20-751 ecommerce technology summer 2002 copyright © 2002 michael i. shamos cryptographic security

20-751 ECOMMERCE TECHNOLOGY

SUMMER 2002

COPYRIGHT © 2002 MICHAEL I. SHAMOS

Cryptographic Security


SUMMER 2002


Outline

• Information security• Encryption and keys• Symmetric encryption

– DES• Public-key cryptosystems

– RSA• Digital signatures• Digital certificates


SUMMER 2002


Information Security

• Keep data secret from unauthorized parties• Authenticate identity of users • Verify that messages have not been altered in transit• Prove that a party engaged in a transaction

– Make it impossible for him to deny (nonrepudiation)


SUMMER 2002


The Encryption Process

MATERIALWE WANT TOKEEP SECRET

UNREADABLEVERSION OFPLAINTEXT

DATA TO THEENCRYPTIONALGORITHM

MATHEMATICALSCRAMBLINGPROCEDURE (TELLS HOW TO

SCRAMBLE THISPARTICULAR MESSAGE)

MIGHT BE:TEXTDATAGRAPHICSAUDIOVIDEOSPREADSHEET. . .

SOURCE: STEIN, WEB SECURITY

OBJECT: HIDE A MESSAGE(PLAINTEXT) BY MAKING ITUNREADABLE (CIPHERTEXT)


SUMMER 2002


Role of the Key in Cryptography

• The key is a parameter to an encryption procedure• Procedure stays the same, but produces different

results based on a given key

NOTE: THIS METHOD IS NOT USED IN ANY REAL CRYPTOGRAPHY SYSTEM.IT IS AN EXAMPLE INTENDED ONLY TO ILLUSTRATE THE USE OF KEYS.

S P E C I A L T Y B D F G H J K M N O Q R U V W X ZA B C D E F G H I J K L M N O P Q R S T U V W X Y Z

C O N S U L T I N G

D S R A V G H E R MEXAMPLE:


SUMMER 2002


Symmetric Encryption

SAME KEY USED FORBOTH ENRCYPTIONAND DECRYPTION

SENDER AND RECIPIENT MUSTBOTH KNOW THE KEYTHIS IS A WEAKNESS



SUMMER 2002


Data Encryption Standard (DES)

• Symmetric, key-based encryption-decryption standard. No public keys

• Block cipher: operates on 64-bit blocks• Uses 56-bit key• 16 “rounds” -- key for each round is a 48-bit function

of the original 56-bit key. Each key bit participates in an average of 14 rounds

• Completely symmetric. Same algorithm decrypts.• Fast implementation in hardware: 1 gigabit/second


SUMMER 2002


Data Encryption Standard (DES)

64 BITS OF MESSAGE INPUT PERMUTATION

INVERSE OF INPUTPERMUTATION

SUBKEYS:EACH IS A 48-BITFUNCTION OF A56-BIT KEY

OUTPUT: 64 BITS OFENCRYPTED TEXT

LEFT HALF OFBLOCK (32 BITS)

f IS A COMPLICATEDFUNCTION INVOLVINGVARIOUS PERMUTATIONS

SOURCE: SCHNEIER, APPLIED CRYPTOGRAPHY

IS EXCLUSIVE-OR


SUMMER 2002


Information Loss with Exclusive-OR

• x y = 1 if either x or y is 1 but not both:

• If x y = 1 we can’t tell which one is a 1• Can’t trace backwards to determine values

xy 0 1

0 0 1

1 1 0x

y


SUMMER 2002


Cracking Symmetric Encryption

KEYLENGTH

SPEND$$THOUSANDS

SPEND$$MILLIONS

SPEND$100 MILLION

40 bits seconds < 1 second < .01 second

56 bits days minutes 1 second

64 bits months days minutes

80 bits million years millennia centuries

128 bits > age of Universe > age of Universe > age of Universe

(40-bit symmetric key = 384-bit PKE key)

ESTIMATED TIME TO CRACK KNOWNSYMMETRIC ENCRYPTION ALGORITHMS


SUMMER 2002


Public-Key (Asymmetric) Encryption

1. USERS WANT TO SEND PLAINTEXT TO RECIPIENT WEBSITE

2. SENDERS USE SITE’S PUBLIC KEY FOR ENCRYPTION

3. SITE USES ITS PRIVATE KEY FOR DECRYPTION

4. ONLY WEBSITE CAN DECRYPT THE CIPHERTEXT. NO ONE ELSE KNOWS HOW



SUMMER 2002


Public-Key Encryption• Alice wants to send Bob a secure message M.• Alice uses Bob’s public key to encrypt M.• Bob uses his private key to decrypt M.• Bob is the ONLY ONE who can do this,

so M is secure.• Problem: Anyone could have sent it. Was it really Alice?

ALICE’SCLEARTEXT

ALICE’SCODEDTEXT

ALICE’SCODEDTEXT

ALICE’SCLEARTEXT

TRANSM ISSION

BOB DECRYPTS WITHHIS PRIVATE KEY

ALICE ENCRYPTS WITHBOB’S PUBLIC KEY

BOB’SPUBLIC

KEY

BOB’SPRIVATE

KEY


SUMMER 2002


Digital Authentication• Alice wants to send Bob a message M so that Bob is sure Alice

is the sender.• Alice uses her own private key to encrypt M.• Bob uses Alice’s public key to decrypt M.• Alice is the ONLY ONE who could have sent it.• Problem 1: Anyone can read it! Problem 2: Replay attack!

ALICE’SCLEARTEXT

ALICE’SCODEDTEXT

ALICE’SCODEDTEXT

ALICE’SCLEARTEXT

TRANSM ISSION

BOB DECRYPTS WITHALICE’S PUBLIC KEY

ALICE ENCRYPTS WITHHER PRIVATE KEY

ALICE’SPRIVATE

KEY

ALICE’SPUBLIC

KEY


SUMMER 2002


Secure Authenticated Messages• Alice must send Bob a secret & authenticated message M so

Bob is sure it was sent by Alice. Use both encryption and signature.

ALICE’SCODEDTEXT

ALICE’SCODEDTEXT

(AUTHENTICATED)

ALICE’SCLEARTEXT

BOB DECRYPTS WITHALICE’S PUBLIC KEY

ALICE ENCRYPTS WITHHER PRIVATE KEY

ALICE ENCRYPTS WITHBOB’S PUBLIC KEY

ALICE’SCODED AND

SIGNED TEXT

ALICE’SCODED AND

SIGNED TEXT

T R A NSMI

T

ALICE’SCLEAR TEXT

(DECRYPTED ANDAUTHENTICATED)

BOB DECRYPTS WITHHIS PRIVATE KEY

BOB’S PUBLIC

ALICE’S PUBLIC

BOB’S PRIVATE

ALICE’S PRIVATE

4 KEYSNEEDED:


SUMMER 2002


Rivest-Shamir-Adelman (RSA)

• It is easy to multiply two numbers but apparently hard to factor a number into a product of two others.

• Given p, q, it is easy to compute n = p • q• Example: p = 5453089; q = 3918067• Easy to find n = 21365568058963• Given n, hard to find two numbers p, q with p • q = n• Now suppose n = 7859112349338149

What are p and q such that p • q = n ?• Multiplication is a one-way function• RSA exploits this fact in public-key encryption


SUMMER 2002


RSA Encryption

• Select two large prime numbers p, q (> 100 digits)• Let n = p • q• Choose a small odd integer e that does not divide

m = (p - 1)(q - 1). Then x(p-1)(q-1) = 1 (mod n)• Compute d = e-1(mod m)

– That is, d • e gives remainder 1 when divided by m

• Public key is the pair (e, n)• Private key is the pair (d, n)• Knowing (e, n) is of no help in finding d. Still need p

and q, which involves factoring n• DEMO


SUMMER 2002


0 1 2 3 4 5 6

0 0 0 0 0 0 0 0

1 0 1 2 3 4 5 6

2 0 2 4 6 1 3 5

3 0 3 6 2 5 1 4

4 0 4 1 5 2 6 3

5 0 5 3 1 6 4 2

6 0 6 5 4 3 2 1

MULTIPLICATIONMOD 7

Multiplicative InversesOver Finite Fields

• The inverse e-1 of a number e satisfies e-1 • e = 1• The inverse of 5 is 1/5• If we only allow numbers from 0 to n-1 (mod n), then for special

values of n, each e has a unique inverse

6 • 2 = 12WHEN DIVIDED BY 7GIVES REMAINDER 5

EACH ROW EXCEPTTHE ZERO ROWHAS EXACTLY ONE 1

EACH ELEMENT HASA UNIQUE INVERSE


SUMMER 2002


RSA Encryption

• Message M is a number

• To encrypt message M using key (e, n):• Compute C(M) = M

e (mod n)

• To decrypt message C using key (d, n):• Compute P(C) = C

d (mod n)

• Note that P(C(M)) = C(P(M)) = (M e)d (mod n)

= M e•d (mod n) = M

because e • d = 1 and m = (p-1)(q-1)


SUMMER 2002


Message Digest (Hash)

• A message digest is a “fingerprint” of a message• Much shorter than the original message (e.g. 160 bits)• Easy to compute• Can’t recover the message from the digest• Changing the message changes the digest

MESSAGE (VERY LONG)

DIGEST

DIGEST CAN BE USED TO VERIFY THATTHE MESSAGE HAS NOT BEEN ALTERED


SUMMER 2002


Single Step of SHA-1

Operates on 16-word (512-bit) blocks

Expands 16 words to 80 words Wt

Performs 80 operations as shown for t = 0..79

a, b, c, d, e are special constants

Kt are special constants

SOURCE: SCHNEIER, APPLIED CRYPTOGRAPHY

INITIALLY CONSTANTS

80 WORDS INPUT HERE, 1 EACH STEP

MAGIC CONSTANTS

“<<< 5” means “cyclic left shift 5 bits”

+ + ++

REVISEDCONSTANTSFOR NEXTSTEP


SUMMER 2002


Digital Signature• A function of both the message AND the signer’s private key

(different for every message)

MESSAGE (LONG)

HASH

SIG

USE SECURE HASH ALGORITHM (SHA) TO PRODUCE HASH (MESSAGE DIGEST)

ENCRYPT HASH USING SIGNER’S PRIVATE KEYPRIVATE KEY

MESSAGE (LONG)SIG

APPEND SIGNATURE TO MESSAGE; SEND BOTHDIGITALLYSIGNEDMESSAGE


SUMMER 2002


Authentication by Digital Signature

MESSAGE (LONG)

HASHHASH

RECIPIENT USES SHATO COMPUTE HASH

RECIPIENT DECRYPTS SIGWITH SIGNER’S PUBLIC KEY

MESSAGE (LONG)SIG

IF HASHES ARE EQUAL, MESSAGE IS AUTHENTIC.

WHY? IF ANY BIT OF M OR SIG IS ALTERED, HASH CHANGES.

RECIPIENT RECEIVES SIG + MESSAGE

=?


SUMMER 2002


X.509 Version 2 Certificate

SOURCE: FORD & BAUM,SECURE ELECTRON IC COMMERCE

VERSION # OF X.509

UNIQUE # ASSIGNED BY CA

EXAMPLES: MD5RSA,sha1RSA

USUALLY A DOMAIN NAME

EXAMPLES: RSA


SUMMER 2002


QA&

20-751 ecommerce technology summer 2002 copyright © 2002 michael i. shamos cryptographic security

Documents

symmetric key

ecommerce technology

shamos symmetric encryption

key output

shamos information security

web security slide

gigabitsecond slide

nonrepudiation slide