Cryptography and Security Technologies

Internet and Computer Network

2

Road Map

1. Basic Concepts

2. Introduction to Cryptography

3. Digital Signature

4. Digital Certificate and Certification Authority

3

Basic Concepts

4

How are things done?

In the E-Commerce world, transactions are performed between computers in different locations.

Merchant Customer

Product

Payment andother info.

Our focus: Information Security

5

Four Objectives of Information Security

Confidentiality: Ensure that information is not disclosed or revealed to unauthorized persons.

Integrity: Ensure consistency. Prevent unauthorized creation or alteration of data.

Authentication: Verify the identity of the sender.

Non-repudiation: One cannot deny that he/she has taken part in the transaction.

6

Examples in Physical World

Confidentiality Sealed letterOpaque envelopeInvisible Ink

Integrity Indelible ink

Authentication Photo ID cardDriving license

Non-repudiation Notarized signatureCertified or registered mail

7

Among the Four SecurityConcerns….

1. Confidentiality – protection against?

2. Integrity – protection against?

3. Authentication – protection against?

4. Non-repudiation – protection against?

Therefore, non-repudiation is fundamentally different from other security services.

8

Introduction to Cryptography

9

Cryptosystem

PlainInformation

PlainInformation

Cipher text

Encryption

EncryptionKey

Decryption

DecryptionKey

10

What is Encryption?

Encryption is a process of scrambling (mutating) a message such that it becomes unreadable to unintended receivers.

Decryption is simply a process to recover the cipher text into readable form.

Obviously, a cryptosystem provides confidentiality.

11

Symmetric Cryptosystem

Uses the same key for encryption and decryption.

PlainInformation

PlainInformation

Cipher text

Encryption Decryption

12

Symmetric Key Cryptography

The key must be secretly held between the sender and receiver.

How many keys are needed when we have a community of n users? Ans: n(n – 1)/2, or order of n2.

Direct Implication: Distribution and key management. Does not support spontaneous transaction.

13

Symmetric Cryptosystems

Normally operates either as block cipher or stream cipher. Block cipher: input text is divided into fixed-size

blocks of n-bits. The encryption function is then applied. The cipher text blocks are also n-bits in length. Typically, n = 64 bits.

Stream cipher: processes the data as a sequence of characters.

Common symmetric cryptosystems:DES, Triple-DES, RC2, RC4, RC5, etc.

14

The Data Encryption Standard (DES)

Developed by IBM in the 1970s, and was adopted as a US federal standard in 1977.

Uses 56-bit key on 64-bit blocks of data. Encryption and decryption involves 16 rounds

of permutations, letter substitutions, and exclusive-OR operations.

The output displays no correlation to the input. Every bit of the output depends upon every bit

of the input and the key.

15

How Good is DES?

No general guideline on attack except brute-force search (i.e., exhaustively search the key space).

For DES, that means 256 70 million billion trials.

Using 1994 technology, a US$1 million investment can crack the key in 3.5 hours.

That’s why we need Triple-DES and others!

16

Other Services…..

Authentication and integrity: uses integrity check-value.

Plaintext Plaintext

Integritycheck-value

Plaintext

Equal?

Computeintegrity

check

Transmitted Message

Computeintegrity

checkSharedKey

Confirmor indicatefailure

17

Integrity Check Value

Can it check for integrity? Yes, because the computed value must be consistent

with the transmitted value. Can it authenticate the sender?

Yes, because only 2 users hold the secret key. The recipient knows that it is sent by the other key holder.

Can it prevent repudiation? NO! What if one user generates the message by

himself and claim that it was done by the other user?

18

Public Key Cryptosystems

Uses a pair of related keys: one for encryption and one for decryption.

One key, called the private key, is kept only to the owner.

The other key, called the public key, can be made publicly known.

Given the public key, one cannot derive the private key and vice versa.

19

Public Key Cryptosystems

Plaintext A

Plaintext B

Cipher text A

Cipher text B

Recipient’s public key

Plaintext A

Plaintext B

Recipient’s private key

20

Alternatively…..

Plaintext

Cipher text A

Sender’s private key

Plaintext

Sender’s public key

21

Public Key Cryptosystems

Confidentiality: (let p be our message)Public-KeyRecipient(p) = cipher textPrivate-KeyRecipient(cipher text) = p

Authentication, integrity, non-repudiation:Private-KeySender(p) = cipher textPublic-KeySender(cipher text) = p

Commonly used public key systems include RSA and PGP (Pretty Good Privacy).

22

The RSA Algorithm

Developed by Ron Rivest, Adi Shamir, and Len Adleman of MIT.

Based on modular arithmetic and prime number operations.

While multiplying two prime numbers is easy, factoring the product of such numbers is difficult, especially when the product is large!

23

Modular Arithmetic

a b (mod n) if a differs from b by an exact multiple of n.

That is, a b + Ln, L being an integer. Examples:

242 2 (mod 10)164 4 (mod 5)146 3 (mod 11)

24

The RSA Algorithm

1. Find two prime numbers, p and q, and compute their product, n.

2. Find a pair of integers d and e such thatde 1 (mod (p – 1)(q – 1)).

3. Now, for any message m not being multiple of p or q,

Encryption: c me (mod n)Decryption: cd (mod n) m

25

The RSA Algorithm

The two numbers, n and e, form the public encryption key. d is the private decryption key.

Example: try p = 5, q = 7, n = 35, e = d = 5.de = 25 = 1 (mod (p – 1)(q – 1)) = 1 (mod 24)Let’s say the message m is 3,

c = 35 (mod 35) = 33335 (mod 35) = 3 = m.

26

Performance of RSA

Rough estimates: In year 2000, attacker with US$25,000 can

factor a 425-bit public modulus (n). US$25 million can factor a 619-bit modulus. In year 2020, US$25,000 will be able to

factor a 515-bit modulus, while 25 million can factor 799-bit modulus.

In any case, a 1024-bit modulus should be sufficient for the coming years.

27

Public Key Cryptosystems

Advantages: Higher security Easy key distribution Supports spontaneous transactions

Weaknesses: Processing costs (e.g., time requirements

for encryption/decryption).

28

How to Make Things Better?

Use a hybrid approach that combines the strengths of secret-key (symmetric key) and public-key based encryption techniques.

Encrypt message with secret key, and then encrypt the secret key using public key.

Transmitted Message = Secret-key(m) + Public-keyreceiver(Secret-key)

The Second term is called a Digital Envelope.

29

Digital Signature

30

What is Digital Signature?

A data item that accompanies a digitally encoded message and that can be used to: ascertain the identity of the sender. ensure the message has not been altered during

transmission.

Normally involves a sign and a verify operation.

31

Digital Signature

Plaintext

Transmitted Message

DigitalSignature

Sign

Sender’sPrivate Key

Verified?Yes/No

Plaintext

Sender

Plaintext

Receiver

Verify

Sender’sPublic Key

32

But……

This is very similar to the integrity check value in the symmetric key system!

Difference: now it supports non-repudiation, because the private key is only held by the sender.

Notice that the signature itself does not provide confidentiality.

33

RSA Digital Signature

Apply the sender’s private key to the entire message to create the signature.

Encryption and decryption have to be applied to the entire message. Signature length is the same as the message itself.

Implication: High processing and communication overhead

costs.

34

Any Help?

One-way Hash function: maps values from a very large domain (the message) into a relatively small range.

Any change in the original message, even just one single bit, will result in a different value.

For security applications, normally hashes to fixed length data (e.g., 128 bits) known as message digest.

35

Digital Signature with Hashing

Plaintext

Transmitted Message

Plaintext

Sender

Plaintext

Receiver

DigitalSignature

Messagedigest

HashSign

Sender’sPrivate Key

Sender’sPublic Key

Decrypt

Computeddigest

Hash

Expecteddigest

Are they equal?

36

Digital Certificate and Certification Authority

37

Distribution of Public Key

Confidentiality is not required. How about integrity? What if an intruder

substitutes the key with his own public key? In that case, all four security objectives are

achieved, but you are simply dealing with a wrong person!

That’s why we need a trusted third party to notarize the public key and its owner.

38

Digital Certificate

A digital ID card that notarizes the connection between a public-key and its owner.

Issued by certification authorities (CA). Contains a public-key value and information

that uniquely identifies the holder. Digitally signed by the issuing CA. Implication?

Must trust the CA for the certificate to be useful.

39

Digital Certificate

Advantage: Easy distribution without the need to worry about

confidentiality, integrity, and authentication. User simply needs to trust the CA. No need to

store the keys or certificates of other users. However, practically, no CA can handle all

users. Therefore, we need a chain-like model to link

up multiple CAs hierarchically. This is called a certification path.