Kriptografi Algoritma RSA #kriptografi #kriptografialgoritma

Summary

This tutorial provides an in-depth explanation of the RSA encryption algorithm, covering its history, key generation, and both encryption and decryption processes. Developed by Rivest, Shamir, and Adleman, RSA relies on the difficulty of factoring large composite numbers to ensure security. The video walks through practical examples, demonstrating how to generate keys, encrypt and decrypt messages using modular arithmetic. Ideal for anyone looking to understand RSA, from the theoretical background to step-by-step execution in cryptographic applications.

Takeaways

• 😀 RSA is a widely used public-key encryption algorithm, developed by Ron Rivest, Adi Shamir, and Leonard Adleman in 1977.
• 😀 The strength of RSA encryption lies in the difficulty of factoring large composite numbers into prime factors, which is computationally challenging.
• 😀 RSA involves the use of two keys: a public key for encryption and a private key for decryption. These keys are mathematically related but cannot be derived from one another easily.
• 😀 The process of generating RSA keys starts by choosing two large prime numbers, P and Q, and computing the modulus N as their product (N = P * Q).
• 😀 The next step is to calculate Euler's totient function (Teta N), which is used to generate the public and private keys for encryption and decryption.
• 😀 The public key (E) is chosen such that it is relatively prime to Teta N. The private key (D) is then computed as the modular inverse of E modulo Teta N.
• 😀 RSA encryption is done by raising the plaintext message to the power of E and taking the modulus N to produce the ciphertext.
• 😀 Decryption is the reverse process: the ciphertext is raised to the power of D and then the modulus N is applied to recover the original plaintext message.
• 😀 The key size in RSA is typically 1024 or 2048 bits, and the modulus N is kept secret, while the public key E can be shared with anyone.
• 😀 RSA's security depends on the difficulty of factoring large numbers. For secure RSA encryption, the values of P and Q must be sufficiently large, and the difference between them must be significant to make factorization difficult.

Q & A

What is the main concept behind RSA encryption?

The main concept behind RSA encryption is that it relies on the difficulty of factoring large composite numbers into prime factors. The algorithm uses two keys: a public key for encryption and a private key for decryption, ensuring secure communication.

Who developed the RSA algorithm and when was it first published?

The RSA algorithm was developed by Ron Rivest, Adi Shamir, and Leonard Adleman in 1977, and it was first published in 1978.

What is the significance of the modulus 'n' in the RSA algorithm?

In RSA, 'n' is the modulus used for both encryption and decryption operations. It is the product of two prime numbers (P and Q), and its size determines the security level of the encryption. For example, a 1024-bit key means n is a 1024-bit integer.

How is the public key in RSA encryption calculated?

The public key in RSA is composed of two values: 'e' (the public exponent) and 'n' (the modulus). The value of 'e' is chosen such that it is relatively prime to the totient of 'n' (denoted as TT(n)), which is calculated as (P-1)*(Q-1) where P and Q are prime numbers.

What is the role of the private key in RSA?

The private key in RSA consists of the value 'd', which is the modular multiplicative inverse of 'e' modulo TT(n). The private key is used for decryption, ensuring that only the intended recipient, who knows 'd', can decrypt the ciphertext.

Can you explain the process of key generation in RSA?

Key generation in RSA involves selecting two large prime numbers, P and Q, then calculating 'n' as the product of P and Q. After calculating TT(n) (the totient), a public exponent 'e' is chosen that is relatively prime to TT(n), and finally, the private exponent 'd' is computed as the modular inverse of 'e' modulo TT(n).

What is the encryption process in RSA?

In RSA, the encryption process involves taking the plaintext message (represented as an integer 'P'), raising it to the power of the public exponent 'e', and taking the result modulo 'n'. The ciphertext 'C' is given by C = P^e mod n.

How is decryption performed in RSA?

Decryption in RSA involves taking the ciphertext 'C', raising it to the power of the private exponent 'd', and taking the result modulo 'n'. The decrypted message 'P' is given by P = C^d mod n.

What is the significance of choosing 'e' in RSA encryption?

The value of 'e' in RSA is chosen such that it is relatively prime to TT(n) (the totient of n), ensuring that there is a modular inverse 'd' that satisfies the equation e * d ≡ 1 mod TT(n). A common choice for 'e' is 65537 because it is a large prime and provides efficient encryption.

How are large values of n handled in RSA encryption and decryption?

In RSA encryption and decryption, large values of 'n' are handled by using modular exponentiation. This allows for efficient computation even with large numbers, as direct exponentiation is impractical for very large values.