has shifted, and cryptography now

makes extensive use of mathematics, including aspects of information theory, computational

complexity, statistics, combinatory, abstract algebra, number theory, and finite mathematics

generally. Cryptography is, also, a branch of engineering, but an unusual one as it deals with active,

intelligent, and malevolent opposition (see cryptographic engineering and security engineering);

other kinds of engineering (e.g., civil or chemical engineering) need deal only with neutral natural

forces. There is also active research examining the relationship between cryptographic problems

and quantum physics (see quantum cryptography and quantum computing).

1.4 Cryptography Terminology

a) Plaintext: The original intelligible message.

b) Cipher text: The transformed message.

c) Cipher: An algorithm for transforming an intelligible message to unintelligible by transposition.

d) Key: Some critical information used by the cipher, known only to the sender & receiver.

e) Encipher :( Encode) the process of converting plaintext to cipher text using a cipher and a key.

f) Decipher :( Decode) the process of converting cipher text back into plaintext using a cipher &

key.

g) Cryptanalysis: The study of principles and methods of transforming an unintelligible message

back into an intelligible message without knowledge of the key. Also called code breaking

h) Cryptology: Both cryptography and cryptanalysis

9

i) Code: an algorithm for transforming an intelligible message into an unintelligible one using

codes.

j) Hash algorithm: Is an algorithm that converts text string into a string of fixed length.

k) Secret Key Cryptography (SKC): Uses a single key for both encryption and decryption

l) Public Key Cryptography (PKC): Uses one key for encryption and another for decryption

m) Pretty Good Privacy (PGP): PGP is a hybrid cryptosystem.

n) Public Key Infrastructure (PKI): PKI feature is Certificate authority.

10

Chapter 2

2.1 Cryptography Services

Any new design of Cryptographic technique must accomplish the above requisites.

Cryptography not only protects data from theft or alteration, but can also be used for user

authentication.

Hence, the various security requirements for a Cryptographic technique including:

Authentication: The process of proving one's identity. (The primary forms of host-to-

host authentication on the Internet today are name-based or address-based, both of which

are notoriously weak.)

Privacy/confidentiality: Ensuring that no one can read the message except the intended

receiver.

Integrity: Assuring the receiver that the received message has not been altered in any

way from the original.

Non-repudiation: A mechanism to prove that the sender really sent this message.

Access-control: A method in which the access to unauthorized users is prohibited, i.e.

only the authorized user can have access to its documents.

Availability: This method guarantees that the system services are always available when

needed.

Security-Audit: With the help of this mechanism a record of all the previous transactions

are kept which may provide useful information at a later stage.

11

Source Destination

Unauthorized user

Key-Management: This method allows negotiating, as well as setup and maintaining

keys between the communicating entities.

2.2 Fundamental Requirements

Confidential: Is the process of keeping information private and Secret so that only the intended

recipient is able to understand the information.

Authentication: Is the process of providing proof of identity of the sender to the recipient, so that

the recipient can be assured that the person sending the information is who and what he or she

claims to be.

Integrity: Is the method to ensure that information is not tampered with during its transit or its

storage on the network. Any unauthorized person should not be able to tamper with the information

or change the Information during transit

Non-repudiation: Is the method to ensure that information cannot be disowned. Once the non-

repudiation process is in place, the sender cannot deny being the originator of the data.

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2.3 Attacks

According to the cryptanalyst Kent, there are many ways in which the personal information

shared between two peoples can be interrupted with. Here an intermediate person, known as an

attacker, has an access to the information being transferred called as passive attacker, and can even

change the information being exchanged with the help of some technology and is called as an

active attacker.

2.3.1 Passive Attacks:

This kind of attacks is generally carried by a passive intruder who only has an access to the

information or message being exchanged. Considering the trivial case of Bob and Alice where Bob

wants to send a message to Alice. Here the intruder has access to the contents only i.e. he can read

the message but cannot tamper with it. So due to the inability to create any changes the intruder is

called as a passive attacker.

13

2.3.2 Active Attacks:

This kind of attacks is generally carried by an active intruder who not only has an access to the

information or message being exchanged but can also tamper or manipulate the message being

exchanged. So due to the ability to create any changes the intruder is called as an active attacker.

Some other types of attack can also be considered such as:

2.3.3 Cipher Text Only Attack:

This is the situation where the attacker does not know anything about the contents of the message,

and must work from cipher text only. In practice it is quite often possible to make guesses about

the plaintext, as many types of messages have fixed format headers. Even ordinary letters and

documents begin in a very predictable way. It may also be possible to guess that some cipher text

block contains a common word.

14

2.3.4 Known Plaintext Attack:

The attacker knows or can guess the plaintext for some parts of the cipher text. The task is to

decrypt the rest of the cipher text blocks using this information. This may be done by determining

the key used to encrypt the data, or via some shortcut.

2.3.5 Chosen Plaintext Attack:

The attacker is able to have any text he likes encrypted with the unknown key. The task is to

determine the key used for encryption. Some encryption methods, particularly RSA, are extremely

vulnerable to chosen-plaintext attacks. When such algorithms are used, extreme care must be taken

to design the entire system so that an attacker can never have chosen plaintext encrypted.

2.4 Security Attacks

Interruption: In an attack where one or more of the systems of the organization become unusable

due to attacks by unauthorized users. This leads to systems being unavailable for use.

Interception: An unauthorized individual intercepts the message content and changes it or uses it

for malicious purposes. After this type of attack, the message does not remain confidential.

Modification: The content of the message is modified by a third party. This attack affects the

integrity of the message. So for maintaining the data secretly while communicating data between

two persons or two organizations data is to be converted to other format and the data is to be

transmitted. So now we deal with the Cryptography which is process of transmitting data securely

without any interruption. Network security is the security of data transmission in the

communication.

15

2.5 Common Security Threats

Identity interception: It means that someone might steal your identity and use it as their own.

Masquerading. If you send your username and password in clear text form, someone might be able

to grab it from the network and use it elsewhere with the intention of perpetrating fraud.

Replay attack: They might capture your request of withdrawing 1000 dollars from your Bank

account and then replay that request over the network.

Data interception and manipulation: If someone can read your credit card information while it

is on the wire, they could cause a lot of trouble for you.

Repudiation: When someone performs a transaction and then deny it later can be a big problem

in ecommerce.

For example, if you are manufacturer of something and you received a 1 million dollar purchase

request from a customer, you will want to make sure that person does not deny it after the

transaction has been completed. We all know what denial of service means.

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Chapter 3

3.1 CIPHER

A cipher is an algorithm for performing encryption or decryption using a series of well-

defined steps that can be followed as a procedure.

For a cipher to be of practical value:

1. It must be difficult to be broken by enemy cryptanalyst.

2. It must be easy to encrypt decrypt with knowledge of secret key.

Data that can be read and understood without any special measures is called plaintext or clear text.

The method of disguising plaintext in such a way as to hide its substance is called encryption.

Encrypting plaintext results in unreadable gibberish called cipher text. You use encryption to make

sure that information is hidden from anyone for whom it is not intended, even those who can see

the encrypted data. The process of reverting cipher text to its original plaintext is called decryption.

3.2 CLASSICAL CIPHER

Historical pen and paper ciphers used in the past are sometimes known as classical ciphers.

They include simple substitution ciphers or Caesars cipher and transposition ciphers. For

example GOOD DOG can be encrypted as PLLX XLP where L substitutes for O, P for

17

G, and X for D in the message. Transposition of the letters GOOD DOG can result in

DGOGDOO. Julius Caesar used to substitute each alphabet key characters down or up

accordingly and where the key used by him was 3.

Figure: Caesar Cipher

These simple ciphers and examples are easy to crack, even without plaintext-cipher text

pairs. Simple ciphers were replaced by polyalphabetic substitution ciphers which changed the

substitution alphabet for every letter. For example GOOD DOG can be encrypted as PLSX

TWF where L, S, and W substitute for O. With even a small amount of known or

estimated plaintext, simple polyalphabetic substitution ciphers and letter transposition ciphers

designed for pen and paper encryption are easy to crack. Another advancement in the theory was

the transposition cipher where the characters retain their plaintext form but change their positions

to create the cipher text. Here the text is organized into two dimensional tables, and the rows and

columns are interchanged according to a key. Consider the plaintext attackatxdawn and the

cipher text obtained using the transposition algorithm is xtawxnattxadakc as shown in the

figure below. In the following example the rows 1-5 and columns 1-3 are permutated to give new

set of rows (3,5,1,4,2) and columns (1,3,2).

18

Figure: Double Transposition

3.3 MODERN CIPHER

In cryptography several new ways of encrypting the message was further devised. These

algorithms were a bit more complicated than the previous classical ciphers. Generally modern

ciphers are classified according to their input size based or key based.

3.3.1 INPUT BASED CIPHERS:

The most common input size based ciphers are block cipher and stream cipher and are

described as follows.

3.3.1.1 BLOCK CIPHER:

In cryptography, a block cipher is a symmetric key cipher operating on fixed-length groups

of bits, called blocks, with an unvarying transformation. A block cipher encryption algorithm

might take (for example) a 128-bit block of plaintext as input, and output a corresponding 128-bit

block of cipher text. The exact transformation is controlled using a second input the secret key.

Decryption is similar: the decryption algorithm takes, in this example, a 128-bit block of cipher

text together with the secret key, and yields the original 128-bit block of plaintext.

Permute rows and columns

19

A message longer than the block size (128 bits in the above example) can still be encrypted with

a block cipher by breaking the message into blocks and encrypting each block individually.

However, in this method all blocks are encrypted with the same key, which degrades security

(because each repetition in the plaintext becomes a repetition in the cipher text). To overcome this

issue, modes of operation are used to make encryption probabilistic.

3.3.1.2 STREAM CIPHER:

In cryptography, a stream cipher is a symmetric key cipher where plaintext bits are combined

with a pseudorandom cipher bit stream (key stream), typically by an exclusive-or (xor) operation.

In a stream cipher the plaintext digits are encrypted one at a time, and the transformation of

successive digits varies during the encryption. An alternative name is a state cipher, as the

encryption of each digit is dependent on the current state. In practice, the digits are typically single

bits or bytes.

20

Stream ciphers represent a different approach to symmetric encryption from block ciphers.

Block ciphers operate on large blocks of digits with a fixed, unvarying transformation. This

distinction is not always clear-cut: in some modes of operation, a block cipher primitive is used in

such a way that it acts effectively as a stream cipher. Stream ciphers typically execute at a higher

speed than block ciphers and have lower hardware complexity. However, stream ciphers can be

susceptible to serious security problems if used incorrectly: see stream cipher attacks in

particular, the same starting state must never be used twice.

3.3.2 KEY BASED CIPHER:

Apart from the block and stream ciphers a more enhanced methods were developed involving

the usage of a public and private key. The most widely used amongst them are described as follows.

3.3.2.1 SYMMETRIC KEY CRYPTOGRAPHY:

With secret key cryptography, a single key is used for both encryption and decryption. As

shown in figure, the sender uses the key (or some set of rules) to encrypt the plaintext and sends

the cipher text to the receiver. The receiver applies the same key (or rule set) to decrypt the message

and recover the plaintext. Because a single key is used for both functions, secret key cryptography

is also called symmetric encryption. Secret key cryptography schemes are generally categorized

as being either stream ciphers or block ciphers. Stream ciphers operate on a single bit (byte or

computer word) at a time and implement some form of feedback mechanism so that the key is

constantly changing. A block cipher is so called because the scheme encrypts one block of data at

a time using the same key on each block. In general, the same plaintext block will always encrypt

to the same cipher text when using the same key in a block cipher whereas the same plaintext will

encrypt to different cipher text in a stream cipher.

21

Figure: Symmetric Key Cryptography

It can be seen that symmetric key cryptography requires less time to encrypt a message so its

efficiency is high but on the other hand it must also be noted that each pair of users must have a

unique key, so N users need N(N-1)/2 keys. As a result the key distribution becomes difficult.

The most commonly used algorithms in symmetric key cryptography to encrypt the message are:

DES (Data Encryption Standard) and derivatives: double DES and triple DES

IDEA (International Data Encryption Algorithm)

Blowfish

RC5 (Rivest Cipher #5)

AES (Advance Encryption Standard)

22

3.3.2.2 PUBLIC KEY CRYPTOGRAPHY:

Public-key cryptography has been said to be the most significant new development in secure

communication over a non-secure communications channel without having to share a secret key.

Public Key Cryptography or Asymmetric cryptography provides the same message security

guarantees as symmetric cryptography, but additionally provides the non-repudiation guarantee.

Asymmetric refers to the fact that different keys are used for encryption and decryption. One

key is kept secret (secret key) and the other is made public (public key), and are both unique.

The recipients public key should be used during the encryption process to ensure message

confidentiality as only the recipient has the necessary secret key to decrypt the message. If,

however, the message is encrypted using the senders private key the sender cannot deny sending

the message as his private key is unique and is only known to him. Asymmetric cryptography is

extremely powerful, but this comes at a cost. Especially for longer messages and keys, it is much

slower than its symmetric cryptography counterparts. This is due in part to the fact that, in order

to achieve comparable security, asymmetric keys are generally around an order of magnitude

longer than symmetric keys.

Figure: Public Key Encryption

Typically used asymmetric key algorithm includes:

23

RSA (Rivest, Shamir, Adleman)

DH (Diffie-Hellman Key Agreement Algorithm)

ECDH (Elliptic Curve Diffie-Hellman Key Agreement Algorithm)

RPK (Raike Public Key)

3.4 HASH FUNCTIONS:

The system described above has some problems. It is slow, and it produces an enormous

volume of dataat least double the size of the original information. An improvement on the above

scheme is the addition of a one-way hash function in the process. A one-way hash function takes

variable-length input in this case, a message of any length, even thousands or millions of bits

and produces a fixed-length output; say, 160 bits.

The hash function ensures that, if the information is changed in any wayeven by just one

bitan entirely different output value is produced. PGP uses a cryptographically strong hash

24

function on the plaintext the user is signing. This generates a fixed-length data item known as a

message digest. Then PGP uses the digest and the private key to create the signature. PGP

transmits the signature and the plaintext together. Upon receipt of the message, the recipient uses

PGP to recompute the digest, thus verifying the signature. PGP can encrypt the plaintext or not;

signing plaintext is useful if some of the recipients are not interested in or capable of verifying the

signature. As long as a secure hash function is used, there is no way to take someones signature

from one document and attach it to another, or to alter a signed message in any way. The slightest

change to a signed document will cause the digital signature verification process to fail. Digital

signatures play a major role in authenticating and validating the keys of other PGP users.

25

Chapter 4

4.1 ENCRYPTION MODES

The ciphers in use are generally following these four encryption modes:

4.1.1 ELECTRONIC CODEBOOK (EBC):

Electronic Codebook (ECB) mode is the simplest, most obvious application: the secret key is

used to encrypt the plaintext block to form a cipher text block. Two identical plaintext blocks,

then, will always generate the same cipher text block. Although this is the most common mode

of block ciphers, it is susceptible to a variety of brute-force attacks

4.1.2 CIPHER BLOCK CHAINING:

Cipher Block Chaining (CBC) mode adds a feedback mechanism to the encryption scheme. In

CBC, the plaintext is exclusively-O Red (XORed) with the previous cipher text block prior to

encryption. In this mode, two identical blocks of plaintext never encrypt to the same cipher

text.

4.1.3 CIPHER FEEDBACK (CFB):

Cipher Feedback (CFB) mode is a block cipher implementation as a self-synchronizing stream

cipher. CFB mode allows data to be encrypted in units smaller than the block size, which might

be useful in some applications such as encrypting interactive terminal input. If we were using

1-byte CFB mode, for example, each incoming character is placed into a shift register the same

size as the block, encrypted, and the block transmitted. At the receiving side, the cipher text is

decrypted and the extra bits in the block (i.e., everything above and beyond the one byte) are

discarded.

4.1.4 OUTPUT FEEDBACK (OFB):

Output Feedback (OFB) mode is a block cipher implementation conceptually similar to a

synchronous stream cipher. OFB prevents the same plaintext block from generating the same

26

cipher text block by using an internal feedback mechanism that is independent of both the

plaintext and cipher text bit streams.

4.1.5 LRW Encryption Mode

BestCrypt uses LRW encryption mode with all encryption algorithms supported by the

software. "LRW" is derived from the names Liskov, Rivest, Wagner - the authors of the

encryption mode. The Institute of Electrical and Electronics Engineers (IEEE) has published a

description of the LRW mode in IEEE P1619 document.

LRW mode is less susceptible to attack or being compromised than other current techniques

such as Counter-Mode encryption or Cipher Block Chaining (CBC) encryption. The mode

addresses threats such as copy-and-paste and dictionary attacks. LRW mode is specially

designed for encryption of storage at the sector level.

LRW mode uses its own secret Secondary Encryption Key that is completely different from a

Primary Encryption Key used by certain encryption algorithms. The size of an LRW Secondary

Key is equal to the block size of the particular encryption algorithm. For example, if the block

size of an AES encryption algorithm is 128 bits, the LRW mode requires a 128-bit Secondary

Key.

As a result, the effective key length for the pair LRW mode + AES becomes higher than AES

originally has. While the AES key length is 256 bits, LRW+AES pair uses 256+128 = 384 bits

key.

Depending on your system, there can be some read /write performance degradation when using

LRW. Please use the Benchmark Utility to test.

4.1.6 XTS Encryption Mode

Best Crypt uses XTS encryption mode with AES (Rijndael), RC6, Serpent, and Two fish

encryption algorithms.

27

The Institute of Electrical and Electronics Engineers (IEEE) has approved XTS mode for

protection of information on block storage devices according to IEEE 1619 standard released

on 19th December, 2007. The IEEE 1619 document states the following for AES encryption

algorithm used as subroutine in XTS mode:

"XTS-AES is a tweak able block cipher that acts on data units of 128 bits or more and uses the

AES block cipher as a subroutine. The key material for XTS-AES consists of a data encryption

key (used by the AES block cipher) as well as a "tweak key" that is used to incorporate the

logical position of the data block into the encryption. XTS-AES is a concrete instantiation of

the class of tweak able block ciphers described in Rogaway article (Phillip Rogaway - author

of the mode). The XTS-AES addresses threats such as copy-and-paste attack, while allowing

parallelization and pipelining in cipher implementations."

XTS mode uses its own secret key (a "tweak key") that is completely different from Primary

Encryption Key used by certain encryption algorithm.

For example, if block size of AES encryption algorithm is 128 bits, XTS mode requires 128-

bit key. As a result, the effective key length for the pair XTS mode + AES becomes higher

than AES originally has. While AES key length is 256 bits, XTS+AES pair uses 256+128 =

384 bits key.

The size of XTS key is equal to block size of the certain encryption algorithm, and IEEE 1619

standard states that it must be 128 bits or more. It is the reason why Best Crypt uses XTS mode

only with encryption algorithms with block sizes not less than 128 bits.

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Chapter 5

5.1 APPLICATIONS

Cryptography is best known as a way of keeping the contents of a message secret.

Confidentiality of network communications, for example, is of great importance for e-commerce

and other network applications. However, the applications of cryptography go far beyond simple

confidentiality. In particular, cryptography allows the network business and customer to verify the

authenticity and integrity of their transactions. If the trend to a global electronic marketplace

continues, better cryptographic techniques will have to be developed to protect business

transactions.

Sensitive information sent over an open network may be scrambled into a form that cannot be

understood by a hacker or eavesdropper. This is done using a mathematical formula, known as an

encryption algorithm, which transforms the bits of the message into an unintelligible form. The

intended recipient has a decryption algorithm for extracting the original message. There are many

examples of information on open networks, which need to be protected in this way, for instance,

bank account details, credit card transactions, or confidential health or tax records.

In order to allow different users to use the same algorithm, the algorithm is used in

conjunction with a secret key, a long sequence of binary numbers, as shown in the illustration,

which is known only by the legitimate users. Only users sharing the same key will be able to

29

decrypt each other's encrypted messages. Since the key allows access to the encrypted information,

it is of paramount importance that it is kept secret and is frequently changed.

Before two parties can send information securely, they must first exchange a secret key.

This however presents a dilemma, sometimes called the Catch 22 of Cryptography how can

the two parties exchange a key secretly before they can communicate in secret? Even if the sender

and receiver found a channel that they believed to be secure, in the past there has been no way to

test the secrecy of each key. Quantum cryptography solves this problem. It allows the sender and

receiver to test and guarantee the secrecy of each individual key. There are various types of

applications which are given below.

1. Defense Services

2. Secure Data Manipulation

3. E Commerce

4. Business Transactions

5. Internet Payment Systems

6. Pass Phrasing

7. Secure Internet Comm.

8. User Identification Systems

9. Access Control

10. Computational Security

11. Secure access to Corp Data

12. Data Security.

30

5.2 Public-Key Encryption for Digital Signatures

A major benefit of public key cryptography is that it provides a method for employing digital

signatures. Digital signatures enable the recipient of information to verify the authenticity of the

information's origin, and also verify that the information is intact. Thus, public key digital

signatures provide authentication and data integrity. A digital signature also provides non-

repudiation, which means that it prevents the sender from claiming that he or she did not actually

send the information. These features are every bit as fundamental to cryptography as privacy, if

not more.

A digital signature serves the same purpose as a handwritten signature. However, a handwritten

signature is easy to counterfeit. A digital signature is superior to a handwritten signature in that it

is nearly impossible to counterfeit, plus it attests to the contents of the information as well as to

the identity of the signer.

5.3 Public-Key Encryption for Digital Certificates

Digital certificates, or cert., simplify the task of establishing whether a public key truly belongs

to the purported owner. A certificate is a form of credential. Examples might be your birth

certificate.

Each of these has some information on it identifying you and some authorization stating that

someone else has confirmed your identity. Some certificates, such as your passport, are important

enough confirmation of your identity that you would not want to lose them, lest someone use them

to impersonate you.

5.4 Digital Certificate

A digital certificate is data that functions much like a physical certificate. A digital certificate is

information included with a person's public key that helps others verify that a key is genuine or

valid.

31

Digital certificates are used to thwart attempts to substitute one person's key for another.A digital

certificate consists of three things:

A public key.

Certificate information. ("Identity" information about the user, such as name, user ID, and

so on.)

One or more digital signatures.

The purpose of the digital signature on certificate is to state that the certificate information has

been attested to by some other person or entity. The digital signature does not attest to the

authenticity of the certificate as a whole; it vouches only that the signed identity information goes

along with, or is bound to, the public key. Thus, a certificate is basically a public key with one or

two forms of ID attached, plus a hearty stamp of approval from some other trusted individual.

5.4.1 Cryptographic Technologies

Based on Layers

Link layer encryption

Network layer encryption

IPSEC, VPN, SKIP

Transport layer

SSL, PCT(Private Communication Technology)

Application layer

PEM (Privacy Enhanced Mail)

PGP (Pretty Good Privacy)

SHTTP

Cryptographic process can be implemented at various layers starting from the link Layer all the

way up to the application layer. The most popular encryption scheme is SSL and it is implemented

at the transport layer. If the encryption is done at the transport layer, any application that is running

on the top of the transport layer can be protected.

32

5.4.2 Based on Algorithms

Secret-key encryption algorithms (Symmetric algorithms)

DES (Data Encryption Standard) -- 56 bit key

Triple DES --112 bit key

IDEA (International Data Encryption Algorithm) --128bit key

33

34

Chapter 6

6.1 RSA (cryptosystem)

RSA is one of the first practicable public-key cryptosystems and is widely used for secure data

transmission. In such a cryptosystem, the encryption key is public and differs from the decryption

key which is kept secret. In RSA, this asymmetry is based on the practical difficulty of factoring

the product of two large prime numbers, the factoring problem. RSA stands for Ron Rivest, Adi

Shamir and Leonard Adleman, who first publicly described the algorithm in 1977. Clifford Cocks,

an English mathematician, had developed an equivalent system in 1973, but it was not declassified

until 1997.

A user of RSA creates and then publishes a public key based on the two large prime numbers,

along with an auxiliary value. The prime numbers must be kept secret. Anyone can use the public

key to encrypt a message, but with currently published methods, if the public key is large enough,

only someone with knowledge of the prime numbers can feasibly decode the message. Breaking

RSA encryption is known as the RSA problem; whether it is as hard as the factoring problem

remains an open question.

6.2 History

The RSA algorithm was publicly described in 1977 by Ron Rivest, Adi Shamir, and Leonard

Adleman at MIT; the letters RSA are the initials of their surnames, listed in the same order as on

the paper.

MIT was granted U.S. Patent 4,405,829 for a "Cryptographic communications system and method"

that used the algorithm, on September 20, 1983. Though the patent was going to expire on

September 21, 2000 (the term of patent was 17 years at the time), the algorithm was released to

the public domain by RSA Security on September 6, 2000, two weeks earlier. Since a paper

describing the algorithm had been published in August 1977, prior to the December 1977 filing

date of the patent application, regulations in much of the rest of the world precluded patents

elsewhere and only the US patent was granted. Had Cocks' work been publicly known, a patent in

the US might not have been possible, either.

From the DWPI's abstract of the patent,

35

The system includes a communications channel coupled to at least one terminal having an

encoding device and to at least one terminal having a decoding device. A message-to-be-

transferred is enciphered to ciphertext at the encoding terminal by encoding the message as a

number M in a predetermined set. That number is then raised to a first predetermined power

(associated with the intended receiver) and finally computed. The remainder or residue, C, is...

computed when the exponentiated number is divided by the product of two predetermined prime

numbers (associated with the intended receiver).

Clifford Cocks, an English mathematician working for the UK intelligence agency GCHQ,

described an equivalent system in an internal document in 1973, but given the relatively expensive

computers needed to implement it at the time, it was mostly considered a curiosity and, as far as

is publicly known, was never deployed. His discovery, however, was not revealed until 1998 due

to its top-secret classification, and Rivest, Shamir, and Adleman devised RSA independently of

Cocks' work.

6.3 Operation

The RSA algorithm involves three steps: key generation, encryption and decryption.

6.3.1 Key generation

RSA involves a public key and a private key. The public key can be known by everyone and is

used for encrypting messages. Messages encrypted with the public key can only be decrypted in a

reasonable amount of time using the private key. The keys for the RSA algorithm are generated

the following way:

1. Choose two distinct prime numbers p and q.

o For security purposes, the integers p and q should be chosen at random, and should

be of similar bit-length. Prime integers can be efficiently found using a primality

test.

2. Compute n = pq.

o n is used as the modulus for both the public and private keys. Its length, usually

expressed in bits, is the key length.

36

3. Compute (n) = (p)(q) = (p 1)(q 1) = n - (p + q -1), where is Euler's totient function.

4. Choose an integer e such that 1 < e < (n) and gcd(e, (n)) = 1; i.e., e and (n) are coprime.

o e is released as the public key exponent.

o e having a short bit-length and small Hamming weight results in more efficient

encryption most commonly 216 + 1 = 65,537. However, much smaller values of e

(such as 3) have been shown to be less secure in some settings.[5]

5. Determine d as d e1 (mod (n)); i.e., d is the multiplicative inverse of e (modulo (n)).

This is more clearly stated as: solve for d given de 1 (mod (n))

This is often computed using the extended Euclidean algorithm. Using the

pseudocode in the Modular integers section, inputs a and n correspond to e and

(n), respectively.

d is kept as the private key exponent.

The public key consists of the modulus n and the public (or encryption) exponent e. The private

key consists of the modulus n and the private (or decryption) exponent d, which must be kept

secret. p, q, and (n) must also be kept secret because they can be used to calculate d.

An alternative, used by PKCS#1, is to choose d matching de 1 (mod ) with = lcm(p

1, q 1), where lcm is the least common multiple. Using instead of (n) allows more

choices for d. can also be defined using the Carmichael function, (n).

The ANSI X9.31 standard prescribes, IEEE 1363 describes, and PKCS#1 allows, that p

and q match additional requirements: being strong primes, and being different enough that

Fermat factorization fails.

6.3.2 Encryption

Alice transmits her public key (n, e) to Bob and keeps the private key d secret. Bob then wishes to

send message M to Alice.

37

He first turns M into an integer m, such that 0 m < n by using an agreed-upon reversible protocol

known as a padding scheme. He then computes the ciphertext c corresponding to

This can be done efficiently, even for 500-bit numbers, using Modular exponentiation. Bob then

transmits c to Alice.

Note that at least nine values of m will yield a ciphertext c equal to m,[note 1] but this is very unlikely

to occur in practice.

6.3.3 Decryption

Alice can recover m from c by using her private key exponent d via computing

Given m, she can recover the original message M by reversing the padding scheme.

38

Chapter 7

CONCLUSION

Cryptography is a particularly interesting field because of the amount of work that is, by necessity,

done in secret. The irony is that today, secrecy is not the key to the goodness of a cryptographic

algorithm. Regardless of the mathematical theory behind an algorithm, the best algorithms are

those that are well-known and well-documented because they are also well-tested and well-

studied! In fact, time is the only true test of good cryptography; any cryptographic scheme that

stays in use year after year is most likely a good one. The strength of cryptography lies in the

choice (and management) of the keys; longer keys will resist attack better than shorter keys.

Cryptography protects users by providing functionality for the encryption of data and

authentication of other users. This technology lets the receiver of an electronic message verify the

sender, ensures that a message can be read only by the intended person, and assures the recipient

that a message has not be altered in transit. This paper describes the cryptographic concepts of

symmetric key encryption, public-key encryption, types of encryption algorithms, hash algorithms,

digital signatures, and key exchange. The Cryptography Attacking techniques like Cryptanalysis

and Brute Force Attack. This Paper provides information of Network Security Needs and

Requirements.

Cryptography is a particularly interesting field because of the amount of work that is, by necessity,

done in secret. The irony is that today, secrecy is not the key to the goodness of a cryptographic

algorithm. Regardless of the mathematical theory behind an algorithm, the best algorithms are

those that are well known and well-documented because they are also well-tested and well-studied!

In fact, time is the only true test of good cryptography; any cryptographic scheme that stays in use

year after year is most likely a good one. The strength of cryptography lies in the choice (and

management) of the keys; longer keys will resist attack better than shorter keys.

39

Chapter 8

Reference

Cryptography and Network Security By William Stallings.

Introduction to Cryptography By Aysel Ozgur

http://en.wikipedia.org/wiki/RSA_%28cryptosystem%29

http://www-users.cs.umn.edu/