17 Questions
What is the primary principle behind RSA cryptography?
Prime factorization
What is the purpose of the public key in RSA?
To encrypt the plaintext
What is the output of the encryption process in RSA?
Ciphertext
What is the role of the padding scheme in RSA?
To convert plaintext to numerical values
What is the decryption process in RSA?
Computing the plaintext using the private key
What is the relationship between 'n' in the public and private keys?
They are the same
What is the security aspect of RSA relying on?
Difficulty of factoring large composite numbers
What is the output of the decryption process in RSA?
Plaintext message
What is the role of the private key in RSA?
To decrypt the ciphertext
What is the significance of the condition gcd(e, φ(n)) = 1 in the RSA key generation process?
It ensures that e and φ(n) are coprime, guaranteeing that d can be computed such that d * e ≡ 1 (mod φ(n))
How does the modulus n relate to the prime numbers p and q in the RSA key generation process?
The modulus n is the product of the two prime numbers p and q, i.e., n = p * q
What is the purpose of the Euler's totient function φ(n) in the RSA key generation process?
It is used to compute the public exponent e and the private exponent d
What is the mathematical operation used to encrypt a message m in the RSA encryption process?
The encryption formula is c = m^e (mod n)
What is the range of values that the ciphertext c can take in the RSA encryption process?
The ciphertext c is a number between 0 and n-1
How does the decryption process in RSA recover the original message m from the ciphertext c?
The decryption formula is m = c^d (mod n)
What is the relationship between the public exponent e and the private exponent d in the RSA key pair?
They satisfy the equation d * e ≡ 1 (mod φ(n))
Why is it necessary to convert the message m into a numerical value before encryption in the RSA algorithm?
To enable the mathematical operations required for encryption and decryption
Study Notes
RSA Cryptography: Encryption and Decryption
Overview
- RSA (Rivest-Shamir-Adleman) 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).
Understand the basics of RSA cryptography, including key components, encryption and decryption processes, and the security aspect of this asymmetric encryption algorithm.
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