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J2T Crypto
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How does RSA Key work?


RSA, one of the classification methods, may not be the most secure due to its development over 40 years ago. Despite advancements in security technology, RSA is still in use today, particularly for transmitting classified keys. So, what exactly is RSA, and how does it work?

How Does RSA Work, and Who Invented It?

The RSA algorithm was developed in 1977, named after its creators: Rivest, Shamir, and Adleman, represented by the acronym ‘RSA’. This naming approach highlights their contributions to this coding technology.

Despite RSA’s official inception in 1977, the foundation of the system was laid by English mathematician Clifford Cocks in 1973. Initially, Cocks’ algorithm was used exclusively by classified individuals, and the technology was not available to the general public.

How Does the RSA Algorithm Work?

The RSA algorithm operates by generating keys. A user creates a public key based on two large prime numbers and auxiliary values. The security of the message depends on the key length; longer keys are more complex and harder to decipher.

The encryption process involves three steps:

  1. Preparation: Generating both official (private) and open (public) keys.

  2. Encryption: Using the open (public) key generated in the preparation step.

  3. Decryption: Utilizing the official (private) key to decipher the encrypted message.

Rivest-Shamir-Adleman, a type of encryption, provides adequate security by increasing key length, though this can slow down other operations. Designed for straightforward tasks, it’s not ideal for high-security needs.

Over time, the RSA algorithm has been extensively studied, revealing limitations in efficiency and security. The time it takes to encrypt and decrypt using RSA is a notable drawback.

RSA is commonly used for transmitting shared access codes in an encrypted form. It allows a symmetric key, used for encrypting and decrypting large amounts of data, to be securely sent to its recipient.

Asymmetric keys, thanks to the innovations of Diffie and Hellman in 1976, are now widespread in cryptography. However, their concept couldn’t be fully utilized initially due to incomplete understanding of factorization principles.

The development was advanced by a trio of programmers who refined the one-way function mechanism, increasing the difficulty of decoding. The asymmetric encryption system they developed, known for its decoding complexity, later became known as RSA.

How RSA Works in Digital Signatures

The rise of electronic documents necessitated the development of digital signatures for official recognition. A digital signature is essentially data transformed into cryptographic language, ensuring confidentiality and security.

In RSA-based digital signatures, numerical encryption and the Rivest-Shamir-Adleman algorithm are inseparably linked, as the former relies on the latter for its operation. There are two key types in cyberspace: private (inofficial) and public (open). The private key is confidential, used for data protection, while the public key is accessible to all users.

With RSA encryption, a document is encrypted and remains accessible. The signature’s decryption for verification uses a private key, allowing access to the certified document via the public key.

Speed of Operation

RSA operations involve exponentiation (repeated multiplication). For practicality, the public key is often raised to a small exponent. It’s common for groups to use the same exponent with different moduli, enhancing the speed of decryption and verification compared to encryption and signing.

The operation’s speed can be measured in terms of a conditional unit ‘k’, representing the number of bits:

To accelerate RSA procedures, new methods like ‘fast multiplication’ are continually explored. Fast Fourier Transform (FFT) hasn’t become mainstream due to its complex software requirements and the need for uniform key sizes for efficient operation.


1. RSA Algorithm in Daily Life

The Rivest-Shamir-Adleman (RSA) system is widely used in various commercial products, with its application continually expanding. Companies like Microsoft, Apple, Sun, and Novell implement it, as do many operating systems. RSA is also found in secure phones, smart cards, and crypto hardware.

2. Main Advantage of RSA

The key strength of RSA lies in its public key system; knowing the public key alone does not enable one to decrypt the encoded message. The PGP encryption program operates on the RSA algorithm, integrated into hash functions.

3. Impact of Knowing the Encoded Session Key’s Length

If an intruder knows the length of the encoded session key, it could potentially compromise the security, increasing the chance of breaking the private encryption key, given the public key and the encrypted message.

4. Current Popularity of Rivest-Shamir-Adleman

Despite being an older technology, RSA remains relevant and widely used today.

5. Creation of RSA

The RSA algorithm was invented over 45 years ago, in 1977.

6. RSA in Cryptography

In RSA cryptography, each participant has both private and public keys. The keys are a pair of integers. Participants generate a private key (private + public) and keep the private key secret, while the public keys can be shared openly. In RSA, each participant’s private and public keys form a ‘matched pair,’ meaning they are mutually reciprocal.

7. Difference Between DSA and RSA

RSA can be used both for digital signatures and encryption by altering the order of component usage, with its encryption/decryption process being commutative.

8. Advantages of ECC Over RSA

ECC (Elliptic Curve Cryptography) offers several benefits over RSA, including stronger resistance to attacks, lower CPU and memory usage, reduced network consumption, and faster encryption.

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