In the world of cryptography, RSA (Rivest–Shamir–Adleman) is a popular public-key cryptosystem widely used for secure data transmission. It’s based on the principle that while multiplying large prime numbers is computationally easy, factoring their product is not — which ensures security.
This post will walk you through how RSA encryption and decryption work using a simple Java program. You’ll learn how the sender encrypts a message using the recipient’s public key, and how the receiver decrypts it using their private key.
What Happens Under the Hood?
The RSA algorithm follows these steps:
Key Generation
Choose two large prime numbers p and q.
Compute N = p * q.
Compute the totient function: phi = (p-1)(q-1).
Choose an integer e such that 1 < e < phi and gcd(e, phi) = 1.
Compute d, the modular inverse of e modulo phi.
Encryption
The sender uses the recipient’s public key (e, N) to compute ciphertext: c = m^e mod N.
Decryption
The recipient uses their private key (d, N) to decrypt: m = c^d mod N.
In classical cryptography, a product cipher is a cipher that applies multiple transformations (substitution and permutation) to secure the plaintext. The goal is to combine the strengths of various techniques to produce a more secure encryption scheme.
In this post, we’ll walk through the basic concept of a product cipher and demonstrate a simple Java program that implements both encryption and decryption using:
Additive Caesar Cipher (a type of substitution cipher)
Transposition Cipher (reordering the characters)
By combining these two, we create a more secure scheme than using either one alone.
What is a Product Cipher?
A product cipher involves multiple rounds or stages of encryption where each stage transforms the message using a different method. Common combinations include:
Substitution followed by transposition
Multiple rounds of substitution and transposition
This layered approach makes it harder to crack using frequency analysis or brute force.
In our Java implementation, we use:
Additive Caesar Cipher: Each character is shifted by a fixed key (k1).
Transposition Cipher: The encrypted text is written row-wise into a matrix and read column-wise using a given number of rows (k2).
In modern cryptography, digital signatures ensure the authenticity and integrity of a message. One of the most widely used techniques for digital signing is based on the RSA algorithm. This post will guide you through the basic concept of how RSA digital signatures work and provide a simple Java implementation to illustrate the signing and verification process.
What is an RSA Digital Signature?
An RSA Digital Signature is a cryptographic method where the sender signs the message using their private key, and the receiver verifies it using the sender’s public key. This ensures:
The message is not altered during transit.
The message truly comes from the claimed sender.
Here’s how it works conceptually:
The sender selects two large prime numbers p and q.
Computes N = p * q and phi = (p - 1)(q - 1).
Chooses a public exponent e such that 1 < e < phi and gcd(e, phi) = 1.
Computes the private keyd = e^(-1) mod phi.
To sign a message m, the sender calculates the signature s = m^d mod N.
To verify, the receiver computes m' = s^e mod N and checks if m' == m.
In modern cryptography, secure key exchange is essential for private communication over public channels. One of the earliest practical implementations of public key exchange is the Diffie-Hellman Key Exchange. This post will guide you through the concept and a simple Java implementation to illustrate how two parties can securely generate a shared secret key.
What is Diffie-Hellman Key Exchange?
The Diffie-Hellman Key Exchange (developed in 1976) is a method that allows two users to exchange cryptographic keys over a public channel securely. The beauty of this method is that both parties can compute the same secret key independently, which can then be used for encrypting future messages.
Here’s how it works conceptually:
Two parties (say, Alice and Bob) agree on a large prime number p and a primitive root g of that number.
Alice chooses a private key x, computes R1 = g^x mod p and sends R1 to Bob.
Bob chooses a private key y, computes R2 = g^y mod p and sends R2 to Alice.
Alice computes the secret key as k1 = R2^x mod p.
Bob computes the secret key as k2 = R1^y mod p.
Both k1 and k2 will be the same due to properties of modular arithmetic: g^(xy) mod p = g^(yx) mod p.
