Cryptography RSA Algorithm RSA Examples

PCIT303: Cryptography and Information Security
Sanjivani Rural Education Society’s
Sanjivani College of Engineering, Kopargaon-423603
(An Autonomous Institute Affiliated to Savitribai Phule Pune University, Pune)
NACC ‘A’ Grade Accredited, ISO 9001:2015 Certified
Department of Information Technology
(UG Programme - NBAAccredited)
Dr. M.A. Jawale
Professor and Head, Dept. of IT

Unit II : Cryptography
 Public Key Cryptosystems,
 Conventional and Public-Key Encryption,
 RSAAlgorithm
 RSA Example
Unit-II: Part-III Cryptography Prof. Dr. Madhuri Jawale Department of Information Technology

Public Key Cryptosystems
 Asymmetric encryption is a form of cryptosystem in which encryption and
decryption are performed using the different keys—one a public key and one a
private key. It is also known as public-key encryption.
 Asymmetric encryption transforms plaintext into ciphertext using a one of two keys
and an encryption algorithm. Using the paired key and a decryption algorithm, the
plaintext is recovered from the ciphertext.
 Asymmetric encryption can be used for confidentiality, authentication, or both.
 The most widely used public-key cryptosystem is RSA. The difficulty of attacking
RSA is based on the difficulty of finding the prime factors of a composite number.

Conventional and Public-Key Encryption,

Public-Key Cryptosystem: Secrecy

Public-Key Cryptosystem: Authentication

Public-Key Cryptosystem: Authentication and Secrecy

RSAAlgorithm

RSA Example
 Select two prime numbers, p = 17 and q = 11
 Calculate n = pq = 17 ×11 = 187
 Calculate f(n) = (p- 1)(q- 1) = 16 ×10 = 160
 Select e such that e is relatively prime to f(n) = 160 and less than f(n); we
choose e = 7
 Determine d such that de = 1 (mod 160) and d < 160.The correct value is d = 23,
because 23 × 7 = 161 = (1 × 160) + 1;
 Public key PU = {7, 187} and Private key PR = {23, 187}.

RSA Example

Reference
1. William Stallings, “Cryptography and Network Security Principles and
Practice”, Fourth Edition, Chapter 9.

Cryptography RSA Algorithm RSA Examples

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