Genetic Algorithm for Fully Homomorphic Encryption Model Analysis

This report delves into a genetic algorithm (GA)-based model for Fully Homomorphic Encryption (FHE). The introduction highlights the importance of security and confidentiality in cloud computing and introduces the use of GAs for enhanced randomness and security in cryptographic systems. The report explains the concept of genetic algorithms, emphasizing their application in key generation for public key cryptography, and discusses the GA operations of selection, crossover, and mutation. Related works explore the use of GAs in public key cryptosystems, key generation, and homomorphic encryption. The FHE model section details key generation using GA, including parameters like generation numbers, population size, and crossover types, followed by the encryption and decryption processes. The analysis and results section evaluates the GA's effectiveness, focusing on execution time for generating a randomized 4096-bit RSA key, and discusses the impact of population size and generation numbers on complexity. The report concludes by emphasizing the GA's role in enhancing security through increased randomness in key generation, crucial for secure cloud computing and other applications.

Summary

Table of Contents
Introduction......................................................................................................................................1
Genetic Algorithm...........................................................................................................................1
Related Works..................................................................................................................................1
FHE Model Using GA Key Generation...........................................................................................2
Analysis & Result............................................................................................................................2

Introduction
The people associated with computing solutions and economic advantages through cloud
computing results into worrying about security & confidentiality of information. It includes OTP
and PRNG to ensure security which used in more innovative manner is known as genetic
algorithm. The present report will focus on genetic algorithm based on generation of fully
homomorphic encryption.
Genetic Algorithm
Genetic algorithm is basically known as randomised search and optimization of algorithm
which has several application and proved as powerful & independent technique. It is helpful to
be applied on cryptosystem which provide strong randomness that hardens the attacking
procedure for ciphertext. However, it provide support to make PKC more secure with the help of
utilising genetic algorithm in appropriate manner. Moreover, it includes the key generating
method for public key cryptography in order to make it highly random and distinctive. In
addition to this, they are helpful in certain ways such as to generate keys, enhance standards
encryption for improving its degree of security and to produce new symmetric or asymmetric
algorithm. Furthermore, it involves three operations regarding generation of population which
includes selection, crossover and mutation. At the other hand, it involves to a working
mechanism involving create initial population, selection, crossover and mutation in respect of
establishing new population accordingly. Finally, the superior complexity is procedure of
generating the key make ciphertext tough for cryptanalyst to decipher.
Related Works
There are various kinds of aspects which are relevant to genetic algorithm and utilise to
conduct several procedure or activities to analyse required results. It can be utilise in field of
security in order to contribute to area of public key cryptosystem (PKC). However, different
researchers and scientist use GA in various research activities or procedure which facilitate to
gain desired outcomes respectively. Initially, it is used in three different tests to analyse the
replication of chromosome which helps to gain an effective and enhanced performance output on
proper manner. Secondly, it is helpful to generate asymmetric key pair for effective encryption
and decryption of message with help of utilising randomness in crossover & mutation processes.
Thirdly, it is also used in autocorrelation test and first encryption scheme is fully homomorphic
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which is based on ideal lattices. Meanwhile, homomorphic encryption can be described as kind
of encryption which permits computation on ciphertexts through creating an encrypted result or
when it get decrypted then matched with operational outcomes as if they had been performed in
plaintext. Furthermore, public key encryption scheme is relied on the “Polynomial Learning with
Errors” (PLWE) assumption through which circular security can be ensured.
FHE Model Using GA Key Generation
This part includes several practical methods which involves the criteria of generating
keys for FHE scheme using a GA procedure, RSA modulo, FHE processes along with analysing
efficiencies of the same. It is basically used for secured outsourced computation including
secured cloud computing services as well as securely chaining together different facilities
without exposing sensitive information respectively. However, the key generation process
through utilising GA mechanism is required to be used in fully homomorphic encryption (FHE)
including desired parameters accordingly. Moreover, it involves number of generations, initial
population size, selection function, crossover type and mutation rate. Meanwhile, after analysing
required parameters, modulo keys creation takes place with help of GA inputs for calculation in
order to find out appropriate result. In addition to this, encryption process needed to gain input
i.e. user should enter message then conversion to ASCII code is performed to start encryption
through utilising modular exponentiation. Furthermore, fully homomorphism includes the
implementation of number of different operators which vary from mathematical to logistics i.e.
addition, multiplication, oring, anding etc. without decryption. Additionally, the final stage is
known as decryption which involves to recover plaintext from encrypted text with help of using
secret vector respectively.
Analysis & Result
From the above summary, it has been analysed that main objective of preferring genetic
algorithm is about to gain maximum randomness for 4096 bits RSA key which facilitate
guaranteeing more security. It includes a very simple manner to evaluate effectiveness of an
algorithm is to analyse execution time for specific size of inputs as per speed of processor.
However, this paper include 10000 iteration with 30 mutations which performed on 64
chromosomes and execution takes place on i3 Dual code processor with 4 GB RAM.
Additionally, the number of generations are 500, 1000, 2000, 5000 and 10000 and the time taken
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for generating final randomized key is 3.5760 milliseconds whereas time is about 75.382
seconds. Finally, huge difference it determined in population size, maximum number of
generations and factor of complexity.
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