A Study of Cryptography

8/14/2019 A Study of Cryptography

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A Study ofA Study of

CryptographyCryptography

Submitted BySubmitted By

Vartika Bajpai (26057)Vartika Bajpai (26057)

Brijesh Kumar Gupta(26058)Brijesh Kumar Gupta(26058)

Ankit Srivastava (26402)Ankit Srivastava (26402)


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Cryptography is the science of protecting data, which provides means and methods ofCryptography is the science of protecting data, which provides means and methods of

converting data into unreadable form , so thatconverting data into unreadable form , so that

The data cannot be accessed for unauthorized use.The data cannot be accessed for unauthorized use.

The content of the data frames is hidden.The content of the data frames is hidden.

The authenticity of the data can be established.The authenticity of the data can be established.

The undetected modification of the data is avoided.The undetected modification of the data is avoided.

The data cannot be disowned by the originator of the message.The data cannot be disowned by the originator of the message.

Cryptography is especially useful in the cases of financial and personalCryptography is especially useful in the cases of financial and personal

data, irrespective of the fact that the data is being transmitted over a mediumdata, irrespective of the fact that the data is being transmitted over a medium

or is stored on a storage device. It provides a powerful means of verifyingor is stored on a storage device. It provides a powerful means of verifying

the authenticity of data and identifying the culprit, if the confidentiality andthe authenticity of data and identifying the culprit, if the confidentiality and

integrity of the data is violated.integrity of the data is violated.


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Terms Related toTerms Related to


Plain Text :The message that has to be transmitted to theThe message that has to be transmitted to therecipient .recipient .

Encryption :The process of changing the content of aThe process of changing the content of amessage in amessage in a

manner such that it hides the actual message.manner such that it hides the actual message.

Cipher Text:The output that is generated after encryptingThe output that is generated after encryptingthe plain text.the plain text.

Decryption :The reverse of encryption and is the process ofThe reverse of encryption and is the process ofretrieving the original message from its encrypted form. Thisretrieving the original message from its encrypted form. Thisprocess converts ciphertext to plaintext.process converts ciphertext to plaintext.

Key :Is a word, number, or phrase that is used to encrypt theIs a word, number, or phrase that is used to encrypt thecleartext.cleartext.


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Cryptography FundamentalsCryptography Fundamentals

Cryptography Privacy :Cryptography Privacy :

Cryptography Authentication :Cryptography Authentication :


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Types of CiphersTypes of Ciphers

Substitution Cipher :In this cipher , each letter or a group ofIn this cipher , each letter or a group ofletters is replaced by another letter or group of letters.letters is replaced by another letter or group of letters.

These are of two types-These are of two types- Monoalphabetic Cipher : In this cipher , character in theIn this cipher , character in the

plain text is always changed to the same character in theplain text is always changed to the same character in the

cipher text regardless of the position in the text.cipher text regardless of the position in the text.-For Example:-For Example:

Plaintext : H E L L OH E L L O

Ciphertext : K H O O RK H O O R Polyalphabetic Cipher : In this cipher , each occurrence ofIn this cipher , each occurrence of

a character can have a different substitute.a character can have a different substitute.

-For Example:-For Example:

Plaintext : H E L L OH E L L O

Ciphertext : A B N Z FA B N Z F


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Transposition Cipher :Transposition Cipher : In this cipher, there is noIn this cipher, there is no

substitution of the characters instead their locations change.substitution of the characters instead their locations change.

In other words , it reorders the symbol in a block of symbols.In other words , it reorders the symbol in a block of symbols.

- For Example : The MEGABUCK is the key.- For Example : The MEGABUCK is the key.

Plaintext : please transfer one million dollar to.M E G A B U C KM E G A B U C K

7 4 5 1 2 8 3 67 4 5 1 2 8 3 6

p l e a s e t rp l e a s e t r

a n s f e r o na n s f e r o n

e m i l l i o ne m i l l i o n

d o l l a r t od o l l a r t o

Ciphertext : afllselatootlnmoesilrnnopaederir


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Cryptographic TechniquesCryptographic Techniques

Two types of Cryptographic Techniques :Two types of Cryptographic Techniques :

Single Key CryptographySingle Key Cryptography

Public Key CryptographyPublic Key Cryptography


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Comparison of Symmetric andComparison of Symmetric and

Asymmetric EncryptionAsymmetric Encryption

Encryption DecryptionCiphertext

Original

PlaintextPlaintext

Secret Key

Symmetric (Single Key) CryptographySymmetric (Single Key) Cryptography

Encryption DecryptionCiphertext

Original

Plaintext

Private KeyPublic Key

Plaintext

Asymmetric (Two Key) CryptographyAsymmetric (Two Key) Cryptography


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Single Key CryptographySingle Key Cryptography

The process of encryption and decryption of information by using aThe process of encryption and decryption of information by using a

single key is known as secret key cryptography orsingle key is known as secret key cryptography or symmetric keysymmetric key

cryptographycryptography..

In symmetric key cryptography, the same key is used to encrypt asIn symmetric key cryptography, the same key is used to encrypt as

well as decrypt the data. The main problem with symmetric keywell as decrypt the data. The main problem with symmetric key

algorithms is that the sender and the receiver have to agree on aalgorithms is that the sender and the receiver have to agree on acommon key.common key.

A secure channel is also required between the sender and theA secure channel is also required between the sender and the

receiver have to exchange the secret key.receiver have to exchange the secret key.

Symmetric key Algorithm :Symmetric key Algorithm :The algorithm takes an n-bitThe algorithm takes an n-bit

block of plaintext as input n transform it using the key into n-block of plaintext as input n transform it using the key into n-

bit block of cipher text .bit block of cipher text .

Two types of symmetric key algorithm:Two types of symmetric key algorithm:

Data Encryption Standard (DES)Data Encryption Standard (DES)

Triple Data Encryption Standard (3-DES)Triple Data Encryption Standard (3-DES)


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Data Encryption StandardData Encryption Standard

DES was developed as a standard for communications andDES was developed as a standard for communications anddata protection by an IBM research team, in response to adata protection by an IBM research team, in response to apublic request for proposals by the NBS - the National Bureaupublic request for proposals by the NBS - the National Bureauof Standards (which is now known as NIST).of Standards (which is now known as NIST).


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The S-P NetworkThe S-P Network

P-BoxP-Box ::A permutationA permutationbox for bits parallels thebox for bits parallels the

traditional transpositiontraditional transposition

cipher for characters. Itcipher for characters. It

performs a transposition atperforms a transposition atthe bit level.the bit level.

S-BoxS-Box :: A SubstitutionA Substitutionbox parallels the traditionalbox parallels the traditional

substitution cipher forsubstitution cipher for

characters.characters.

P-box

Decod

er

:3to

S-box

Enco

der

:8to


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DES : OverviewDES : Overview

It takes 64 bits inputIt takes 64 bits input

at a time gives 64 bitat a time gives 64 bit

outputoutput

Initial permutationInitial permutation

rearranges 64 bits (norearranges 64 bits (no

cryptographic effect)cryptographic effect)

Encoding is in 16Encoding is in 16

roundsrounds

plaintext

INITIAL PERMUTATION

ROUND 1

ROUND 2

ROUND 16

INITIAL PERMUTATION-1

...

ciphertext


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DES : Encryption RoundDES : Encryption Round

64 bits divided into64 bits divided into

left, right halves.left, right halves.

Right half goesRight half goes

through function f,through function f,

mixed with key.mixed with key.

Right half added toRight half added to

left half.left half.

Halves swappedHalves swapped

(except in last round)(except in last round)

Li-1 Ri-1

Li Ri

f


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DES FunctionDES Function

Expand right side fromExpand right side from

32 to 48 bits (some32 to 48 bits (some

get reused)get reused)

Add 48 bits of keyAdd 48 bits of key

(chosen by schedule)(chosen by schedule)

S-boxes: each set of 6S-boxes: each set of 6

bits reduced to 4bits reduced to 4

P-box permutes 32P-box permutes 32

bitsbits

Ri-1

Expansion

Ki

Eight S-boxes

P-box

Output


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DES :Decryption RoundDES :Decryption Round

Equations for round i:Equations for round i:

In other words:In other words:

So decryption is theSo decryption is thesame as encryptionsame as encryption

Last round, no swap:Last round, no swap:really is the samereally is the same

Li=R

i1

Ri = Li 1 f Ri 1( )

Ri 1 = Li

Li 1 = Ri f Li( )

Li-1 Ri-1

Li Ri

f


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Insecurity In DESInsecurity In DES

The key in DES is too short that it can be broken intoThe key in DES is too short that it can be broken into

2^n time if it has n bit of key.2^n time if it has n bit of key.

Why not 2-DES?Why not 2-DES?

Then to improve the security of the block cipherThen to improve the security of the block cipher

, two independent keys are used to encrypt the data, two independent keys are used to encrypt the datathinking that this would square the security of the data butthinking that this would square the security of the data but

this will take only double the time to break the singlethis will take only double the time to break the single

encryption scheme and causingencryption scheme and causing MEET In The MIDDLEMEET In The MIDDLE attackattack


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Triple Data EncryptionTriple Data Encryption

StandardStandard Critics of DES contend that the key is too short.Critics of DES contend that the key is too short.

To increase the length of key Triple DES has been proposed andTo increase the length of key Triple DES has been proposed and

implemented.implemented.

This uses 3 DES blocksThis uses 3 DES blocks

-The encrypting block uses an-The encrypting block uses an Encryption Decryption Encryption Decryption

EncryptionEncryptioncombination of DESs.combination of DESs.

-- 3-DES encrypts 64 bit block I into 64 bit block O.-- 3-DES encrypts 64 bit block I into 64 bit block O.

O=EO=Ek3k3 (D(Dk2k2 (E(Ek1k1 (I)))(I)))

-The decrypting block uses an-The decrypting block uses an Decryption Encryption Decryption Encryption

DecryptionDecryptioncombination of DESs.combination of DESs.

-- 3-DES encrypts 64 bit block I into 64 bit block O.-- 3-DES encrypts 64 bit block I into 64 bit block O.

O=DO=Dk1k1 (E(Ek2k2 (D(Dk3k3 (I)))(I)))


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Encryption/DecryptionEncryption/Decryption

Triple DES ModelTriple DES Model


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3 DES : Keying Option3 DES : Keying Option

The standards define three keying options:The standards define three keying options: Keying option 1: All three keys are independent.Keying option 1: All three keys are independent.

Keying option 1 is the strongest, with 3 x 56 = 168Keying option 1 is the strongest, with 3 x 56 = 168independent key bits.independent key bits.

Keying option 2: K1 and K2 are independent, and K3 = K1.Keying option 2: K1 and K2 are independent, and K3 = K1.

Keying option 2 provides less security, with 2 x 56 =Keying option 2 provides less security, with 2 x 56 =112 key bits. This option is stronger than simply DES112 key bits. This option is stronger than simply DESencrypting twice, e.g. with K1 and K2, because itencrypting twice, e.g. with K1 and K2, because itprotects againstprotects against MEET IN THE MIDDLEMEET IN THE MIDDLE attack.attack.

Keying option 3: All three keys are identical, i.e. K1 = K2 =Keying option 3: All three keys are identical, i.e. K1 = K2 =K3.K3.

Keying option 3 is no better than DES, with only 56Keying option 3 is no better than DES, with only 56key bits. This option provides backward compatibilitykey bits. This option provides backward compatibilitywith DES, because the first and second DESwith DES, because the first and second DESoperations simply cancel out.operations simply cancel out.


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Public Key CryptographyPublic Key Cryptography

Public key cryptography is that the key used to encrypt a message isPublic key cryptography is that the key used to encrypt a message isnot the same as the key used to decrypt it. Each user has a pair ofnot the same as the key used to decrypt it. Each user has a pair ofcryptographic keys acryptographic keys a public keykey and aand a private key. The private key. The private keyis kept secret, whilst the public key may be widely distributed.is kept secret, whilst the public key may be widely distributed.

In public key cryptography, the data that is encrypted with the publicIn public key cryptography, the data that is encrypted with the publickey can only be decrypted with the corresponding private key and vicekey can only be decrypted with the corresponding private key and vice

versa. Due to this asymmetry public key cryptography is known asversa. Due to this asymmetry public key cryptography is known asasymmetric cryptographyasymmetric cryptography..

The public key cryptography solves one of the most vexing problems ofThe public key cryptography solves one of the most vexing problems ofall prior cryptographyall prior cryptography the necessity of establishing a securechannel for the exchange of the key.

For example:-

An analogy to Public Key Encryption is that of a locked mailbox andmail slot. Mailslot is accessible to public but mailbox can be opened byone who has the Key to it.


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Public Key Algorithm

The Encryption algorithm, E and the decryptionThe Encryption algorithm, E and the decryption

algorithm, D has to meet three requirements which are asalgorithm, D has to meet three requirements which are as

follows :follows :

D(E(P))=P;D(E(P))=P;

It is exceedingly difficult to deduce D from E;It is exceedingly difficult to deduce D from E; E cannot be broken by a chosen plaintext attack..E cannot be broken by a chosen plaintext attack..

One of the most widely used Public key algorithm isOne of the most widely used Public key algorithm is

RSA..


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RSARSA

In cryptography , RSA( which stands for Rivest, Shamir and Adleman whoIn cryptography , RSA( which stands for Rivest, Shamir and Adleman who

first publicly described it ) is an algorithm for public key cryptography.first publicly described it ) is an algorithm for public key cryptography.

RSA can be summarized in the following steps:RSA can be summarized in the following steps:

1.1. Choose 2 distinct prime numbers p and q.Choose 2 distinct prime numbers p and q.

- For security purposes, the integers p and q should be chosen- For security purposes, the integers p and q should be chosen

uniformly at random and should be of similar bit-length.uniformly at random and should be of similar bit-length.

2.2. Compute n= p*q and z= (p-1)*(q-1)Compute n= p*q and z= (p-1)*(q-1)

3.3. Choose a number relative prime to z and name it as d.Choose a number relative prime to z and name it as d.

4.4. Find e such that e*d=1 mod z.Find e such that e*d=1 mod z.

Thus inorder toThus inorder to encryptencrypt a message P, computea message P, compute C=PC=P ee mod nmod n..

and toand to decryptdecrypt C,computeC,compute P=CP=Cdd

mod n.mod n.

TheThe Public KeyPublic Key consists of pairconsists of pair (e,n)(e,n) and theand the Private KeyPrivate Key consists ofconsists of(d,n)(d,n)..


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RSA ExampleRSA Example

Let we have to encrypt Plain text SUZANNE , as perLet we have to encrypt Plain text SUZANNE , as peralgorithm there will be following steps :algorithm there will be following steps :

1.1. Let p=3 and q=11Let p=3 and q=11

2.2. n=3*11=33 and z=2*10=20n=3*11=33 and z=2*10=20

3.3. a suitable number which is relative prime to 20 isa suitable number which is relative prime to 20 is7,which is d7,which is d

4.4. e can be found by solving equation 7e=1(mode can be found by solving equation 7e=1(mod20),which yields 3.20),which yields 3.

Thus cipher text C=PThus cipher text C=P33mod 33 and after decryption P=Cmod 33 and after decryption P=C77mod33.mod33.


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Symbolic

Numeric

P3 P3(mod33)

C7 C7(mod 33)

Symbolic

S 19 6859 28 13492928512

19 S

U 21 9261 21 1801088541

21 U

Z 26 17576 20 1280000000

26 Z

A 01 1 1 1 01 AN 14 5 5 78125 14 N

N 14 5 5 78125 14 N

E 05 26 26 803180176 05 E


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RSA ISSUESRSA ISSUES

RSA is computationally intense.RSA is computationally intense.

Commonly used key lengths are 512 bits.Commonly used key lengths are 512 bits.

The plain text should be smaller than the key length.The plain text should be smaller than the key length.

The encrypted text is same size as the key length.The encrypted text is same size as the key length.

Generally used to encrypt secret keys.Generally used to encrypt secret keys. Basis: Factoring a big number is hard.Basis: Factoring a big number is hard.


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Digital SignatureDigital Signature

A digital signature or digital signature scheme is aA digital signature or digital signature scheme is a

mathematical scheme for demonstrating the authenticity ofmathematical scheme for demonstrating the authenticity of

a digital message or document. A valid digital signaturea digital message or document. A valid digital signature

gives a recipient reason to believe that the message wasgives a recipient reason to believe that the message was

created by a known sender, and that it was not altered increated by a known sender, and that it was not altered in

transit.transit.

Why Digital Signature is Used?Why Digital Signature is Used?

To provideTo provide authenticity ,integrity and non repudiationauthenticity ,integrity and non repudiation

to electronic documents.to electronic documents.To useTo use Internet as the safe and secure mediumInternet as the safe and secure medium for e-for e-

commerce.commerce.


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Continued.Continued.

One possible method for creating a digital signature is forOne possible method for creating a digital signature is forthe originator of data to create the signature by encryptingthe originator of data to create the signature by encryptingall of the data with the originator's private key and enclosingall of the data with the originator's private key and enclosingthe signature with the original data.the signature with the original data.

Anyone with the originator's public key can decrypt theAnyone with the originator's public key can decrypt thesignature and compare the decrypted message to thesignature and compare the decrypted message to theoriginal message. Because only someone with the privateoriginal message. Because only someone with the privatekey can create the signature, the integrity of the message iskey can create the signature, the integrity of the message isverified when the decrypted message matches the original.verified when the decrypted message matches the original.

If an intruder alters the original message during transit, theIf an intruder alters the original message during transit, the

intruder cannot also create a new valid signature. If anintruder cannot also create a new valid signature. If anintruder alters the signature during transit, the signatureintruder alters the signature during transit, the signaturedoes not verify properly and is invalid.does not verify properly and is invalid.


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However,However,encrypting all data to provide a digital signature isencrypting all data to provide a digital signature isimpractical for three reasons:impractical for three reasons:

The ciphertext signature is the same size as the correspondingThe ciphertext signature is the same size as the correspondingplaintext, soplaintext, so message sizes are doubledmessage sizes are doubled,, consuming largeconsuming largeamounts of bandwidth and storage space.amounts of bandwidth and storage space.

Public key encryption is slow and places heavy computationalPublic key encryption is slow and places heavy computationalloads on computer processors, so network andloads on computer processors, so network and computercomputerperformance can be significantly degraded.performance can be significantly degraded.

Encrypting the entire contents of information produces largeEncrypting the entire contents of information produces large

amounts of ciphertext, which can be used for cryptanalysisamounts of ciphertext, which can be used for cryptanalysisattacks, especially knownattacks, especially known plaintext attacksplaintext attacks (where certain(where certainparts of the encrypted data, such as e-mail headers, areparts of the encrypted data, such as e-mail headers, areknown beforehand to the attacker).known beforehand to the attacker).


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Digital Signature AlgorithmsDigital Signature Algorithms

Digital signature algorithms use more efficient methods toDigital signature algorithms use more efficient methods tocreate digital signatures. The most common types ofcreate digital signatures. The most common types ofdigitaldigitalsignatures today are created by signing message digestssignatures today are created by signing message digestswith the originator's private keywith the originator's private key to create a digitalto create a digitalthumbprint of the data.thumbprint of the data.

Because onlyBecause only the message digest is signed, the signature isthe message digest is signed, the signature isusually much shorter than the data that was signedusually much shorter than the data that was signed..

Therefore, digital signatures place a relatively low load onTherefore, digital signatures place a relatively low load oncomputer processors during the signing process, consumecomputer processors during the signing process, consumeinsignificant amounts of bandwidth, and produce smallinsignificant amounts of bandwidth, and produce smallamounts of ciphertext for cryptanalysis.amounts of ciphertext for cryptanalysis.

Two of the most widely used digital signature algorithmsTwo of the most widely used digital signature algorithmstoday are the RSA digital signature process and the Digitaltoday are the RSA digital signature process and the DigitalSignature Standard (DSS).Signature Standard (DSS).


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RSA Digital Signature ProcessRSA Digital Signature Process

In the RSA digital signature process, the private key isIn the RSA digital signature process, the private key isused to encrypt only the message digest. The encryptedused to encrypt only the message digest. The encryptedmessage digest becomes the digital signature and ismessage digest becomes the digital signature and isattached to the original data.attached to the original data.

Digital signing :Digital signing : Sender A does the following:-Sender A does the following:- Creates a message digest of the information to beCreates a message digest of the information to be

sent.sent. Uses her private key (n, d) to compute the signatureUses her private key (n, d) to compute the signature

s=m^d mod n.s=m^d mod n.

Sends this signature s to the recipient, B.Sends this signature s to the recipient, B.


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Signature verification:Signature verification:

Recipient B does the following:-Recipient B does the following:-

Uses sender A's public key (n, e) to compute integer v =Uses sender A's public key (n, e) to compute integer v =

s^e mod n.s^e mod n.

Extracts the message digest from this integer.Extracts the message digest from this integer. Independently computes the message digest of theIndependently computes the message digest of the

information that has been signed.information that has been signed.

If both message digests are identical, the signature is valid.If both message digests are identical, the signature is valid.


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RSA Digital Signature ProcessRSA Digital Signature Process


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Digital signature : ApplicationDigital signature : Application

The Private key isThe Private key isgenerated in the cryptogenerated in the cryptomodule residing in themodule residing in thesmart card.smart card.

The key is kept in theThe key is kept in thememory of the smart card.memory of the smart card.

The key is highly securedThe key is highly securedas it doesnt leave theas it doesnt leave thecard, the message digest iscard, the message digest issent inside the card forsent inside the card forsigning, and the signaturessigning, and the signaturesleave the card.leave the card.

The card gives mobility toThe card gives mobility tothe key and signing can bethe key and signing can bedone on any system.done on any system.(Having smart card reader)(Having smart card reader)

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A Study of Cryptography