Cryptography History of Crypto Based on Slides by Alfred C. Weaver.

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Cryptography

History of Crypto

Based on Slides byAlfred C. Weaver

References

Easy to read Computer Networks, by Andrew Tanenbaum

Authoritative (1652 references) Applied Cryptography, by Bruce Schneier

Historical Crypto, Stephen Levy The Code Book, Simon Singh

AES (FIPS approved May 26, 2002) Info: http://csrc.nist.gov/encryption/aes/ Code: http://csrc.nist.gov/encryption/aes/

round2/r2algs-code.html

Privacy and Security

What are they? When do we need them? Cryptography

Symmetric key crypto (e.g., DES, IDEA, AES) Public key crypto (e.g., RSA, PGP, GPG)

How powerful are they? Digital signatures Leads to SSL and SET

Privacy data is available only to authorized users imagine the complexity of a medical

record, with different parts visible to doctor, patient, hospital, insurance company, social agencies, courts, government

Security data is meaningless to an unauthorized

user security is achieved via cryptography

Security

There are two kinds of security: one kind stops your kid brother from

reading your mail the other kind stops major government

agencies from reading your files We are talking about the latter

Security

Locking a document in a safe is not security.

Locking a document in a safe, giving the safe to the best safecrackers in the world, plus the design specs for the safe, plus as many safes as they want, keyed to the combinations they specify, and as much time as they want...

If then they can’t open the safe, that’s security!

Some information is public and never needs protection stock ticker Mars Pathfinder images airlines schedules telephone books university course offerings vacation offerings restaurant menus electronic product catalogs

Most e-commerce transactions need serious security invoices transactions payments medical records

Weaver’s First Law states that electronic commerce requires security algorithms that are: easy to use (low hassle factor) provably correct (low risk) convenient (handle multiple data types) universal (world-wide acceptance) used only when needed (because they

are computationally expensive)

Cryptography

Cryptography provides confidentiality authentication integrity non-repudiation

Security achieved by intelligent storage on computer encrypted transmission over the Internet proper choice of encryption algorithm secure management of encryption keys

Encryption

The big picture

EncryptionAlgorithmC=E(P)

DecryptionAlgorithmP=D(C)

PlaintextP

CiphertextC

PlaintextP

D( E (P) ) = P

Cryptography

The goal of cryptography is to protect the data in such a way that one could freely distribute encrypted data to everyone on the planet, knowing that only authorized users could reveal the plaintext

You would not intentionally do this, but you could without fear of compromise

Caesar Cipher

Shift the alphabet by three letters a becomes d b becomes e c becomes f, etc.

attack transmitted as dwwdfn Suitable for Green Hornet decoder

rings in Cracker Jack boxes Works for children, but that’s all

Substitution Cipher

Circularly shift the alphabet by k characters

Still no power because k < 26 Using N brute force trials,

1<=N<=25, is guaranteed to reveal the plaintext P: a b c d e f g h i j k l N=1: b c d e f g h i j k l m N=2: c d e f g h i j k l m n N=3: d e f g h i j k l m n o N=25:z a b c d e f g h i j k

Monoalphabetic Substitution

Make an arbitrary mapping between plaintext and ciphertext

For simplicity, use just the English alphabet a b c d e f g h i j k l m ... q w e r t y u i o p a s d ...

Looks pretty hard to reverse

Monoalphabetic Substitution

There are 26 ways to pick the first substitution (although a=a may not be a good one), 25 ways to pick the second, 24 ways to pick the third...

So 26! ~= 4 x 1026 possible mappings

Testing 106/sec would take 1013 years Is it secure?

Substitution Cipher

All natural languages have statistical properties—in English: most common letters most common digrams most common trigrams most common word endings most common doubled letters most common words

Letter Frequency

E 13.0 A 7.3

T 9.3 S 6.3

N 7.8 D 4.4

R 7.7 H 3.5

I 7.4 L 3.5

O 7.4 C 3.0

Letter % Letter %

Frequency of Usage

•th •he •at •st •an •in •ea •nd •er •en •re •nt •to •es •on •ed •ti

•the •and •tha •hat •ent •ion •for •tio •has •edt •tis •ers •res •ter •con •ing •men

•ll •tt •ss •ee •pp •oo •rr •ff •cc •dd •nn

Digrams Trigrams Doubles

•e •t •s •d •n •r •y

Endings Words

•the •of •are •I •and •you •a •can •to •he •her •that •in •was •is •has •it •him •his

Decrypting a Substitution Cipher

Count relative frequency of letters, digrams, trigrams, endings, doubles, and words in the ciphertext

If you have enough encrypted text, it can be analyzed and broken by high-speed computers

But must have a body of encrypted text of sufficient size to permit analysis

Substitution Ciphers

Suppose we have a block of ciphertext ctbmn byctc btjds qxbns gstjc btswx ctqtz cqvuj qjsgs tjqzz

and the text comes from an accounting firm where we would expect the word financial in communications

Look for pattern: _ x y _ y _ x _ _

Transposition Ciphers

Need to break the relationship between repeated letters in the plaintext resulting in repeated letters in the ciphertext

Try a transposition cipher

Transposition Cipher

Pick a word with no repeated letters Write it horizontally Number the columns in alphabetic

order Write the plaintext beneath it in

word-wrapped rows Read out the ciphertext in columns,

starting with column 1, then 2, ...

PLAINTEXT:please transfer one million dollars to my swiss bank account six two two

CIPHERTEXT:

afllsksoselawaia

toossctclnmomant

esilyntwrnntsowd

paedobuoeriricxb

M E G A B U C K 7 4 5 1 2 8 3 6 p l e a s e t r a n s f e r o n e m i l l i o n d o l l a r s t o m y s w i s s b a n k a c c o u n t s i x t w o t w o a b c d

To break it: must know it is a transposition cipher look at frequency of letters if normal frequency, code is probably

transposition cipher since each letter represents itself

guess the code word length guess the order of columns try all combinations of number of columns and

order of columns complicated and difficult, but that’s what

computers are for

PLAINTEXT:move army acrossdelaware at midnight

I N T E R C O M

m o v e a r m ya c r o s s d el a w a r e a t m i d n i g h t

CIPHERTEXT:rsegeoanmalmyettocaimdahasrivrwd

3 5 8 2 7 1 6 4

Jefferson Cipher Wheel

Thomas Jefferson designed an ingenious way to encode and decode messages while serving as Sec. State in 1790-93

This is a reproduction at Monticello

Jefferson Wheel Cipher

Twenty-six cylindrical wooden pieces threaded onto an iron bar

Each wheel had all 26 characters in random order around the circumference

Wheels are numbered 1-26 and can be assembled in any order

Assemble the 26 wheels in some order (and remember it)

Spin wheels to align a message (up to 26 characters) on one line THOMASJEFFERSONWASAGOODMAN

Look at any other line (say the one above or below) and read what is there JRPNFJTIAHREIDBRPFDKEJSBGJTHDKS

Transmit the encoded message The wheel ordering must be known to the

receiver via some other method

Receiver assembles wheels in proper order

Set wheel to display the encoded message

Look at the other 25 rows—one will make sense and that’s the message

Double Encryption

Obviously, you can encrypt with one scheme, then encrypt the ciphertext with another scheme

Adds to complexity May or may not add to security

(depends upon your choices) Using two successive monoalphabetic

substitution ciphers is more complex, but not more secure

One-Time Pad

One-time pad is mathematically unbreakable!

Choose a random bit string as a key Convert plaintext into bitstring Compute exclusive-or of the two

strings Ciphertext contains no redundancy

information because every combination is equally likely

One-Time Pad

K=10101010 10101010 10101010 P= C=

‘c’=9910=011000112

‘a’=9710=011000012

‘t’=11610=011101002

Decrypt: exclusive-or of the ciphertext with the key reveals the plaintext

01100001 01110100

110111101100101111001001

01100011

One-Time Pad

Key must be at least as long as message

Key can not be memorized (too long), so has to be written down and shared between transmitted and receiver

Anything written down is dangerous Key could be a few gigabits of random

data embedded in a music CD prefixed by a few songs to avoid suspicion

One-Time Pad

Generating, remembering, storing, transferring, recalling, and using the key are all potential vulnerabilities of the overall end-to-end system (not the algorithm itself)

Physical one-time pads used in WW II

One-Time Pad

key=‘cat’= 01100011 01100001 01110100

P=‘dog’=

‘d’=10010=011001002

‘o’=11110=011011112

‘g’=10310=011001112

01100100 01100100 01100111

00000111 00000101 00010011

Fundamental Realization

Anything based upon a secret (hardware design, software details, algorithm, techniques, locations) has a fundamental vulnerability

Secrets don’t keep Can bribe or torture designers and/or

users to reveal secrets Design has to be open (public) Thus, must minimize reliance on

secrets or sharing of secrets

Modern Cryptography

Uses encryption with a key sender and receiver share the same

algorithm algorithm is public assume eavesdropper knows the

algorithm assume eavesdropper can see all the

ciphertext All the security is in the key, none in the

algorithm Key is a secret, and thus a vulnerability

Two Main Classes

Symmetric key encryption sender and receiver share the same key key must remain a secret for the lifetime of

the encrypted message Public key encryption

uses a two-part key, one part public and one part private

private key is never shared encrypt with public key decrypt with private key private key must remain secret forever

The Big Difference Symmetric key is fast

sharing the key is its vulnerability Public key is arbitrarily powerful and

there is no key to share slow to compute keys require management

So today we use both generate a random symmetric key and

use that to encode data use PKC to encrypt and transmit the

symmetric key

Cryptography History of Crypto Based on Slides by Alfred C. Weaver.

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