2. Virtualization
Making a virtual image or version
Server
Operating System
Network Devices
It manage Workload
It reduces hardware utilization
saves energy and costs
It possible to run multiple applications and various operating systems on the same
SERVER at the same time.
3. Need virtualization
Isolation Among Users
• One user should be isolated from the other users so that he/she may not get information about
the others user’s data and usage and cannot even access other’s data.
Resource Sharing
• A big resource can be fragmented into multiple virtual resources so that it can be used by
multiple users using virtualization technique.
Dynamical Resources
• Reallocation of resources such as storage and computational resources is very difficult but if
they are virtualized then they can be easily re-allocated.
Aggregation of Resources
• The small resources available can be increased at a large extent with the help of virtualization
4. Hypervisor
Virtualization Manager
Allows multiple operating systems to
share a single hardware host.
Each guest operating system appears
to have the host's processor, memory,
and other resources all to itself.
Controlling the host processor and
resources.
7. Definition
Homomorphism
A transformation of one set into another that preserves in the second set the relations between
elements of the first.
Homomorphic Encryption
An operation performed on a set of ciphertexts such that decrypting the result of the operation is
the same as the result of some operation performed on the plaintexts
8. Why Homomorphic Encryption?
Confidentiality problems
Ability to compute over ciphertext instead of plaintext
One could use information without knowing the content of that information
Privacy guaranteed
10. Definition: A crypto-system that allows another party to perform operations on cipher
text (Encrypted Text) without having knowledge of your secret key/Password.
So if X1 and X2 are two numbers , E(X1) and E(X2) represents the encryption of these
numbers with a secret key, another party would be able to compute E(X1 + X2) or
E(X1 * X2) without knowing the secret key.
11. Types of Homomorphic System
1. PHE (Partially Homomorphic Encryption)
2. FHE (Fully Homomorphic Encryption)
Plenty of encryption schemes allow partial Homomorphic encryption which let users
perform some mathematical functions on encrypted data, but not others.
A feasible FHE Has not been developed yet.
12. Partially Homomorphic Encryption
When You can only perform certain mathematical operations on the cipher text but not
others.
• RSA Cryptosystem is Partially Homomorphic with respect to Multiplication.
• Caesar Cipher is Partially Homomorphic With respect to addition.
13. How It Works !
Suppose I have a file with my phone number
Message = [9, 0, 2, 6, 7, 2, 8, 1, 6, 8]
And I encrypt it with Caesar cipher* by adding 2 to each digit, Key = 2
Cipher = [11, 2, 4, 8, 9, 4, 10, 3, 8, 10]
Want to find the sum of all the numbers in Message.
Sum up all the elements of Cipher and give the encrypted result. Summation(Cipher) = 69
Summation(Message) = 49
Remove Encryption on Summation(Cipher)
= 69 – 10*2
= 49
This Is partially Homomorphic for only addition and subtraction.
14.
15. How It Works !
RSA Cryptosystem : basic RSA scheme is partially Homomorphic, it allows
multiplication but not addition on cipher text.
If we denote encrypted form of message x as
Then with encryption key pair (m, e) and encrypted message is
Then this property proves RSA is partially Homomorphic
16. Fully Homomorphic Encryption
Plaintext and Ciphertext are both in 𝑧2 ring
Function E in homomorphic for both addition and multipication if;
E(x) + E(y) = E(x + y)
E(x) * E(y) = E(x * y)
