May 03, 2025
Plagiarism Scan Report
Characters:4494 Words:656
25% 75%
Plagiarized Unique Speak Time:
Sentences:28
6 Min
11% Exact Matched 14% Partial Matched
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Content Checked for Plagiarism
Plagiarism Scan Report : Discrete Mathematics Project PROJECT NO: 1 A
Project Submitted 1 . in Partial Fulfillment of the Requirements for the Degree
of Bachelor of Technology in CSE/ME/EComE SUBMITTED BY: GROUP NO: 1
Group Members: Chakshit kumar Dhruv Seghal Dhruva Jhanjhari Cheshta
Aggarwal SCHOOL OF ENGINEERING AND TECHNOLOGY BML MUNJAL
UNIVERSITY GURGAON May, 2025 Problem Statement:- The goal of this
project is to research the RSA algorithm, an open-key cryptographic system
developed by Ron Rive, ADI Shamir and Lena Adlman that is in common use.
It is the most fundamental element in ensuring links of the newest digital
systems and safeguarding secret information. This project will consider RSA
theory, mathematical foundations, and real applications, particularly the RSA
digital signature system. It also incorporates a digital signature algorithm in
terms of programming languages like encryption and cryptocurrency of RSA,
e.g., Python, C or C. Introduction:- 2 . RSA is a public-key cryptographic
algorithm widely used by Ron Rivest, Adi Shamir, and Leonard Adleman, who
created it in 1977. It was the first to propose asymmetric encryption, using two
distinct keys-one for encryption (public) and another for decryption (private).
The security of RSA relies on the mathematical hardness of factoring large
prime numbers. It applies principles such as modular arithmetic and Euler's
theorem to encrypt and decrypt information. RSA is critical in contemporary
applications such as digital signatures, secure messaging, and online data
protection. Analytical Solutions:- The basic steps of RSA are as follows: 1. Key
Generation: * Select two large prime numbers, p and q * Compute * Compute
Euler’s Totient Function: * 3 . * Select a public exponent eee such that and e is
coprime with ϕ(n) implies - * Compute the private exponent ddd such that
#calculate d by using hit and trail or either Eulear Euclidean Algorithm *
public key = * private key = 2. Encryption: * The public key is composed of 7 . *
The plaintext message m is encrypted by computing the ciphertext as: 3 .
Decryption: * The private key is composed of * The ciphertext c is decrypted by
computing the plaintext message as: 4 . RSA Digital Signature Scheme: 4 . *
The sender signs a message by computing the signature using their private
key * The receiver verifies the signature by checking EXAMPLE BY TAKING
THE REAL VALUE : Key Generation: Let p=61, q=53 be two prime numbers. *
Compute * Compute * Choose e=17 (which is coprime with 3120). * Compute
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ddd such that) The modular inverse of 17 modulo 3120 is 2753, so d=2753d *
The Public Key is (n=3233,e=17) * THE Private Key is (n=3233,d=2753) Encryption
and Decryption: If the message is m=65 * Encryption: * Decryption: Results of
Simulations: - Python code OUTPUT : Conclusions:- The RSA algorithm is an
imperative factor in facilitating safe digital communication. Its application of
asymmetric keys and reliance on number theory render it both theoretically
fascinating and practically efficient. In the course of this project, we delved
into RSA's history, theoretical basis, and practical applications, particularly in
protecting information and authenticating identities with digital signatures.
By applying a simplified version of RSA in Python, we were able to better
understand how encryption and decryption are done through modular
arithmetic. This practical experience helped solidify how RSA makes
theoretical mathematics a powerful tool for digital security. Overall, this
project showcases both the strength and beauty of RSA in contemporary
cryptography Acknowledgement:- I would like to thank my professors Rishi
Asthana sir and fellow students for their guidance and support. Special
thanks to the open-source community for providing valuable resources that
helped me better understand cryptography and RSA. Reference:- Rivest, R. L.,
Shamir, A., & Adleman, L. (1978). "A Method for Obtaining Digital Signatures
and Public-Key Cryptosystems." Communications of the ACM. 5 . Menezes, A.,
Van Oorschot, P., & Vanstone, S. (1996). "Handbook of Applied Cryptography."
CRC Press. Kaufman, C., Perlman, R., & Speciner, M. (2002). 6 . "Network
Security: Private Communication in a Public World." Prentice Hall.
Sources
4% Plagiarized
It appears in thesis, e.g. "A dissertation submitted in partial satisfaction of the
requirements for the degree Doctor of Philosophy in Mathematics".
https://academia.stackexchange.com/questions/20975/what-does-it-mean-
a-dissertation-submitted-in-partial-satisfaction
4% Plagiarized
Introduced in 1977 by Massachusetts Institute of Technology colleagues Ron
Rivest, Adi Shamir and Leonard Adleman, RSA — its name derived from the
initials of their surnames — is a specific type of public-key cryptography, or
PKC, innovated in 1976 by Whitfield Diffie, Martin Hellman and Ralph Merkle.
https://www.invent.org/inductees/adi-shamir
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Dec 11, 2013 � When choosing the public exponent e, it is stressed that e must
be coprime to ϕ(n), i.e. gcd(ϕ(n),e)=1. I know that a common choice is to have
e�...Missing: eee | Show results with:
https://crypto.stackexchange.com/questions/12255/in-rsa-why-is-it-
important-to-choose-e-so-that-it-is-coprime-to-%25CF%2586n
4% Plagiarized
Mar 30, 2020 � The plaintext, denoted (m) for message, gets encrypted again
and again until finally the corresponding ciphertext (c) of the same length
is�...
Page 2 of 3
https://medium.com/%40emilywilliams_43022/cryptography-101-
symmetric-encryption-444aac6bb7a3
4% Plagiarized
Menezes, A.J., van Oorschot, P.C., & Vanstone, S.A. (1997). Handbook of Applied
Cryptography (1st ed.). CRC Press. https://doi.org/10.1201/9780429466335
https%3A%2F%2Fwww.taylorfrancis.com%2Fbooks%2Fmono%2F10.1201%2F
9780429466335%2Fhandbook%2Dapplied%2Dcryptography%2Dalfred%2D
menezes%2Dkenneth%2Drosen%2Dscott%2Dvanstone%2Dpaul%2Dvan%2
Doorschot
4% Plagiarized
Kaufman, C., Perlman, R. and Speciner, M. (2002) Network Security Private
Communication in a Public World. Prentice Hall PTR, Upper Saddle River.
https://www.scirp.org/reference/referencespapers%3Freferenceid%3D13157
77
4% Plagiarized
Mar 30, 2020 � The plaintext, denoted (m) for message, gets encrypted again
and again until finally the corresponding ciphertext (c) of the same length
is�...
https://medium.com/%40emilywilliams_43022/cryptography-101-
symmetric-encryption-444aac6bb7a3
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