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Table of contents
About RSA
Applications, Predictions and Hardware Implementation
RSA Key Generation
RSA Encryption/Decryption Mechanics
Frequently Asked Questions
Where is RSA being implemented in current date?
What is the full form of RSA in cryptography?
What is the encryption type used in the RSA algorithm?
Last Updated: Mar 27, 2024

Let’s Implement the RSA

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Securing data is a must at this line in time. We all know that there are many ways how cryptosystems work, and we will look at a very known one today. Let us read about the implementation of RSA.

Let’s Implement the RSA

About RSA

RSA (Rivest-Shamir-Adleman) is a popular public-key cryptosystem for secure data transmission. It is also among the oldest. The abbreviation "RSA" is derived from the surnames of three cryptographers, Ron Rivest, Adi Shamir, and Leonard Adleman, who published the method in 1977. In 1973, the Government Communications Headquarters surreptitiously built an equivalent system (GCHQ). This is the British intelligence agency for signals. Clifford Cocks, an English mathematician.

In 1997, that system was declassified. The encryption key of a public-key cryptosystem is public and separate from the decryption key, which is kept secret (private). An RSA user generates and distributes a public key comprised of two huge prime integers plus an auxiliary value. The prime numbers are not revealed. Messages can be encrypted by anyone using the public key, but only those who know the prime numbers can decode them.

The practical difficulty of factoring the product of two huge prime numbers, known as the "factoring issue," underpins RSA's security. The RSA issue is the process of breaking RSA encryption. It is unclear whether it is as complex as the factoring problem.

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The standard method of ensuring a message's privacy is encryption. It ensures that no intruder can break the ciphertext, which is just white noise. However, without property (d), an encryption procedure, such as the NBS standard, is still not a public key. It necessitates that keys be delivered privately via another secure courier," which is an added step that would render NBS, for example, slow, inefficient, and possibly expensive. As a result, RSA is an excellent solution to this problem.

The NBS standard may be beneficial only if it employs a quicker algorithm than RSA. With RSA being used only to securely transmit keys. As a result, an efficient D computing mechanism must be developed in order to make RSA totally self-contained and reliable. To be trustworthy, it would have to employ simple arithmetic. It is easier to compute (a condition of the property (c)) on a general-purpose computer than bit operations, which need better hardware and may be superior to NBS.

Applications, Predictions and Hardware Implementation

This also has implications for electronic fund transfers. Financial data must be kept safe, and checks can be digitally certified using RSA. Additional safeguards, such as implementing special check numbers that permit a check with this specific number to be transmitted/cashed only once, would be required.

In fact, such a system can be applied to any electrical system that requires the implementation of a cryptosystem. The developers of RSA predicted in their 1978 paper that a secure email world would emerge and that RSA would be used to encrypt a real-time telephone call. Because of RSA, these items are now a part of more than just everyday life.

The encryption device should not act as a direct buffer between the terminal and the communications channel. Rather, it should be a hardware subroutine that may be run as needed. This is because it may need to be encrypted/decrypted with many key sequences to ensure better privacy and/or higher signatures.

RSA Key Generation

It is critical to generate cryptographic keys. If the integrity of a cryptographic system is dependent on the security of keys, then it is obvious that care must be given when generating keys. Cryptographic keys must be as randomised as possible in order to be impossible to copy or predict. As a result, a reliable generator of random numbers is needed.

Let e and d be two integers satisfying (e)(d) = 1 (modφ(N)), where φ (N) = m = (p-1) (q-1) = N+1-(p+1) is the Euler φ-function of N, equal to the 1<1<N that are relatively prime to N.

The integers N,e, and d are referred to as the RSA modulus and the encryption exponent, respectively. Two digits are crucial. The RSA modulus, N = (p)(q), is a component of both pairings. The first pair is (N,d). This is known as the RSA private key.

The second pair is known as the RSA public key (N,e). The RSA private exponent is represented by the integer d. The RSA public exponent is denoted by the letter e. We publish or otherwise make the public key available. We keep the private key (specifically d) and the original prime numbers (p and q) safe. To obtain a certificate for the public key (N,e), one typically transmits it to a certificate authority (CA).

RSA Encryption/Decryption Mechanics

The RSA encryption algorithm starts with the selection of two large primes, p and q, at random and independently. Let's use p = 773 and q = 557 for simplicity. The following step is to determine N = (773)(557) = 430561. Next, an integer e is chosen between 3 and N-1 (inclusive) that has no factors in common with (p-1) (q-1). m = (773-1)(557) = 429232 in this case. The prime factorisation of the number 429232 is 24139193. Consequently, e cannot be a multiple of 2,139 or 193.


We are not required by the algorithm to choose a prime number for e. For example, 83 or 95 would work. Let us use e = 5 to keep the numbers short and easy. (It should be noted that the public exponent can be as low as e = 3).

The algorithm then needs an integer d, commonly known as the decryption key. This is so that (d)(e) = 1. (mod m). The optimisation that consists of first determining the hidden exponent d and then finding the public exponent e can be employed. However, d must be chosen at random. If the value of d is too tiny, there are known attacks that can factor in the modulus. A prudent or conservative approach would be to choose d at random from a range of at least N1/2. This is between its maximum and minimum values. In practice, picking d uniformly from the range [3, N] has a negligible chance of yielding a usable or exploitable value.

For security reasons, d should never be less than N. Wiener demonstrated that if d is less than n/4, or more precisely, d1/3 N1/4, an unauthorised individual who just knows the public key can compute d very efficiently. Thus, it is recommended that communicating partners always select d with greater than n/2 bits. It is preferred that d should have n-bits. However, Bob can most likely get away with a modest public exponent e (that is needed for message encryption and signature verification). In fact, the majority of RSA implementations utilise e = 3 or e = 1216+1 = 65537. However, when e is small, a flaw can be seen.


This problem can be overcome by padding messages or inserting a short series of random symbols into message units before transmitting them. In that situation, the recipient can simply erase the extra symbols before reading the text. Of course, each time Bob sends a message, a new random sequence must be entered.

Moreover, for the sake of protection and safe communication, every user of the signature method must use a new modulus N. Even if distinct public exponents are used, a modulus cannot be shared between two users. Furthermore, even if numerous keys are computed, the probability of producing two keys with the same modulus or secret exponent is completely low if the RSA keys are generated, as mentioned above.

The remainder operator is the Java equivalent of e = 5. Because e = 5 and (N) = m = 429232 in this case, the number d necessitates that 5d = 1. (mod m). One method is to look at one more than 429232 multiples (because 5d =429232k+1, where k is an integer in the range [0, N-1]), then seek for the first one that is divisible by 5. In other words, you'd look up 429232, 8584465, and so on (or just compute d = e-1 (mod m) = 5-1 (mod 429232) = 171693). Because the integer 858465 can be divided by 5 (i.e., 171693 multiplied by 5 equals 858465), d = 171693.

Remember that in practice, public-key encryption techniques are many orders of magnitude slower than their symmetric-key equivalents. Furthermore, public key crypto schemes can only process modest block sizes, typically 8 or 16 bytes. Asymmetric cryptographic systems, on the other hand, are thought to be far more adaptable and flexible.

Thus, RSA is generally used to encrypt a short message. Duch as a credit card number. This can also be used to encrypt a randomly chosen key k, which is then used with a symmetric-key encryption scheme or algorithm that uses a variable length buffer to encrypt the message itself, such as DES, 3DES, or Advance Encryption Standard (AES). Because the key k is usually fairly short (e.g., 128, 192, or 256 bits for the AES), it can be treated as an integer M in the range [0, N-1].

Frequently Asked Questions

Where is RSA being implemented in current date?

RSA is used in many online website browsers, VPNs, emails, chatting applications, digital transactions and other communication tools. RSA is used to establish secure connections between a VPN(Virtual Private Network) server and a client. TLS(Transport Layer Security) handshakes can exchange keys and create a secure channel using the RSA method when using protocols like OpenVPN.

What is the full form of RSA in cryptography?

RSA in cryptography stands for the RSA algorithm investors named as Rivest, Shamir and Adleman. The RSA algorithm is a public-key cryptosystem for the secured transfer of data that is based on the public-key technology of encryption.

What is the encryption type used in the RSA algorithm?

The RSA algorithm is asymmetric. It uses two unique but connected keys. Both the private and public keys can encrypt a message using RSA cryptography. A message is decrypted using the opposite key to that which was used to encrypt it.


RSA is a powerful encryption technique that has withstood the test of time. RSA is a public-key cryptosystem that enables secure communications and digital signatures," and its security is based in part on the challenge of factoring huge integers. The authors challenged anyone to try to hack or break their code, whether through factorisation or otherwise, and no one appears to have succeeded thus far. This has effectively validated RSA and will continue to ensure its security for as long as it can withstand such break-ins. Refer to our courses and explore Coding Ninjas Studio to find more exciting stuff. You can also look into the interview experiences and solve different problems. Look into our Guided paths, test series, libraries and resources to know more.

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