Encryption

Encryption

The problem

It is possible for an unauthorized agent to acquire transmissions

The extent of the danger varies:– Listen only -- the intruder learns information that

should not be available. Use is separate from the acquisition of the information

– Active intrusion -- the intruder intercepts message transmission and substitutes a modified message, or redirects the original message. Effect is immediate.

Message interception

Original message

EncodingMethod Ciphertext

DecodingMethod

Received messageEavesdropping Masquerading

Intruder

(Plain text) (Plain text)

Encryption/Decryption Keys Key-based encryption is an old idea

– Caesar’s code• “May have fooled the Gauls, but hasn’t fooled anyone since”

Problem is that you have to get the key to the receiver, secretly and accurately.

• If you can get the key there, why not use the same method to send the whole message? (Efficiency of scale)

• If the key is compromised without the communicators knowing it, the transmissions are open.

– WWII Enigma code» http://home.us.net/~encore/Enigma/enigma.html

Goals, requirements for an encryption method High level of data protection Simple to understand Complex enough to deter intruders Protection based on the key, not the algorithm Economical to implement Adaptable for various applications Available at reasonable cost

Data Encryption Standard

Complex sequence of transformations– hardware implementations speed performance– modifications have made it very secure

Known algorithm– security based on difficulty in discovering the

key

http://www.itl.nist.gov/fipspubs/fip46-2.htm

The Data Encryption Standard Illustrated

64 bit blocks, 64 bit key

INTERNET-LINKED COMPUTERS CHALLENGE DATA ENCRYPTION STANDARD

LOVELAND, COLORADO (June 18, 1997). Tens of thousands of computers, all across the U.S. and Canada, linked together via the Internet in an unprecedented cooperative supercomputing effort to decrypt a message encoded with the government-endorsed Data Encryption Standard (DES).

Responding to a challenge, including a prize of $10,000, offered by RSA Data Security, Inc, the DESCHALL effort successfully decoded RSADSI's secret message.

According to Rocke Verser, a contract programmer and consultant who developed the specialized software in his spare time, "Tens of thousands of computers worked cooperatively on the challenge in what is believed to be one of the largest supercomputing efforts ever undertaken outside of government."

Using a technique called "brute-force", computers participating in the challenge simply began trying every possible decryption key. There are over 72 quadrillion keys (72,057,594,037,927,936). At the time the winning key was reported to RSADSI, the DESCHALL effort had searched almost 25% of the total. At its peak over the recent weekend, the DESCHALL effort was testing 7 billion keys per second.

Public Key encryption Eliminates the need to deliver a key Two keys: one for encoding, one for

decoding Known algorithm

– security based on security of the decoding key Essential element:

– knowing the encoding key will not reveal the decoding key

Effective Public Key Encryption Encoding method E and decoding method D are

inverse functions on message M:– D(E(M)) = M

Computational cost of E, D reasonable D cannot be determined from E, the algorithm, or

any amount of plaintext attack with any computationally feasible technique

E cannot be broken without D (only D will accomplish the decoding)

Any method that meets these criteria is a valid Public Key Encryption technique

It all comes down to this:

key used for decoding is dependent upon the key used for encoding, but the relationship cannot be determined in any feasible computation or observation of transmitted data

Rivest, Shamir, Adelman (RSA)

Choose 2 large prime numbers, p and q, each more than 100 digits

Compute n=p*q and z=(p-1)*(q-1) Choose d, relatively prime to z Find e, such that e*d=1 mod (z)

– or e*d mod z = 1, if you prefer. This produces e and d, the two keys that

define the E and D methods.

Public Key encoding Convert M into a bit string Break the bit string into blocks, P, of size k

– k is the largest integer such that 2k<n– P corresponds to a binary value: 0<P<n

Encoding method – E = Compute C=Pe(mod n)

Decoding method– D = Compute P=Cd(mod n)

e and n are published (public key) d is closely guarded and never needs to be

disclosed

In class exercise Create your own public and private keys

– (keep the numbers very small to make it reasonable for you to do the computation)

Give someone else a paper with your values for n and e (Put your name on it)

Write a short message and encode it using the n,e values given to you.– Keep it simple. Use all capital letters. Code A=1, B=2, etc.

Return it to the person whose key you have. Decode the message sent to you.

An example: P=7; q=11; n=77; z=60 d=13; e= 37; k=6 Test message = CAT Using A=1, etc and 5-bit representation:

– 00011 00001 10100 Since k=6, regroup the bits (arrange right to left so that any padding

needed will put 0's on the left and not change the value): – 000000 110000 110100 (three leading zeros added to fill the block)

decimal equivalent: 0 48 52 Each of those raised to the power 37 (e) mod n: 0 27 24 Each of those values raised to the power 13 (d) mod n (convert back to

the original): 0 48 52

On a practical note: PGP

You can create your own real public and private keys using PGP (Pretty Good Privacy)

See the following Web site for full information.

http://web.mit.edu/network/pgp.html

Issues Intruder vulnerability

– If an intruder intercepts a request from A for B’s public key, the intruder can masquerade as B and receive messages from B intended for A. The intruder can send those same or different messages to B, pretending to be A.

– Prevention requires authentication of the public key to be used.

Computational expense– One approach is to use Public Key Encryption to send the

Key for use in DES, then use the faster DES to transmit messages

Digital Signatures

Some messages do not need to be encrypted, but they do need to be authenticated: reliably associated with the real sender– Protect an individual against unauthorized

access to resources or misrepresentation of the individual’s intentions

– Protect the receiver against repudiation of a commitment by the originator

Digital Signature basic technique

Sender A

Receiver B

Intention to send

E(Random Number)where E is A’s public key

Message and D(E(Random Number))

Public key encryption with implied signature

Add the requirement that E(D(M)) = M Sender A has encoding key EA, decoding key

DA

Intended receiver has encoding (public) key EB. A produces EB(DA(M)) Receiver calculates EA(DB(EB(DA(M))))

– Result is M, but also establishes that only A could have encoded M

Digital Signature Standard (DSS)

Verifies that the message came from the specified source and also that the message has not been modified

More complexity than simple encoding of a random number, but less than encrypting the entire message

Message is not encoded. An authentication code is appended to it.

Encryption summary

Problems– intruders can obtain sensitive information– intruder can interfere with correct information

exchange

Solution– disguise messages so an intruder will not be

able to obtain the contents or replace legitimate messages with others

Important methods

DES– fast, reasonably good encryption– key distribution problem

Public Key Encryption– more secure

• based on the difficulty of factoring very large numbers

– no key distribution problem– computationally intense

Digital signatures

Authenticate messages so the sender cannot repudiate the message later

Protect messages from changes during transmission or at the receiver’s site

Useful when the contents do not need encryption, but the contents must be accurate and correctly associated with the sender