CRYPTOGRAPHY

Krunal M. Chavada

(09DCE217)

INDEX

CONTENTS PAGE NO.

Cryptography 1

History of Cryptography 2

Types of Cryptography 5

Secret-key Cryptography 15

Public-key Cryptography 16

Hash function Cryptography 17

Cryptographic key types 18

CRYPTOGRAPHY

A cryptographic system that uses two keys -- a public key known to everyone and a private or secret key known only to the recipient of the message. When John wants to send a secure message to Jane, he uses Jane's public key to encrypt the message. Jane then uses her private key to decrypt it.

HISTORY OF CRYPTOGRAPHY

Cryptography is a technique used to hide the meaning of a message and is derived from the Greek

word kryptos (hidden). This is different from steganography techniques in that one is not hiding the actual message, only the meaning of the message. If a message were to fall into the hands of the wrong person, cryptography should ensure that that message could not be read. Typically the sender and receiver agree upon a message scrambling protocol beforehand and agree upon methods for encrypting and decrypting messages. Cryptography is further divided into two implementation techniques and those include transposition and substitution.

Rail Fence Transposition -- Rail Fence Transposition is a technique where a message is written on two or more lines with each consecutive letter of the message being written on the next consecutive line. The text on the second and third lines are then appended to the first line to create the scrambled message. A simple 2 line rail fence transposition of the message "Hello World" is demonstrated below:

Simple 2 Line Rail Fence Transposition

Hello World (Original Message)

H l o W r d (Line 1)

e l o l (Line 2)

HloWrdelol (Transposed Message)

Substitution -- Substitution is a cryptographic

technique where each letter of the plaintext message is replaced by a different letter. Each letter retains its original position in the message text, but the identity of the letter is changed. This type of technique was documented during Julius Caesar's Gallic Wars.

Simple Substitution Cipher

A B C D E (Plain Alphabet)

D C E G H (Cipher Alphabet)

If one were to send the message 'BAD' to someone using this simple cipher, the encrypted message text would read 'CDG'.

Caesar Shift Cipher -- A simple

substitution cryptographic technique where the cipher alphabet is shifted a certain number of spaces relative to the original plain alphabet. It was named for Julius Caesar who employed the

technique to secure military communications. This is generally a weak encryption method in that there are only 25 distinct variations of shifts before the original message is revealed. A simple 4 letter shift example is demonstrated below :

Letter Shift Cipher

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z (Plain Alphabet)

E F G H I J K L M N O P Q R S T U V W X Y Z A B C D (Cipher Alphabet)

If one were to encrypt the plain text message "MEET ME AT MIDNIGHT", the cipher text would read "QIIX QI EX QMHRMKLX".

There are Three types of Cryptography.

1. Secret-key Cryptography.2. Public-key Cryptography3. Hash function Cryptography.

There are main Five types of protocol are used in Cryptography.

1) Internet Key Exchange

2) IPsec3)Kerberos4)Point to Point Protocol5)Transport Layer Security

1. Substitution cipher wheels -- You could make your cipher text a

little tougher to decode if you threw 26 pieces of paper into a hat, each with a letter of the alphabet written on it, drew them out one at a time, and put them side-by-side under a normal alphabet. The result might look like this (I just used the order of the keys on my keyboard, so you might call this a "Qwerty" code):

Plaintext letter A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Cipher text letter Q W E R T Y U I O P A S D F G H J K L Z X C V B N M

You can construct a secret message from the above table. Every time you see an "I" you would substitute the "O" beneath and so on for the other characters. The message "Meet me after school behind the gym," would read

"DTTZ DT QYZTK LEIGGS WTIOFR ZIT UND."

Word lengths - especially the short words - give great clues as to the nature of the code (see frequency charts). To help conceal your message, ignore the spaces and break the message up into equal-sized chunks. Five letters are customary in the spy biz, so your message comes out like this (Note that an extra "dummy" character "M" is added at the end to make it come out with a 5-letter group. Your recipient should have no trouble with the extra character.):

DTTZD TQYZT KLEIG GSWTI OFRZI TUNDM

Another popular system called a diagrammatic cipher, used by many children in school, substitutes’ symbols for letters instead of other letters. This system is, in essence, the same as the letter substitution system, but it's easier to remember than 26 randomly

picked letters. It uses the tic-tac-toe boards and two X's as shown below.

Even though it looks like undecipherable outer-space alien text, this would take an arm-chair cryptologist only about 10 minutes or less to figure out. Why? Given enough ciphertext, certain patterns become obvious. Notice how often the empty four-sided box appears: six times out of a total of 29 characters or about 20% of the time. This would immediately indicate that the empty box was almost certainly the symbol for "E," the most frequently used letter in English. Other letters can also be determined by their frequency and by their association with other nearby characters (see "Frequencies"). Almost all substitution ciphers are open to this kind of analysis.

Francis Bacon created one of the more interesting substitution ciphers. He used two different type faces slightly differing in weight (boldness). He broke up his cipher text into 5 character groups, each of which would represent one character in his plaintext. Depending on which characters of the group were bold, one could determine the plaintext character using the following table (* stands for a plain character and B for a bold character)

A=***** G=**BB* M=*BB** S=B**B* Y=BB***

B=****B H=**BBB N=*BB*B T=B**BB Z=BB**B

C=***B* I=*B*** O=*BBB* U=B*B**

D=***BBJ=*B**B P=*BBBB V=B*B*B

E=**B** K=*B*B* Q=B**** W=B*BB*

F=**B*B L=*B*BB R=B***B X=B*BBB

Our same secret message as above would appear thusly (Bacon's bold and plain characters were less obvious than those below):

To be or not to be that is the question.

Whether 'tis nobler in the mind to

suffer the slings and arrows of

outrageous fortune or to take arms

against a sea of troubles and by

opposing end them?

To decipher, we just break the characters into groups of 5 and use the key above to find the plaintext message.

M E E T M E B E

Tobeo rnott obeth atist heque stion Wheth ertis

H I N D T H E G

noble rinth emind tosuf ferth eslin gsand arrow

Y M A F T E R S

sofou trage ousfo rtune ortot akear msaga insta

C H O O L

seaof troub lesan dbyop posin gendt hem?

Transposition ciphers -- Going back to your school days, oo-day oo-yay emember-ray ig-pay atin-lay? Pig-latin is a form of transposition cipher where the original letters are kept intact (albeit with the addition of the suffix "ay"), but rearranged in some way.

Going back way before your school days, to the 5th century B.C., the Spartans used an interesting transposition cipher called a scytale. The scytale utilized a cylinder with a ribbon wrapped helically around it from one end to the other. The message was written across the ribbons, and then unwrapped from the cylinder. Only someone with an identical diameter cylinder could re-wrap and read the message.

The scytale depended on a piece of hardware, the cylinder, which if captured by the enemy, compromised the whole system. Also, the receiver could lose or break the cylinder and therefore lose the ability to decipher any message. It would be better if the method were completely "intellectual" and could be remembered and used without resorting to a physical device.

Since both the sender and receiver of a transposed ciphertext must agree on and remember this algorithm or method for enciphering and deciphering, something easy would be nice. Since geometrical figures are easy to remember, they serve as the basis for a whole class of transposition ciphers. Let's put our message into the shape of a box. Since there are 29 characters, we'll add a dummy ("O") to make 30 and write the message in a six by five box.

M E E T M E

A F T E R S

C H O O L B

E H I N D T

H E G Y M O

We can now transcribe the message by moving down the columns instead of across the rows. Once again we'll break the characters into groups of five to give no clues about word sizes. The result looks like this :

MACEH EFHHE ETOIG TEONY MRLDM ESBTO

The real variety begins when you realize that you don't have to write your plaintext into the box row by row. Instead, you can follow a pattern that zigzag’s horizontally, vertically or diagonally, or one that spirals in or spirals out (clockwise or counterclockwise), or many other variations (see diagram below).

Once you've put the text in the chosen form using one route, you can then encipher it by choosing a different route through the text.

You and your partner just have to agree on the reading route, the transcription (enciphering) route, and the starting point to have yourselves a system. These systems are called route transcriptions.

Here's our message again. The reading route spirals counterclockwise inward, starting at the lower right corner (left diagram). The transcription route (right diagram) is zig-zag diagonal starting at the lower left corner. The ciphertext becomes:

EAMTN FTDIE EHOTE RHMEM BYESC GLOHO

To decipher, you fill the in box following the zig-zag route and read the message using the spiral route.

Another type of transposition cipher uses a key word or phrase to mix up the columns. This is called columnar transposition. It works like this: First, think of a secret key word. Ours will be the word SECRET. Next, write it above the columns of letters in the square, and number the letters of the key word as they would fall if we placed them in alphabetical order. (If there are duplicate letters, like the "E", they are numbered from left to right.)

5 2 1 4 3 6

S E C R E T

M E E T M E

A F T E R S

C H O O L B

E H I N D T

H E G Y M O

Now write the columns down in the order indicated by the numbers. The resulting ciphertext looking like this:

ETOIG EFHHE MRLDM TEONY MACEH ESBTO

As you can see, this is just a different arrangement of the previous ciphertext, but at least it isn't in some regular pattern. We could have easily made it a little more difficult by filling the square following a more complicated path. We could also use a geometric shape other than a rectangle and combine substitution and transposition. The only problem that might occur is that the deciphering may become so complicated that it will remain a secret at the receiving end forever! Come to think of it, she never did meet me behind the gym...

SECRET-KEY CRYPTOGRAPHY

Uses a single key for both encryption and decryption. Secret-key encryption uses one key, the secret key, to both encrypt and decrypt messages. This is also called symmetric encryption. The term "private key" is often used inappropriately to refer to the secret key. A private key is one of the keys in the public/private key pair for asymmetric cryptography. In

this scheme, a user has two keys, one that is made public and one that is held privately. Refer to "Public-Key Cryptography."

PUBLIC-KEY CRYPTOGRAPHY

Uses one key for encryption and another for decryption. Public-key cryptography refers to a cryptographic system requiring two separate keys, one to lock or encrypt the plaintext, and one to unlock or decrypt the cypher text. Neither key will do both functions. One of these keys is published or public and the other is kept private. If the lock/encryption key is the one published then the system enables private communication from the public to the unlocking key's owner. If the unlock/decryption key is the one published then the system serves as a signature verifier of documents locked by the owner of the private key. This cryptographic approach uses asymmetric key algorithms, hence the more general name of "asymmetric key cryptography". Some of these algorithms have the public key / private key property, that is, neither key is derivable from knowledge of the other; not all asymmetric key algorithms do. Those with this property are particularly useful and have been widely deployed and are the source of the commonly used name. The public key is used to transform a message into an unreadable form, decrypt able only by using the (different but matching) private key. Participants in such a system must create a mathematically linked key pair (i.e., a public and a private key). By publishing the public key, the key producer empowers anyone who gets a copy of the public key to produce messages only he can read -- because

only the key producer has a copy of the private key (required for decryption). When someone wants to send a secure message to the creator of those keys, the sender encrypts it (i.e., transforms it into an unreadable form) using the intended recipient's public key; to decrypt the message, the recipient uses the private key. No one else, including the sender can do so.

HASH FUNCTION CRYPTOGRAPHY

Uses a mathematical transformation to irreversibly "encrypt" information. A hash function is any well-defined procedure or mathematical function that converts a large, possibly variable-sized amount of data into a small datum, usually a single integer that may serve as an index to an array

(cf. associative array). The values returned by a hash function are called hash values, hash codes, hash sums, checksums or simply hashes.

CRYPTOGRAPHIC KEY TYPES

Private signature key --

Private signature keys are the private keys of asymmetric (public) key pairs that are used by public key algorithms to generate digital signatures with possible long-term implications. When properly handled, private signature keys can be used to provide authentication, integrity and non-repudiation.

Public signature verification key --

A public signature verification key is the public key of an asymmetric (public) key pair that is used by a public key algorithm to verify digital signatures, either to authenticate a user's identity, to determine the integrity of the data, for non-repudiation, or a combination thereof.

Private authentication key --

A private authentication key is the private key of an asymmetric (public) key pair that is used with a public key algorithm to provide assurance as to the integrity of information, and the identity of the originating entity or the source of messages, communication sessions, or stored data.

Public authentication key --

A public authentication key is the public key of an asymmetric (public) key pair that is used with a public key algorithm to determine the integrity of information and to authenticate the identity of entities, or the source of messages, communication sessions, or stored data.

Symmetric data encryption key --

These keys are used with symmetric key algorithms to apply confidentiality protection to information.

Symmetric key wrapping key --

Symmetric key wrapping keys are used to encrypt other keys using symmetric key algorithms. Key wrapping keys are also known as key encrypting keys.

Symmetric master key --

A symmetric master key is used to derive other symmetric keys (e.g., data encryption keys, key wrapping keys, or authentication keys) using symmetric cryptographic methods.

Private key transport key --

Private key transport keys are the private keys of asymmetric (public) key pairs that are used to decrypt keys that have been encrypted with the associated public key using a public key algorithm. Key transport keys are usually used to establish keys (e.g., key wrapping keys, data encryption keys or MAC keys) and, optionally, other keying material (e.g., initialization vectors).

Public key transport key --

Public key transport keys are the public keys of asymmetric (public) key pairs that are used to encrypt keys using a public key algorithm. These keys are used to establish keys (e.g., key wrapping keys, data encryption keys or MAC keys) and, optionally, other keying material (e.g., Initialization Vectors).

Symmetric key agreement key --

These symmetric keys are used to establish keys (e.g., key wrapping keys, data encryption keys, or MAC keys) and, optionally, other keying material (e.g., Initialization Vectors) using a symmetric key agreement algorithm.

Private static key agreement key --

Private static key agreement keys are the private keys of asymmetric (public) key pairs that are used to establish keys (e.g., key wrapping keys, data encryption keys, or MAC keys) and, optionally, other keying material (e.g., Initialization Vectors).

Public static key agreement key --

Public static key agreement keys are the public keys of asymmetric (public) key pairs that are used to establish keys (e.g., key wrapping keys, data encryption keys, or MAC keys) and, optionally, other keying material (e.g., Initialization Vectors).

Private ephemeral key agreement key --

Private ephemeral key agreement keys are the private keys of asymmetric (public) key pairs that are used only once to establish one or more keys (e.g., key wrapping keys, data encryption keys, or MAC keys) and, optionally, other keying material (e.g., Initialization Vectors).

Public ephemeral key agreement key --

Public ephemeral key agreement keys are the public keys of asymmetric key pairs that are used in a single key establishment transaction to establish one or more keys (e.g., key wrapping keys, data encryption keys, or MAC keys) and, optionally, other keying material (e.g., Initialization Vectors).

Symmetric authorization key --

Symmetric authorization keys are used to provide privileges to an entity using a symmetric cryptographic method. The authorization key is known by the entity responsible for monitoring and granting access privileges for authorized entities and by the entity seeking access to resources.

Private authorization key --

A private authorization key is the private key of an asymmetric (public) key pair that is used to provide privileges to an entity.

Public authorization key --

A public authorization key is the public key of an asymmetric (public) key pair that is used to verify privileges for an entity that knows the associated private authorization key.

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