Overview of Cryptography
Oct. 29, 2002
Su San Im
CS Dept. EWU
Contents
•
Cryptography
•
Encryption/Decryption Methods
•
Encryption/Decryption Protocols
Cryptography
•
Description: The art and science of keeping
messages secure by altering or transforming them
m: Plaintext
Encryption
c: Ciphertext
Decryption
Original
Plaintext
Key
Key
Criteria of Good Cryptography
Confidentiality
–
Can decrypt only with a secret key
Authentication
–
Identify the person at the other end of the line
Integrity
–
No change during transit (message authentication) &
detecting the loss of integrity
Nonrepudiation
–
Know who sent the message &
Documented proof of identity of sender
Encryption Methods
•
Symmetric Key:
Secret Key Encryption
(Same key for encryption and decryption)
e.g.: DES(Data Encryption Standard),
AES(Advanced Encryption Standard)
•
Asymmetric Key:
Public Key Encryption
(Different keys for encryption and decryption)
e.g.: RSA(Rivest Shamir Adleman)
RSA
•
Named after Ronald
R
ivest, Adi
S
hamir, Leonard
A
dleman
•
Public Key: n, e such that
1. n=p
∙
q
2. e is relatively prime to (p

1)
∙
(q

1)
3. p and q are prime numbers which remain secret
•
Private Key: n, d and d is kept secret
=>
1
= (e
∙
d) mod
•
Encryption: c =
•
Decryption: m =
))
1
)(
1
((
q
p
))
1
)(
1
mod((
1
q
p
e
d
n
m
e
mod
n
c
d
mod
Example: RSA
•
n=3337 (p=47 and q=71, 47
∙71=3337
)
•
Choose e =79
•
Let m=688 be the message
•
d=1019 (
find x 1=(79
∙
x) mod (46
∙
70=3220) )
•
c=688 mod 3337 = 1570 => Encrypted message
•
m=1570 mod 3337 = 688 => Decrypted message
79
1019
Encryption/Decryption Protocols
M
M, K
CK
CK
CK
CM,
K
M
H
H
NoYes
H
S
S
start
a
b
c
d
e
f
g
h
j
k
l
m
n
n
In this chart, boxes contain information, and paths denote activity working with or changing the information.
Initially, Alice has a message M that she wishes to send signed to Bob, via a security protocol.
a.
Alice generates a random key K for DES encryption.
b.
Alice hashes M to create H.
c.
Alice encrypts the key K with Bob’s public key to create CK
Encryption/Decryption Protocols
M
M, K
CK
CK
CK
CM,
K
M
H
H
NoYes
H
S
S
start
a
b
c
d
e
f
g
h
j
k
l
m
n
n
d. Alice encrypts M using DES with key K to create CM.
e. Alice encrypts the hash H with her private key to create signature S.
f. Alice sends the encrypted form CK of the key K to Bob.
g. Alice sends the encrypted form CM of the message M to Bob.
h. Alice sends her “signature”, the encrypted form S of the hash H, to
Bob.
Encryption/Decryption Protocol
M
M, K
CK
CK
CK
CM,
K
M
H
H
NoYes
H
S
S
start
a
b
c
d
e
f
g
h
j
k
l
m
n
n
j. Bob uses his private key to decrypt CK to recover the key K.
k. Bob uses K to decrypt CM to recover the message M.
l. Bob uses Alice’s public key to decrypt her signature S to recover the
hash H.
m. Bob hashes M to create his own version of the hash H.
n. Bob compares for equality his version of the hash H with the version
decrypted from Alice’s signature.
Public Key
Encryption/Decryption Protocols
Start with a letter
s
Convert to a number
19
Encrypt
(
public key
of 3)
39
Decrypt
(
private key
of 27)
19
Convert to a letter
s
Public Key
Encryption/Decryption Protocols
•
Encryption:
n = 55, e = 3, p = 5, q = 11
Let m = 19
•
Decryption:
3d = 1 mod 40
1= (3d) mod 40
d = 27
m =
= 584,064 mod 55
= 19
3
39
55
mod
6859
55
mod
19
3
c
))
1
11
(
)
1
5
mod((
1
3
d
55
mod
)
39
39
39
39
(
55
mod
39
2
8
16
27
55
mod
)
39
36
26
16
(
Digital Signature
•
Author authentication
•
Message authentication

Assures recipients that
the message was not altered in transit (integrity)
•
Backward of Public Key Encryption & Decryption Processes
Use Private Key to encrypt
Public Key to decrypt
Mathematical Background
•
Information Theory: How to convey info.
through number
•
Complexity Theory: How complex it is
Ex) O(n)
•
Number Theory: Find properties, patterns, and
relationships of numbers.
Ex) Prime Test
•
Probability, Statistics: How to make it secure
Number Theory(Why Prime?)
•
Prime Number: 1 and itself as factors
•
When prime numbers are large enough,
they're nearly impossible to factor the prime
numbers into p and q.
Number Theory(Theorems)
•
Fermat’s Little Theorem
if 0<m < p,
p: prime
Then
•
Euler’s Theorem
if n = p
∙ q
p,q : prime
and if 0<m<n<p
Then
1
mod
1
p
m
p
1
mod
)
1
)(
1
(
n
m
q
p
(so
m
n
m
q
p
k
mod
1
)
1
)(
1
(
)
m
m
m
m
m
m
m
k
k
q
p
q
p
k
ed
d
e
1
)
(
)
(
)
1
)(
1
(
1
)
1
)(
1
(
References
•
Bruce Schneier,
APPLIED CRYPTOGRAPHY:
Protocols, Algorithms, and Source Code in C (2
nd
Eds),
John Wiley & Sons, 1996. (ISBN 0

471

12845

7)
•
Bruce Schneier,
SECRETS AND LIES: Digital
Security in a networked world,
John Wiley &
Sons, 2000. (ISBN 0

471

25311

1)
•
H.M. Mel and Doris Baker,
CRYPTOGRAPHY
DECRYPTED,
Addison

Wesley, 2001. (ISBN 0

201

61647

5)
Thank you for your attention.
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