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A Gentle Introduction to Cryptography

- Extended quote from Bruce Schneier's book, Secrets and Lies.
- Cryptography plays a role in computer security, but buggy computer systems and vulnerable communications are a reality that cryptography has not solved.

Quote from Eugene Spafford

“Using encryption on the Internet is the equivalent of arranging an armored car to deliver credit card information from someone living in a cardboard box to someone living on a park bench.”

Outline of these lectures

- The general goals of cryptographic systems
- Vulnerabilities of cryptographic systems
- Two basic categories of cryptographic algorithms:
- Symmetric
- Asymmetric (public key)
- Methods for sharing keys (including Diffie-Hellman)

Outline (cont.)

- Methods for ensuring data integrity (hash algorithms)
- Methods for authentication (digital signatures)

The General Goals of Cryptography

- Confidentiality; assuring that only authorized parties are able to understand the data.
- Integrity; ensuring that when a message is sent over a network, the message that arrives is the same as the message that was originally sent.

Goals (cont.)

- Authentication; ensuring that whoever supplies or accesses sensitive data is an authorized party.
- Nonrepudiation;ensuring that the intended recipient actually received the message & ensuring that the sender actually sent the message.

Basic Terms

- Encryption: scrambling a message or data using a specialized cryptographic algorithm.
- Plaintext: the message or data before it gets encrypted.
- Ciphertext: the encrypted (scrambled) version of the message.
- Cipher: the algorithm that does the encryption.

Basic Terms (cont.)

- Decryption: the process of converting ciphertext back to the original plaintext.
- Cryptanalysis: the science of breaking cryptographic algorithms.
- Cryptanalyst: a person who breaks cryptographic codes; also referred to as “the attacker”.

More on Confidentiality

- Confidentiality means that only authorized parties are able to understand the data (authorized from the perspective of the party that encrypted the data).
- It is okay if unauthorized parties know that there is data. It is even okay if they copy the data, so long as they cannot understand it.

Authentication

- How can we know that a party that provides us with sensitive data is an authorized party?
- How can we know that the party that is accessing sensitive data is an authorized party?
- This is a difficult problem on the Internet.
- Two solutions are:
- Passwords
- Digital signatures

Integrity

- This involves ensuring that when a message (or any kind of data, including documents and programs) is sent over a network, the data that arrives is the same as the data that was originally sent. It is important that the data has not been tampered with.
- Technical solutions include:
- Encryption
- Hashing algorithms

Nonrepudiation

- Ensuring that the intended recipient actually got the message.
- Ensuring that the alleged sender actually sent the message.
- This is a difficult problem. How do we prove that a person's cryptographic credentials have not been compromised?

An Important Message

- In theory, some crytographic algorithms seem to be EXTREMELY secure.
- Vulnerabilities arise when systems administrators do not deploy the encryption systems securely.
- A fundamental rule: DON'T CODE YOUR OWN CRYPTOGRAPH ALGORITHMS.
- Another rule: When using a cryptographic library, use the intuitive user interfaces provided with those libraries.

Message from Cryptlib Developer,Peter Gutman

“The major design philosophy behind the code [behind Cryptlib] is to give users the ability to build secure apps without needing to spend several years learning crypto. ... [T]he important point is that anybody should be able to employ them [important cryptographic algorithms] without too much effort. ...”

Standard Algorithms areIncredibly Secure

- Using a 128 bit key for a symmetric encryption algorithm, there are 2128 possible keys.
- Even with the computing resources of the US government, most of the software developers alive today will be dead before the government could break such an encryption [Viega and McGraw]

Incredibly secure (cont.)

- Most security experts believe that 256-bit keys are good for the lifetime of the universe (many billions of years).
- The problem is that encryption is just one link in the chain of security. Encryption is a really strong link in that chain, but one weak link breaks the chain.
- It is usually easier for the attacker to hack your machine and steal the plaintext than to break your cipher.

Common Types of Attacks

- Known cipher attacks: the attacker has the ciphertext and she tries to decrypt the message by generating all possible keys.
- Rarely successful because the number of possible keys is enormous.
- Also, the decrypted message (for certain types of data) may not be easy to recognize when it appears.

Common Types of Attacks (cont.)

- Known plaintext attack: the attacker has both the ciphertext and the plaintext.
- Again, this is difficult because there are so many keys, but the plaintext information may make experimentation easier than in the previous case.
- We are assuming that the attacker knows the algorithm that was used for the encryption.

Common Types of Attacks (cont.)

- Chosen plaintext attacks: The cryptanalyst introduces the plaintext into the system and then watches for how that plaintext will be encrypted.
- The Allies used this approach in WWII by sending out false messages about allied troop movements.
- Often the attacker will try to feed a planned sequence of messages that would reveal the most about the way in which the data is being encrypted.

Common Types of Attacks (cont.)

- Side channel attacks use seemingly incidental information that can reveal important information about the key being used.
- Viega and McGraw mention DPA (Differential Power Analysis) attacks on smart cards. A DPA attack analyzes the power output from a processor performing an encryption algorithm in order to get information about the key being used by that algorithm.

Symmetric Cryptography

- Symmetric algorithms are used for:
- Confidentiality
- Data integrity
- Even if an attacker captures the data, the attacker will not be able to manipulate it in any meaningful way.

Symmetric Cryptography (cont.)

- Symmetric algorithms use a single key shared by two communicating parties.
- The shared key must remain secret to ensure the confidentiality of the encrypted data.
- The shared key problem is the main technological challenge for this kind of encryption.
- We will discuss solutions to the key exchange problem a bit later.

Figure A-1 from Viega and McGraw

- The way symmetric encryption works is shown in Figure 1-A from Viega and McGraw.
- The message and the key are provided as input to the encryption algorithm.
- The output is the ciphertext, which can then be transferred over an insecure medium.

Figure 1-A (cont.)

- On the receiver end, the secret key and the ciphertext are inputs to the decryption algorithm.
- The output is the original plaintext.

Symmetric Cryptography (cont.)

- The secret key must be shared securely. Otherwise, the most sophisticated cryptographic algorithm is useless.
- One method of distributing the key is using the sneaker-net.
- Protocols exist for exchanging keys over an insurecure medium, but care must be taken to assure a good authentication process.
- Asymmetric cryptography is a common method for sharing keys.

Symmetric Cryptography

- Two main categories of symmetric algorithms:
- Block ciphers
- Stream ciphers
- Most well-known and well-studied symmetric algorithms use block ciphers.
- Block ciphers break up the message into constant-size blocks and encrypt the code block by block.

Block Ciphers

- Typical block sizes are 64 bits or 128 bits.
- Messages are padded (with extra bits) to fit the block size.
- The simplest type of block ciphers work in ECB (Electronic Code Book) mode. In this mode, each block is encrypted separately, independent of the other blocks (like in our simple XOR example).

Block Ciphers (cont.)

- ECB block ciphers are not secure because given plaintext is always encoded in the same way.
- Thus, the attacker can look look for common linguistic patterns.
- These patterns can help the attacker to figure out the algorithm and key being used.

Block Ciphers (cont.)

- In CBC (Cipher Block Chaining) mode, blocks are also encrypted one at a time, but the initial state for each block is dependent on the ciphertext of the previous block.
- Thus, the same text will be encrypted in many different ways. This makes it much more difficult for the cryptanalyst to crack the cipher.
- CBC mode is the default mode for many block ciphers.

Block Ciphers (cont.)

- A variety of block cipher modes exist (in addition to CBC) for making sure that repeated plaintext is encoded in different ways throughout the message.
- These modes are the default for the standard secure symmetric encryption algorithms (like DES).

Cipher Block Chaining (CBC) Mode

- By adding gibberish into the middle of the ciphertext, the attacker can interfere with the decryption of a CBC encrypted message.
- Two methods are used to defend against this kind of gibberish attack:
- Encode the length of the message at the start of the message or elsewhere to help the receiver figure out if the message has been tampered with.
- Use a cryptographic checksum (or hash) as a signature for your message.

Block Ciphers (cont.)

- The longer the message, the better chance the attacker has of breaking the encryption.
- Bruce Shneier says that a message would have to be at least 34 gigabytes in length for a 64-bit cipher before this would become a genuine risk.

Block Ciphers (cont.)

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

Security is Hard to Prove

- Demonstrating how secure a cryptographic algorithm is remains an extremely hard problem.
- The best test seems to be years of experience and public exposure.
- The “one-time pad” method (which has been used in the military) is absolutely secure, but not very practical because the key changes with each communication.

Extended Quote from Lecture Notes

The two basic goals of a cryptographic algorithm are (a) to make life difficult for the attacker and (b) to produce algorithms that are efficient both in terms of space and time. An algorithm that is too inefficient to be used in practice is of little value even if it were proven to be highly secure ...

Quote (cont.)

It is fairly easy for the cryptography researcher to design an algorithm that is secure against all KNOWN forms of attack. It is far more difficult to design an algorithm that will be secure against types of attacks that are still UNKNOWN. It is nearly impossible to predict new attacks against block ciphers that will be manifesting in future years.

Quote (cont.)

For example, Viega and McGraw state that many people believe that the NSA has developed sophisticated attacks against block ciphers that they have not shared with the rest of the world.

Block Size

- A 64-bit cipher is considered too small for high security applications. According to Bruce Shneier (back in 1995), an organization such as the NSA could break a 64-bit key in under one minute.
- A 256-bit key is believed to be secure enough that a computer made of all the matter in the universe computing for the entire lifetime of the universe would have an infinitesimal probability of finding a key by brute force.

Quantum Computing

But, then there is always Quantum Computing ....

Important Commercial Algorithms

- The most important symmetric algorithms from a commercial point of view are:
- DES (Data Encryption Standard)
- 3DES
- AES (Advanced Encryption Standard)

DES

- This has been a US government standard for many years (although recently complimented with AES).
- It uses a 64-bit key (actually, only 56 bits are used for the encryption, the other 8 bits are parity bits), so it is no longer viable.
- Increased processing speeds (in recent years) are making brute force attacks on DES more viable.

3DES

- Then, came the idea of using DES twice on a given message.
- A subtle form of attack was discovered which made 2DES no better than DES.
- 3DES proved to have the properties that 2DES was supposed to have.
- 3DES is a viable and popular symmetric block algorithm.
- 3DES has one downside: it is inefficient.

DES According to Denning

GET THE IDEA?

3DES

- Despite the fact that it is inefficient, 3DES is considered a very good (and it is a very popular) choice for encryption.
- Several good implementations of 3DES are easily downloaded off the Internet.

AES

- The NIST (National Institute of Standards and Technology) ran a competition for a new encryption standard.
- The winners were announced in October 2000. They were Joan Daemen and Vincent Rijmen. Their algorithm is called RijnDael or AES (Advanced Encryption Standard).
- AES is now an accepted federal standard and is widely available in open source form. Implementations are available in C++ and Java.

AES (cont.)

- 3DES still has the advantage that it has been studied (in DES) form for many years.
- The guestimate is that AES will be a viable encryption standard for the next 50 years, but there could be some surprises down the raod.

The Key Distribution Problem

- For symmetric ciphers, each pair of communicating agents needs a unique key.
- If there are lots of users, this creates a key management problem.
- Key derivation algorithms are used to generate a unique key for each communicating pair.
- If the master key for the key derivation algorithm is compromised, you've got a major problem.

Key Distribution (cont.)

- Some have even attacked derived keys in a key distribution system to get the master key.
- Another approach is to use a key management system that generates session keys for each communication. Even for the same communicating pair, the session keys will change from session to session.
- Kerberos, from MIT, is a highly regarded open source computer security product that supports symmetric key management.

The Great Philosopher, Yogi Berra

“It is difficult to make predictions, especially about the future.”

Asymmetric (Public Key) Cryptography

- Public key cryptography is an attempt to circumvent the key distribution problem completely.
- As it turns out, asymmetric algorithms tend to be very inefficient.
- Their main use is in solving the key exchange problem for symmetric cryptography.

Public Key Crypto (cont.)

- In asymmetric cryptography, each user has two keys: a public key and a private key.
- The public key is made public. For example, it may be published on a Web site.
- The private key must be kept secret. It is never shared with anyone.
- The security of the private key in public key crypto is as important as key security in symmetric crypto.

Public Key Crypto (cont.)

- There is no key distribution problem in public key cryptography.
- Some people have compared public key cryptography to a mailbox. Many people can put mail into the mailbox (in effect, using the public key), but only a postal worker with the appropriate key (corresponding to the private key) can retrieve the mail from the mailbox.

Figure A-2

- Alice wants to send a message to Bob.
- Alice uses Bob’s public key to encrypt the message.
- The encrypted message is sent over the insecure medium.
- Bob uses his private key to decrypt the encrypted message.
- No one but Bob knows the private key.

Public Key Crypto (cont.)

- Public key encryption and decryption algorithms tend to be incredibly slow relative to symmetric key algorithms.
- Public key algorithms tend to be about 100 times slower than DES.
- In general, encrypting large messages using public key cryptography is not considered practical.

Public Key Crypto (cont.)

- The most important use for public key cryptography is for solving the symmetric cryptography key exchange problem.
- Viega and McGraw say that using public key cryptography is a more secure choice than using key derivation algorithms.
- SSL uses this strategy: public key crypto for sharing keys and symmetric algorithms for encrypting the message.

Rivest, Shamir, and Adelman (RSA)

- RSA is the most famous public key algorithm.
- RSA starts with picking two HUMONGOUS prime numbers, p and q. Each of these prime numbers contains hundreds to thousands of bits.
- The two prime numbers remain secret (they are the private key).
- Their product, n = p * q, is the public key.

RSA (cont.)

- The product (the public key) is used to encrypt the message.
- Only someone who knows the prime factors can decrypt the message in a reasonable amount of time.
- The security of RSA is based on the difficulty of factoring n into the prime factors p and q.
- At this point in history, this is seen as a difficult problem.

RSA (cont.)

- RSA is still considered secure after twenty years of use.
- The big security problem is that some implementations of RSA have been flawed and had security problems of their own.
- The software developer should use a well-tested and highly-regarded implementation of RSA.
- Never code your own!!!

RSA (cont.)

- There are huge numbers of large prime numbers.
- There are approximately 10151 primes of length 512 bits or less.
- One interpretation is that there are enough primes of up to 512 bits to assign every atom in the universe 1074 prime numbers without ever repeating one of those primes.

The Future of RSA

- The future of RSA is hard to predict.
- It depends upon what happens in prime number factoring theory.
- Not too many years ago, experts believed that no one would ever have the resources necessary to factor a 128 bit number.
- Now, an organization with adequate resources, can factor a 512 bit number in just a few months.

The Future of RSA (cont.)

- Viega and McGraw recommend that you use no less than a 2,048 bit key for data requiring long-term security (ten or more years).
- It may be that 1,024 bit numbers may be nearing the end of their usefulness even for short-term security.
- The longer the key, the longer it takes to encrypt messages using public key cryptography.

Public Key Crypto Vulnerabilities

- Public Key encryption algorithms are more susceptible to chosen plaintext attacks than symmetric algorithms.
- However, since public key is generally used to encrypt small messages (like keys), plaintext attacks are not a practical problem.
- More significant is the “man-in-the-middle” type of attack.

“Man-in-the-Middle” Attacks

- Figure A-3 depicts a “man-in-the-middle” attack.
- First, let’s consider this kind of attack in terms of Alice trying to send a message to Bob.
- In this kind of attack, Ted sends Alice his own public key, misrepresenting it as Bob’s public key.
- Ted is pretending that he is Bob when he is communicating with Alice.

Man-in-the-Middle (cont.)

- Ted sends Bob Ted’s own public key, misrepresenting it as Alice’s public key.
- Ted is pretending to be Alice when he communicates with Bob.
- Ted is intercepting all traffic between Bob and Alice.

Man-in-the-Middle (cont.)

- When Alice sends Bob a message, she encrypts it using Ted’s public key (she thinks it is Bob’s).
- When Ted receives Alice’s message, he can decrypt it.
- Ted can then send Bob a modified or entirely different message, encrypting it was Bob’s public key.
- Bob decrypts the message, thinking it came from Alice.

“Man-in-the-Middle” (cont.)

- Figure A-3 depicts the situation in terms of a client and a server.
- The client (Alice) asks for the server’s public key so she can send secure information to the server (Bob).
- But, the client is not communicating with the server. She is communicating with the attacker, who sends her his public key.

Man-in-the-Middle (cont.)

- Meanwhile, the attacker establishes his secure connection with the server.
- This gives the attacker access to any information that the client sends to the server and any information that the server sends back to the client.
- This kind of problem motivates the need for a public key infrastructure (PKI).

PKI

- The basic idea behind a Public Key Infrastructure (PKI) is that a trusted third party certifies valid keys.
- Back to Bob and Alice. In this case, Alice would receive Bob’s public key through a trusted third party, a certification authority (CA).
- The CA would say, in effect: “Alice, trust us, Bob is a dependable fellow and this is Bob’s public key.”

PKI (cont.)

- Obviously, this does not solve the matter of trust (the security problem).
- How can Alice be sure that she can trust the so-called trusted authority?
- One of the largest CA’s at this point in time is Verisign.
- Verisign performs background checks on applicants before issuing them a public key for a fee.

PKI (cont.)

- Verisign’s track record is not perfect.
- Several people registered with Verisign under the name “Bill Gates”.
- In March 2001 Microsoft announced that two false keys with MS’s name on them had been issued by a CA.

PKI (cont.)

The problem of trusted identity, taken from Viega and McGraw ….

PKI (cont.)

Advice for developers from Viega and McGraw ...

Cryptographic Hashing Functionsfor Data Integrity

- Cryptographic hashing functions are used to ensure the integrity of data.
- Cryptographic hashing functions are sometimes called cryptographic checksums or integrity checksums.
- Hashing functions are also used for digital signatures, which we shall discuss later.

Integrity Checksums

- Since stuff happens, it is important to have some means of detecting unauthorized changes to files.
- An integrity checksum is a value that is computed from the data that is being protected.
- The integrity checksum is stored separately from the protected data.

Integrity checksums (cont.)

- The recipient of the data recomputes the checksum from the data that is received and compares that checksum to the value that was recorded separately by the provider of the data.
- If the original checksum and the recomputed checksum do not match, then the data has been changed in some way.

Desirable Qualities for Checksum Computations

- The computation must depend upon every single bit in the data, so that if even one bit is changed, that will be reflected in the checksum.
- The computation must be such that it would be rare for two messages to have exactly the same checksums.
- The checksum should not reflect the original data in any obvious way.

Desirable properties (cont.)

The third property implies that an attacker would not be able to figure out how to manipulate the data so that the cryptographic checksums for the valid data and the corrupted data would wind up being the same. Another way of stating this is that it would be difficult for the attacker to reverse engineer the checksum computation.

Hashing functions

- Checksums are computed using hashing functions.
- Hashing functions are one-way functions. This means that the ciphertext (i.e., the checksum) cannot be used to reconstruct the plaintext.
- The checksum (the ciphertext) is much smaller than the plaintext.

Hashing functions (cont.)

- Hashing functions provide a kind of digital fingerprint.
- When we take a fingerprint, we lose a lot of information about the person.
- Still fingerprints and checksums are useful despite the information that is lost.
- Checksums are sometimes called cryptographic or digital fingerprints.

Hashing functions (cont.)

- A checksum is sometimes called:
- A message digest, or
- A message authentication code, or MAC
- The security of the hashing function is related to the size of the resulting checksum (in bits).
- Viega and McGraw suggest using hashing functions that produce a checksum of at least 160 bits.

Checksum Systems

- SHA-1 is a federal standard for computing checksums.
- SHA-1 does not use secret keys. The checksum is computed with a public hashing function and needs to be stored in a safe way. For example:
- On a secure medium an attacker cannot modify
- Encrypted on a completely separate medium from the original data

Checksum systems (cont.)

- SHA-1 uses a 160 bit digest.
- SHA-1 is known to be secure.
- Newer versions of SHA may have security problems because they have not been as thoroughly tested as SHA-1.
- Tripwire is a checksum system that works with the operating system to see if files have been created, deleted, or modified in an unauthorized way.

Hashing Functions and Passwords

- Hashing functions are often used to store passwords for users who are logging onto a multi-user system.
- When the user tries to log in with his or her established password, the login program hashes it, and compares the newly hashed password with the stored hash.
- If the two are equal, the system assumes the user typed in the right password.

Telnet and other Internet Protocols

- With Telnet, the password goes over the network unhashed.
- A packet sniffer could be used to catch the password in transit.
- Telnet authentication provides a very low bar for potential attackers to clear.
- Other protocols that have a similarly weak authentication mechanism include FTP, POP3, and IMAP.

Attacks on Hashing Computations

- A brute force attack involves finding an alternative text that will yield the same hash signature. This is usually fairly difficult because the alternative text is likely to be gibberish.
- An effective attack is called a birthday attack.

A Simple Birthday Attack

Suppose Bob and Alice enter an agreement in which Alice agrees to pay Bob $5.00 per widget. This agreement is sent to Bob with a cryptographic checksum. Bob decides not to store the original document on his server, just the checksum thinking that would be adequate evidence if Alice tries to present an alternative document ...

A Simple Birthday Attack (cont.)

In fact, Alice does try to present an alternative document which states that the agreement is that she pay $1.00 per widget. Bob thinks she will fail in a legal battle because he has the cryptographic checksum. Unfortunately for Bob, Alice's new document has the same checksum as the original and Bob loses in court.

A Simple Birthday Attack (cont.)

What Alice did (what is called a birthday attack) involved taking the original document (with the known checksum) and replacing all references to $5 to $1. Then, she systematically reformats the $1 per widget document by changing spaces to tabs and so forth. Eventually she finds a $1 document that has the same checksum as the original $5 document.

This kind of attack would be difficult with checksums of 512 or even 256 bits.

Digital Signatures for Authentication

- Public key encryption enabled the development of the technology of digital signatures.
- Digital signatures are somewhat analogous to traditional handwritten signatures.
- Digital signatures are strongly bound to the document, but weakly bound to the individual.
- A digital signature is computed, in part, using the contents of the document being signed.

Main Goals of Digital Signatures

- A signature should be proof of authenticity. Its existence on a document should be able to convince people that the person whose signature appears on the document signed the document.
- A signature should be impossible to forge. The person who signed the document should not be able to claim that the signature is not theirs (support for non-repudiation).

Main Goals (cont.)

- After the document is signed, it should be impossible to alter the document without detection. The signature is intrinsically linked to the document that is being signed.
- It should be impossible to transplant the signature to another document. Again, the digital signature is intrinsically linked to the document that is being signed.

Figure 12.1 from Denning

- This figure shows one scheme for digital signatures that uses public key cryptography and hash algorithms (the usual technology).
- As you might have guessed, Alice wants to send a sign and encrypted message to Bob.
- Here's how it works:

Figure 12.1 (cont.)

1. Alice generates a message key, K, for symmetric encryption. Alice encrypts the message M with K, getting the ciphertext message, CM.

2. Alice encrypts K with Bob's public key-encrypting key, Kbobpub, getting the ciphertext key, CK. This will allow Bob to retrieve the key for decrypting the ciphertext.

Figure 12.1 (cont.)

3. Alice uses a hashing function to compute a checksum for the message, M. She then encrypts the checksum (for public key encryption) using her private signature key KSAlicepriv. The encrypted checksum is the signature, S.

4. Alice sends CK (the encrypted message key), CM (the encrypted message), and S (the digital signature) to Bob.

Figure 12.1 (cont.)

5. Bob uses his private key, Kbobpriv, to decrypt CK. This gives him the key, K, that Alice originally sent to encrypt the message, M.

6. Bob uses K to decrypt CM (the encrypted message) to get the message, M.

7. Bob uses Alice's public signature key KSAlicepub to validate S, the digital signature. This requires that Bob use the hashing function to hash the message M. The resulting checksum should be equal to the decrypted signature, S.

Figure 12.1 (cont.)

This technology of digital signatures uses:

- A hash function to help generate the digital signature, S.
- Symmetric (secret key) cryptography to encrypt the message, M.
- Public key cryptography to share the secret key used to encrypt and decrypt the message, M.
- Public key cryptography to encrypt and decrypt the digital signature, S.

Pretty Good Privacy (PGP)

This is how Bob and Alice would accomplish the same goals using a user-friendly e-mail encryption system called Pretty Good Privacy (PGP):

1. Alice composes an e-mail message to Bob. She clicks on a button or menu item that says “send signed and encrypted”.

Pretty Good Privacy (cont.)

2. The encryption system prompts Alice for a password. The password unlocks her private signature key, which is stored encrypted on disk or on a separate storage medium.

3. The encryption system looks up Bob‘s public key (for encrypting messages sent to Bob under public key cryptography) in Alice's address book or on her “digital key ring” which is stored in a file on her disk.

Pretty Good Privacy (cont.)

3 (cont.). The digital key ring generates K, the symmetric key that will be shared with Bob, and computes CK, the encrypted key, CM, the encrypted message, and S, the digital signature. It puts the message in the outbound queue.

4. When the message shows up in Bob's inbox, he clicks on a button to read the message.

Pretty Good Privacy (cont.)

5. Bob's encryption system prompts him for a password, which unlocks his private key. It decrypts CK to retrieve K, and then uses K to decrypt CM, to get the message M.

6. The encryption system on Bob's machine then looks up Alice's public signture key in Bob's address book or key ring. It validates her signature S. The decrypted message is displayed to Bob along with an indication as to whether the signature was valid.

Pretty Good Privacy (cont.)

Alice and Bob each have two digital key rings when they use PGP. They have a private ring that holds their private keys and a public ring that holds their own public keys and the public keys of those they are communicating with.

The key rings are implemented as files stored on the hard drive or on a diskette.

Diffie-Hellman

- Diffie-Hellman is another popular method for sharing secret keys.
- Diffie-Hellman has some similarities to the use of public key encryption to share secret keys.
- This method was developed in 1976 by Whitfield Diffie and Martin Hellman, two cryptographers at Stanford University.
- In 1997 it was revealed that British cryptographers had developed a similar idea in the 1960s and early 1970s.

Diffie-Hellman (cont.)

Here is a simple description of the Diffie-Hellman protocol that allows two parties to compute a message key for symmetric encryption without that secret ever being shared explicitly:

1. Each party independently generates a private key.

2. They each compute a public key as a mathematical function of their individual private keys.

Diffie-Hellman (cont.)

3. They exchange public keys.

4. Each party then computes a message key (the secret key) which is derived from their own private key and the other person's public key. They both arrive at the same message key.

Diffie-Hellman (cont.)

- The public keys must be computed using a one-way function (a hashing function) that makes it imposible to get back the private keys from the publicly exchanged keys.
- If an attacker has access to one party's public key and the other party's private key, the attacker could compute the message key.
- The mathematics is such that the publicly exchanged keys cannot reveal either party's private key.

Diffie-Hellman (cont.)

The mathematics is based on the following relationship:

y = gx mod N

It is easy to compute y if g, x, and N are known, but it is not easy to compute x if y, g, and N are known.

The problem of finding x is called the discrete logarithm problem because x is the logarithm of y base g (mod N). For numbers that are hundreds of digits long, this is a hard problem.

Diffie-Hellman (cont.)

Here is how Diffie-Hellman works, allowing Allice and Bob to establish a secret message key. Assume that p is some prime number and g is a base number:

- Alice generates a secret key, xalice.
- Bob generates a secret key, xbob.
- Alice computes a public key yalice = gxalice mod p.
- Bob generates a public key ybob = gxbob mod p.

Diffie-Hellman (cont.)

- Bob and Alice exchange their public keys.
- Alice now computes the message key, K, as

K = ybobxalice mod p

- Bob now computes the message key, K, as

K = yalicexbob mod p

- Both Bob and Alice end up with the same key, namely:

K = gxalice * xbob mod p

Diffie-Hellman (cont.)

In practice, very large numbers are used (several hundred DIGITS each), but here is an example using small numbers:

p = 11, g = 5, xalice = 2, xbob = 3.

- Alice computes her public key

yalice = 52 mod 11 = 3.

- Bob computes his public key

ybob = 53 mod 11 = 4.

Diffie-Hellman (cont.)

- Bob and Alice exchange their public keys.
- Alice computes the message key, K, as

K = 42 mod 11 = 5.

- Bob computes the message key, K, as

K = 33 mod 11 = 5.

- Both kend up with the same message key, namely:

K = 52*3 mod 11 = 15,625 mod 11 = 5.

Diffie-Hellman (cont.)

- Diffie-Hellman are used in several network protocols and commercial products, including PGP.
- With Diffie-Hellman, keys can be generated as needed (on the fly) and they can be discarded at the end of the conversation.

Software Developers andCryptography

According to Viega and McGraw the most common mistakes developers make with respect to cryptography are:

- Failing to apply cryptographywhen it is needed.
- Applying cryptography in an incorrect manner when it is deployed.

Developers and Crypto (cont.)

- The most important rule is:

Never, Never implement your own cryptographic algorithms!!!

- An experienced cryptanalyst will not be deterred by the fact that an algorithm is secret (not in the public domain). Their tools do not require knowledge of the algorithm.

Developers and Crypto (cont.)

- The safest policy is to use a published, well-used algorithm that has been well-scrutinized by respected cryptographers over a period of at least a few years.

Developers and Crypto (cont.)

- Viega and McGraw note that most of the major network protocols that use encryption have been broken at least once. These include:
- SSL (Secure Socket Layer) version 2 – this should never be used.
- SSH (Secure Shell Protocol) version 1 – this should be avoided.
- MS's Point-to-Point protocol used in MS's Virtual Private Network (VPN).

Developers and Crypto (cont.)

- It is not only important to use well-known encryption algorithms, but also to use well-scrutinized implementations of those algorithms, because the algorithms could be implemented incorrectly.
- Developers also need to understand the legal framework surrounding cryptography. The laws have been weakened somewhat concerning shipping strong crypto stuff overseas, but there are still laws governing this domain.

Developers and Crypto (cont.)

- The best bet, in terms of avoiding legal complications, is to use off-the-shelf, freely available cryptographic packages.
- Handout with reviews of two cryptographic libraries.

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