COEN 150 Information Assurance Essentials of Cryptography.

COEN 150 Information Assurance

Essentials of Cryptography

Cryptography

Scrambles a plain-text into crypto-text.

Enables to descramble plain text.

Symmetric Cryptography

Uses the same key for encryption, decryption

Asymmetric Cryptography

Uses different key for encryption, decryption

Message Authentication Codes

Condenses message into a short hash

• SHA1, … MD5, … are appropriate cryptographically secure hash functions• For example, encrypt only the MAC with a key known to sender and receiver.

Message Authentication Code

Alternatively, use a secret key. This also provides authentication.

Use of Asymmetric Cryptography

Generic idea:Make one key public. How?

Website Website can be spoofed.

On your business card Works for individuals, requires recipient to

type in several lines of gibberish correctly. From a trusted source

Going back and back: Where does the trust stem from?

Use of Asymmetric Cryptography

Notations: E – public key, D – secret key EC (M) – encryption of M using key C.

DC(M) – decryption of M using key C.

Asymmetric cryptography key identities DEED(M) = M

DDEE(M) = M

Use of Asymmetric Cryptography

Secret Transmission of messages Alice uses public key of Bob to

encrypt her messages to him: EE(Bob)

(M). Bob uses his private key to decrypt

the message: DD(Bob)EE(Bob)(M).

Use of Asymmetric Cryptography

Signing a message I: Alice encrypts the message with her private

key: ED(Alice)(M).

Bob decrypts with her public key and

obtains M = DE(Alice) ED(Alice)(M).

If M makes sense, Bob knows that someone with Alice secret key send the message.

Use of Asymmetric Cryptography Signing a message II

This method avoids encryption of the whole message.

Asymmetric cryptography is very compute intensive.

Alice uses a MAC of her message: MAC(M). She sends Bob M and ED(Alice)(MAC(M)). Bob calculates

MAC(M) = DE(Alice) (ED(Alice)(MAC(M))). Bob verifies that this is the correct MAC. Bob concludes that the message was sent

by someone knowing Alice’s private key.

Key Management

Generic Rules: Use symmetric cryptography as much

as possible for performance. Never use keys more than once.

Key Management becomes an issue.

Key Management

Keys have limited lifetimes: Cryptanalysis is easier with more

material. Breaking WEP involves harvesting a large

number of packets. Once found, a compromised key

continues to do damage.

Key Management

Key Management Life Cycles: Key establishment

Key generation Key distribution

Key backup / recovery, key escrow Key replacement / update (rekeying) Key revocation Key expiration / Key termination / Key

destruction

Key Management

Key generation Uses random number generation

Pseudo-random generation derived from a seed

WEP: seed based on user key word. Not as random as appeared.

Hardware random number generation Combined methods

Key Management

Key distribution Has issues of authentication and confidentiality. Diffie-Hellman protocol solves confidentiality:

Allows two parties to agree on a common secret. Subject to the man-in-the-middle attack

Alice thinks that she shares a secret with Bob. In reality, she communicates with M, and shares the

secret with him. M shares another secret with Bob.

Key Management Key backup / recovery

Accidental loss of key hardware failure, forgotten password …

Control of encrypted information Employer cannot entrust enterprise-critical data to

complete control of a single / group of employees. Key escrow

To preserve possibility of access by law enforcement agencies.

In the UK, it is a crime to withhold a key to encrypted data under subpoena.

In the US, such a law is seen to contradict 5th amendment protection.

Key Management

Key destruction Secure key destruction is far easier

than secure file erasure. Key destruction destroys accessibility

to encrypted data. Key archiving

Necessary for validation of old signatures, of integrity of old messages, …

Key Management

Symmetric key transport: Send symmetric key along, protected

by public key of recipient. Saves on processing time

Diffie-Hellman Uses calculation modulo p, p a large

prime. Chooses generator g.

Ideally, gx, x = 0, …, p -2 runs through all numbers 1, … p -1.

Uses the fact that calculating powers gx is computationally feasible.

But discrete logarithm (given gx find x) is not.

Diffie Hellman Alice generates random number a mod p. Bob generates random number b mod p. Alice sends Bob ga mod p. Bob sends Alice gb mod p. Alice calculates (gb)a mod p. Bob calculates (ga)b mod p. These numbers are identical and the

shared key.

Diffie Hellman

Man in the middle attack

Bob AliceMan in the Middle

Diffie Hellman Alice sends Bob ga mod p.

But message goes to alien. Alien sends Bob gc mod p.

Bob sends Alice gb mod p. But message goes to alien. Alien sends

Alice gd mod p. Alice calculates (gd)a mod p. Bob calculates (gc)b mod p. These set up a secure communication

channel between the alien and Bob and one between the alien and Alice.

Diffie Hellman

Secure against eavesdroppers. Can be secured against man-in-

the-middle by using authenticated gb mod p or by using a published value gb mod p.

Diffie Hellman and all other schemes

The problem is one of authentication and trust.