Announcements

A review session is being scheduled for Saturday March 15

Encryption

Encryption encodes information to hide it from everyone else … maintaining your privacy

Maintaining Privacy

To keep information private it must be hidden from “prying” computers

As children, most of us used “secret” codes

Most often the code was a Caesar Cipher -- an alphabetic shift by a constant amount

Breaking Caesar Cipher

Fixed substitutions don’t work, ‘cause letters have a known distribution

In a large text, count the frequency of each letter, match the results to distribution

The twelve most frequent letters account for 80% of English text

ETAOINSHRDLU

Encryption Issue

Traditionally, encryption technology has been “breakable” with effort

Breakable codes let law enforcement and governments watch criminals and spies

Codes are good enough for the honest

ÞNew computer encryption is unbreakableÜ

It’s called “strong encryption” … should it be legal to be able to keep secrets absolutely?

General Encryption Setup

Encryption is most important for when sending information

Problem: Key Exchange

To communicate securely, users must meet before sending/receiving

Revise Encryption Setup

Public Key Encryption is based on publishing the key

Sender uses public key to encrypt

Public Key Encryption

Using the public key, encrypt message

Divide T, the clear text bytes, into blocks

Treat each block as a number

Cube number (raise to 3 pwr), divide by key

Send the remainder for each block

Public Key Cryptography

Does PKC work? Can’t it be cracked?

Recall definition of divide: a=b×c + d

For example, 50/6 implies 50=6×8 + 2

The encryption process is a division:

T³=K_r×c + d

so sending c&d determines clear text T

RSA Encryption

Rivest, Adelman and Shamir invented a PKC scheme called RSA

The secret is to pick the key, K_r, right

Pick two prime numbers -- numbers divisible only by themselves and 1 -- that are 2 greater than a multiple of 3 … weird!

Examples are 5, 11, 17, 23, 29, ...

K_r = p×q so that it is 129 digits

How To Recover Message

Compute s=1/3(2(p-1)(q-1)+1) then compute C^s = K_r×c + T

That is …

The remainders (C) raised to s power equal K_r times some (quotient) c no one cares about plus the original clear text number!

So, raise the remainders to s, divide by K_r and PRESTO! the new remainder is the answer

What Makes RSA Work?

Though the numbers get huge, computer can handle them quickly

These codes are strong because breaking them needs s, which needs p, q, which means factoring K_r

Factoring is computationally tough -- best methods are only somewhat better than grammar school, “try all small primes”

Picking 129 digit key, means no computer can factor it … so the code is unbreakable

RSA Challenge

After inventing their scheme (1977), RSA challenged people to break it

Their first key was broken in 1994 using 1000 computers over 8 months

Their secret message: THE MAGIC WORDS ARE SQUEAMISH OSSIFRAGE

Doomed? No. There are many other 129 digit keys, or if people get nervous make 200 digit keys or more … breaking gets harder very fast; encrypt/decrypt doesn’t

Is Strong Encryption Smart

Should we allow people to use strong encryption? Or should only breakable codes be legal?

It hampers law enforcement and security

Most criminals reveal plans in other ways

PKC exists and is known, so build in escape

-- Trap door

-- Key Escrow

But are these schemes really secure?


	Encryption encodes information to hide it from everyone else … maintaining your privacy


	To keep information private it must be hidden from “prying” computers
			As children, most of us used “secret” codes
			Most often the code was a Caesar Cipher -- an alphabetic shift by a constant amount


	Fixed substitutions don’t work, ‘cause letters have a known distribution
			In a large text, count the frequency of each letter, match the results to distribution
			The twelve most frequent letters account for 80% of English text
			ETAOINSHRDLU


	Traditionally, encryption technology has been “breakable” with effort
			Breakable codes let law enforcement and governments watch criminals and spies
			Codes are good enough for the honest


	To communicate securely, users must meet before sending/receiving


	Public Key Encryption is based on publishing the key
			Sender uses public key to encrypt


	Using the public key, encrypt message
			Divide T, the clear text bytes, into blocks
			Treat each block as a number
			Cube number (raise to 3 pwr), divide by key
			Send the remainder for each block


	Does PKC work? Can’t it be cracked?
			Recall definition of divide: a=b×c + d


			For example, 50/6 implies 50=6×8 + 2
			The encryption process is a division:
			T³=K_r×c + d
			so sending c&d determines clear text T


	Rivest, Adelman and Shamir invented a PKC scheme called RSA
			The secret is to pick the key, K_r, right
			Pick two prime numbers -- numbers divisible only by themselves and 1 -- that are 2 greater than a multiple of 3 … weird!
			Examples are 5, 11, 17, 23, 29, ...
			K_r = p×q so that it is 129 digits


Compute s=1/3(2(p-1)(q-1)+1) then compute C^s = K_r×c + T
	That is …
		The remainders (C) raised to s power equal K_r times some (quotient) c no one cares about plus the original clear text number!
		So, raise the remainders to s, divide by K_r and PRESTO! the new remainder is the answer


	Though the numbers get huge, computer can handle them quickly
			These codes are strong because breaking them needs s, which needs p, q, which means factoring K_r
			Factoring is computationally tough -- best methods are only somewhat better than grammar school, “try all small primes”
			Picking 129 digit key, means no computer can factor it … so the code is unbreakable


	After inventing their scheme (1977), RSA challenged people to break it
			Their first key was broken in 1994 using 1000 computers over 8 months
			Their secret message: THE MAGIC WORDS ARE SQUEAMISH OSSIFRAGE
			Doomed? No. There are many other 129 digit keys, or if people get nervous make 200 digit keys or more … breaking gets harder very fast; encrypt/decrypt doesn’t


	Should we allow people to use strong encryption? Or should only breakable codes be legal?
			It hampers law enforcement and security
			Most criminals reveal plans in other ways
			PKC exists and is known, so build in escape
			-- Trap door
			-- Key Escrow
			But are these schemes really secure?