Questions and Answers
What is the primary principle behind RSA cryptography?
What is the purpose of the public key in RSA?
What is the output of the encryption process in RSA?
What is the role of the padding scheme in RSA?
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What is the decryption process in RSA?
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What is the relationship between 'n' in the public and private keys?
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What is the security aspect of RSA relying on?
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What is the output of the decryption process in RSA?
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What is the role of the private key in RSA?
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What is the significance of the condition gcd(e, φ(n)) = 1
in the RSA key generation process?
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How does the modulus n
relate to the prime numbers p
and q
in the RSA key generation process?
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What is the purpose of the Euler's totient function φ(n)
in the RSA key generation process?
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What is the mathematical operation used to encrypt a message m
in the RSA encryption process?
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What is the range of values that the ciphertext c
can take in the RSA encryption process?
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How does the decryption process in RSA recover the original message m
from the ciphertext c
?
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What is the relationship between the public exponent e
and the private exponent d
in the RSA key pair?
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Why is it necessary to convert the message m
into a numerical value before encryption in the RSA algorithm?
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Study Notes
RSA Cryptography: Encryption and Decryption
Overview
 RSA (RivestShamirAdleman) is an asymmetric encryption algorithm used for secure data transmission.
 It's based on the principle of prime factorization, which makes it computationally infeasible to factorize large composite numbers.
Key Components
 Public Key (e, n): A pair of integers, where 'e' is the public exponent and 'n' is the modulus (product of two large prime numbers, p and q).
 Private Key (d, n): A pair of integers, where 'd' is the private exponent and 'n' is the modulus (same as public key).
Encryption

Encryption Process:
 Convert plaintext message (M) to a numerical value (m) using a padding scheme (e.g., PKCS#1).
 Compute the ciphertext (c) using the public key: c = m^e mod n.
 Example: If M = "Hello", m = 123456789 (after padding), e = 17, and n = 3233, then c = 123456789^17 mod 3233.
Decryption

Decryption Process:
 Compute the plaintext (m) using the private key: m = c^d mod n.
 Convert the numerical value (m) back to the original plaintext message (M) using the padding scheme.
 Example: If c = 2819 (from encryption), d = 2753, and n = 3233, then m = 2819^2753 mod 3233 = 123456789, and M = "Hello".
Security Aspect
 RSA's security relies on the difficulty of factoring large composite numbers (n) into their prime factors (p and q).
 Given the public key (e, n), it's computationally infeasible to determine the private key (d, n) without knowing the prime factors (p and q).
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Description
Understand the basics of RSA cryptography, including key components, encryption and decryption processes, and the security aspect of this asymmetric encryption algorithm.