Project Report
CSE 450/598 Design and Analysis of Algorithms

RSA – Public Key Cryptography Algorithm
(Project Id: P12)

Karthik Karuppaiya
Computer Science Department
Arizona State University
Karthik.k@asu.edu

1. Introduction to Cryptography: 3
1.1 Basic idea of Cryptography: 3
1.2 Basic Terminologies used in Cryptography: 3
1.3 Cryptographic Algorithms: 3
1.4 Two Kinds of Cryptography Systems: 3
2.   Overview of Private Key Cryptography: 4
3. Overview of Public Key Cryptography: 5
4. RSA – Public Key Cryptography Algorithm: 6
4.1 Introduction to RSA Algorithm: 6
4.2 RSA Algorithm: 6
5. Mathematics behind RSA: 7
5.1 Preliminaries: 8
5.2 Finding Prime Numbers and hence the modulus N: 11
6. Computational complexity of the RSA algorithm: 12
7. Primes is in P: 13
7.1 Basic notations: 13
7.2 Algorithm: 14
7.3 Correctness of the Algorithm: 14
7.4 Time Complexity Analysis of the algorithm: 15
8. Comparison of the RSA algorithm with other algorithms: 16
8.1 Comparison with EC algorithm: 16
9. Conclusion: 17
10. References: 18

1. Introduction to Cryptography:

In the era of information technology, the possibility that the information stored in a person’s computer or the information that are being transferred through network of computers or internet being read by other people is very high. This causes a major concern for privacy, identity theft, electronic payments, corporate security, military communications and many others. We need an efficient and simple way of securing the electronic documents from being read or used by people other than who are authorized to do it. Cryptography is a standard way of securing the electronic documents.

1.1 Basic idea of Cryptography:

Basic idea of cryptography is to mumble-jumble the original message into something that is unreadable or to something that... [continues]

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