Encryption obscures information to authorize access while hiding it from others. Private key encryption uses a shared key while public key encryption uses separate keys for encryption and decryption. Digital signatures authenticate information through encryption with a private key. Key management creates, distributes, certifies, protects, and revokes keys, while hierarchical and web of trust models establish trust in encryption systems.

1. Lesson 12-Encryption

2. Overview
Understand basic encryption concepts.
Understand private key encryption.
Understand public key encryption.
Understand digital signatures.
Understand key management.
Understand trust in the system.

3. Understand Basic Encryption
Concepts
Encryption is simply the obfuscation of information in such
a way so as to allow authorized individuals to see it, but to
hide it from unauthorized individuals.
Individuals having the appropriate key to decrypt the
information are defined as authorized.

4. Understand Basic Encryption
Concepts
Security Services with encryption:
Confidentiality: Used to hide information from unauthorized
individuals, either in transit or in storage.
Integrity: Used to identify changes to information either in
transit or in storage.
Accountability: Used to authenticate the origin of information
and prevent the origin of information from repudiating the fact
that the information came from that origin.

5. Understand Basic Encryption
Concepts
Encryption terms:
Plaintex
Ciphertex
Algorithm
Key
Encryption

6. Understand Basic Encryption
Concepts
Encryption terms (continued):
Decryption
Cryptography
Cryptographer
Cryptanalysis
Cryptanalyst

7. Understand Basic Encryption
Concepts
Encryption systems can be attacked in three ways:
Through weaknesses in the algorithm.
Through brute force against the key.
Through weaknesses in the surrounding system.

8. Understand Private Key
Encryption
Private key encryption:
Requires all parties who are authorized to read the information
to have the same key.
Reduces the overall problem of protecting the information to
one of protecting the key.
Is the most widely used encryption.

9. Understand Private Key
Encryption
What is private key encryption?
Substitution ciphers.
One-time pads.
Triple DES.
Data encryption standard.
Password encryption.

10. What is Private Key
Encryption?
Private key encryption is also known as symmetric key
encryption because it uses the same key to encrypt
information as is needed to decrypt.
Private key encryption provides for the confidentiality of the
information while it is encrypted.
Only those who know the key can decrypt the message.

11. What is Private Key
Encryption?
Private key algorithm

12. Substitution Ciphers
Julius Caesar used a K is the key to the cipher.
substitution cipher called the
Ex. K = 3
Caesar cipher. UNIVERSITY
This cipher consists of replacing ↓
XQLYHUVLWB
each letter with the letter three
positions later in the alphabet.

13. Substitution Ciphers
Substitution ciphers suffer from one primary weakness—the
frequency of the letters in the original alphabet does not
change.
Further development of frequency analysis also shows that
certain two- and three-letter combinations show up
frequently.

14. One Time Pads
The One Time Pads (OTPs) system is the only theoretically
unbreakable encryption system.
An OTP is a list of numbers, in a completely random order.
It is used to encode a message.
As its name implies, the OTP is only used once.
OTPs are used (but only for short messages) in very high-
security environments.

15. Data Encryption Standard
The algorithm for the Data Encryption Standard (DES) was
developed by IBM in the early 1970s.
DES uses a 56-bit key. The key uses 7 bits of eight 8-bit
bytes (the 8th bit of each byte is used for parity).
DES is a block cipher that operates on one 64-bit block of
plaintext at a time.
There are 16 rounds of encryption in DES, where each
round uses a different subkey.

16. Data Encryption Standard
DES Block Diagram

17. Data Encryption Standard
There are four modes of operation for DES:
1. Electronic code book.
2. Cipher block chaining.
3. Cipher feedback.
4. Output feedback.

18. ECB

19. CBC

20. CFB Encryption

21. CFB Decryption

22. OFB Encryption

23. OFB Decryption

24. Triple DES
Triple DES functional Diagram

25. Password Encryption
The standard Unix password encryption scheme is a variation of
DES. The password encryption function is actually a one-way
function.
Each user chooses a password. The algorithm uses the first eight
characters of the password.
The system then chooses a 12-bit number based on the system
time. This is called the salt.
Most Unix systems now offer the option of using shadow password
files for just this reason.

26. The Advanced Encryption
Standard: Rijndael
At the end of 2000, NIST announced that Joan Daemen and
Vincent Rijmen, cryptographers from Belgium, had won the
competition with their algorithm Rijndael.
Rijndael is a block cipher that uses keys and blocks of 128,
192, or 256 bits. These key lengths make brute-force
attacks computationally infeasible at this time.
The algorithm consists of 10 to 14 rounds, depending on
the size of the plaintext block and the size of the key.

27. Other Private Key Algorithms
There are several other private key algorithms available in
various security systems. Among them are the following:
The International Data Encryption Algorithm (IDEA) was
developed in Switzerland. IDEA uses a 128-bit key and is also
used in Pretty Good Privacy (PGP).
RC5 was developed by Ron Rivest at MIT. It allows for variable
length keys.

28. Other Private Key Algorithms
Private key algorithms (continued):
Skipjack was developed by the United States government for
use with the Clipper Chip. It uses an 80-bit key, which may be
marginal in the near future.
Blowfish allows for variable length keys up to 448 bits and was
optimized for execution on 32-bit processors.

29. Understand Public Key
Encryption
Public Key encryption is a more recent invention than
private key encryption.
The primary difference between the two types of encryption
is the number of keys used in the operation.
The private key encryption uses a single key to both,
encrypt and decrypt information.
The public key encryption uses two keys. One key is used
to encrypt information and a different key, to decrypt it.

30. Understand Public Key
Encryption
What is public key encryption?
Diffe-Hellman key exchange.
RSA.

31. What is Public Key Encryption
The public key is published with information as to who is
the owner.
Another property of public key encryption is that if you
have one of the keys of a pair, you cannot compute the
other key.
If confidentiality is desired, encryption is performed with
the public key.

32. What is Public Key Encryption
Public key encryption

33. Diffe-Hellman Key Exchange
The Diffe-Hellman key exchange was developed to solve
the problem of key distribution for private key encryption
systems.
The idea was to allow a secure method of agreeing on a
private key without the expense of sending the key through
another method.

34. 最早的公開金鑰加密法之一
Diffie-Hellman Protocol
1. A and B 同意共用兩個大整數 g 、 n, g < n
2. A選擇一個極大隨機亂數 x
R = g x mod n
3. B選擇一個極大的隨機亂數 y , 並且計算
S = g y mod n
4. A和B交換R ,S
5. A計算 K = Sx mod n =(gy mod n)x mod n
6. B計算 K = Ry mod n =(gx mod n)y mod n
K=K'
以上即使R,S在傳送過程中遭竊聽,只要x,y仍保密則K仍不易計算
得到

35. RSA
In 1978, Ron Rivest, Adi Shamir, and
Len Adleman released the Rivest-
Shamir-Adleman (RSA) public key
algorithm.
Unlike the Diffe-Hellman algorithm,
RSA can be used for encryption and
decryption.
Also unlike Diffe-Hellman, the security
of RSA is based on the difficulty of
factoring large numbers.

36. 最有名的公開金鑰演算法
-RSA Algorithm
a block cipher in which the plaintext and ciphertext are
integers between 0 and n-1 for some n.
Given:
public key= (e,n)
private key= (d,n)
C= M e mod n
M= Cd mod n =(Me)d mod n =Med mod n
其中
n=p*q, p,q皆為極大的質數
e和d的關係為先選e值使得gcd(ψ(n), e)=1, ψ(n)為小於n且和n互質
的數目的個數（稱為尤拉函數）﹐然後再選取d使得d=e-1 modψ(n)
（亦即e*d modψ(n) = 1）
2002 ACM Turing Award

37. RSA Algorithm例子
1. 選p=7, q=17
2. 計算n=p q=7*17=119
3. 計算ψ(n)=(p-1)(q-1)=96
4. 選擇e=5﹐然後計算d=77 (因為5*77 mod 96 =1)
如此得到公開密鑰=(5,119), 私人密鑰=(77,119)
假設有一訊息M=19要傳送﹐則
加密： C=195 mod 119 == 66 mod 119
解密： M=6677 mod 119 = 19 mod 119

38. 到底RSA有多難破解？
1977八月號 Scientific American雜誌(RSA129挑戰 4 * 1015)
n=1 1438 1625 7578 8886 7669 2357 7997 6146 6120 1021 8296
7212 4236 2562 5618 4293 5706 9352 4573 3897 8305 9712 3563
9587 0505 8989 0751 4759 9290 0268 7954 3541
e=9007
C=9686 9613 7546 2206 1477 1409 2225 4355 8829 0575 9991 1245
7431 9874 6951 2093
0816 2982 2514 5708 3569 3147 6622 8839 8962 8013 3919 9055
1829 9451 5781 5154
（已知明文中00=空白﹐01=A 02=B, …）
1994, 600人，1600部機器，耗費八個月
p=3490 5295 1084 7650 9491 4784 9619 9038 9813 3417 7646
3849 3387 8439 9082 0577
q=3 2769 1329 9326 6709 5499 6198 8190 8344 6141 3177 6429
6799 2942 5397 9828 8533
得到M= SQUEAMISH OSSIFRAGE

39. RSA
The basic algorithm for confidentiality is very simple:
ciphertext = (plaintext)e mod n
plaintext = (ciphertext)d mod n
private key = {d, n}
public key = {e, n}
The difficulty in calculating d given e and n provides the
security.

40. Generating RSA keys
To generate an RSA key pair, follow these steps:
Choose two prime numbers p and q and keep them secret.
Calculate n = pq.
Calculate φ(n) = (p – 1)(q – 1).
Select e such that e is relatively prime to φ(n).
Determine d such that (d)(e) = 1 mod φ(n) and that d < φ(n).

41. Understand Digital Signatures
Digital signature is a method of authenticating electronic
information using encryption.
Digital signatures protect information from modification after it
has been received and decrypted.
Digital signatures put information through a hash function to
create a checksum that is encrypted with a private key and
travels with the information.
This checksum can be used to verify that the information was not
modified.

42. Understand Digital Signatures
The security and usefulness of a digital signature depend on
the protection of the user’s private key and a secure hash
function.
A hash function is secure if:
the function is one-way, and
it is difficult to construct two pieces of information that provide
the same checksum when run through the function.

43. Understand Digital Signatures
Secure hash functions should create a checksum of at least
128 bits.
The two most common hash functions are MD5 and SHA.

44. Understand Digital Signatures
Digital Signature operation

45. Understand Key Management
Key management is one of the most critical aspects of an
encryption system.
It includes creating strong keys, distributing them securely,
certifying them correct, protecting while in use, and
revoking them when they are compromised or expired.
Most encryption systems have a method for users to
generate keys—in many cases, the user chooses a
password.

46. Understand Key Management
Keys must be transported securely to ensure the integrity
of the keys.
If keys are transmitted, they must be checked on arrival to
ensure they have not been manipulated (usually done
manually or by digital signatures).

47. Understand Key Management
Certificate Authorities (CAs) ensure the integrity of the keys
and prevent an attacker from introducing their own keys.
Public keys require integrity protection (provided by
certification), but they do not require confidentiality
protection. However, all copies of the private key of a
public key system must be protected at all times.

48. Understand Key Management
Session keys may only exist for a given session and may be
deleted after the session.
Public key pairs are generally certified for one or two years.
If a key is lost or compromised, the owner of the key
should inform users that it is not to be used.
In the case of a public key encryption system, the owner
must post the revocation to all of the potential key servers.

49. Understand trust in the
System
Trust is the underlying concept of all security and
encryption.
There are two primary models that are used for trust:
Hierarchical trust
Web of trust

50. Understand trust in the
System
The Hierarchical Trust model is based on a chain of
authority, in which you trust someone if someone higher up
in the chain certifies it.
The Hierarchical Trust model is complicated to put into
practice because there is no real root-level CA.
Establishing an internal CA and public key infrastructure for
a business is a challenging task that demands a lot of
resources.

51. Understand trust in the
System
The Web of Trust model was first used by Pretty Good
Privacy (PGP).
It is based on the concept that each user certifies their own
certificate and passes that certificate off to known
associates.
The primary advantage is that there is no large investment
in infrastructure.
The primary disadvantage is a lack of scalability.

52. Summary
Encryption is simply the obfuscation of information in such
a way so as to allow authorized individuals to see it, but to
hide it from unauthorized individuals.
The Private Key encryption requires all parties authorized to
read the information to have the same key.
The Public Key encryption uses two keys. One key is used
to encrypt information and another key is used to decrypt it.

53. Summary
A digital signature is a method of authenticating electronic
information using encryption.
Key Management includes creating strong keys, distributing
them securely, certifying that they are correct, protecting
them while they are in use, and revoking them when they
are compromised or expired.
There are two primary models that are used for trust:
Hierarchical Trust and Web of Trust.