### Research papers on rsa algorithm

This looks like it will be quite a nasty calculation, but some tools from number theory can be employed here. The RSA algorithm is but one of many systems where a set of mathematical theorems, often from number theory, can be synthesised to construct an encryption scheme. Of course, in reality, large prime numbers guarantee secure encryption, while the calculations are performed by computers.

Importantly, the algorithm parallels the physical situation where one makes open padlocks available to the public. Mathematically speaking, our numbers N and e form the open padlock, and our secret primes p and q combine to form a key that we can use to retrieve the locked information.

But if somebody came up with a brilliant formula for breaking numbers into their prime factors turning padlocks into keys , there would indeed be security issues around the world. The inherent randomness of the primes is the force that currently prevents such a formula from existing.

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Number theorists are at the forefront of this knowledge, but are still a while away from coming up with such a tool. The world should rest assured that, as problems are solved, many more are created, and this progress not only allows the advancement of technology, but also endows the mathematician with endless motivation. And so concludes my defence of the usefulness of useless maths. Did it work? Are you convinced? Courageous Leaders: promoting and supporting diversity in school leadership development — Cambridge, Cambridgeshire. The Maldon UP! Edition: Available editions United Kingdom. Sending secure information?

You could do a lot worse than employing the RSA algorithm. Adrian Dudek , Australian National University. To illustrate this beautiful piece of mathematics, we can return to our fictional lovers. Also, I will use small prime numbers in this example, just to ease the calculations. We will just assume the number scares people and so nobody tries to decompose it. RSA is the most popular Asymmetric cryptosystem as it uses pair of keys, one of which is used to encrypt the data in such a way that it can only be decrypted with the other key.

The keys are generated by a common process, but they cannot be feasibly generated from each other. The security of the RSA system is based on the assumption that factoring of large number is difficult. But if one could factor a large number into its prime factors then he could break the security. DMRJT algorithm is more secure as compared to RSA algorithm as it uses dual modulus based double encryption and decryption with the use of Jordan function. It is shown here that dual modules play an important role in increasing the complexity of decomposing them into its factors and Jordan function increase the size of the private key hence increases the security.

DMRJT algorithm uses double encryption and decryption using double private and public keys to provide security against Brute-force attacks. A public key cryptosystem consists of a public key, which is used for encryption, and a private key, used for decryption. Therefore, anybody can encrypt plain-text since the encryption key is available to everyone, but only the holders of the private key corresponding to the public key used for encryption can decrypt the cipher-text. Cryptography is the science that uses mathematical concepts for encoding message in non readable format. Original text is known as plain Text which is readable and after encoding the plain text the resultant is known as cipher text which is unreadable.

Encryption and Decryption required a key and an algorithm to do this. Published by Elsevier Ltd.

Cipher text is Encoded text which cannot be easily understood by the human being. There are many well known cryptography algorithms. We can divide them according to the number of keys they used and working scenario for encryption and decryption of plain text. In this paper we are going to introduce a modified version of RSA algorithm with the use of Jorden-Totient function. Which have high security than RSA algorithm. Section 2 will describe the types of cryptography briefly. Section 3 contains the explanation of RSA algorithm.

And last one is the conclusion of the research.

## Methods toward Enhancing RSA Algorithm: A Survey

And section 7 contains the references. Designed to be highly secure and highly flexible, well-suited for large microprocessors, 8-bit smart card microprocessors, and dedicated hardware. ARIA : A bit block cipher employing , , and bit keys to encrypt bit blocks in 12, 14, and 16 rounds, depending on the key size. Developed by large group of researchers from academic institutions, research institutes, and federal agencies in South Korea in , and subsequently named a national standard. Camellia has some characteristics in common with AES: a bit block size, support for , , and bit key lengths, and suitability for both software and hardware implementations on common bit processors as well as 8-bit processors e.

Also described in RFC CLEFIA is one of the new-generation lightweight blockcipher algorithms designed after AES, offering high performance in software and hardware as well as a lightweight implementation in hardware. FPE schemes are used for such purposes as encrypting social security numbers, credit card numbers, limited size protocol traffic, etc. FFX can theoretically encrypt strings of arbitrary length, although it is intended for message sizes smaller than that of AES 2 points.

The FFX version 1. Use of this scheme is reportedly one of the reasons that the National Security Agency NSA can easily decode voice and data calls over mobile phone networks. KASUMI is the intended confidentiality and integrity algorithm for both message content and signaling data for emerging mobile communications systems. Using simple arithmetic operations, the algorithms offers fast encryption and decryption by use of efficient implementations.

KCipher-2 has been used for industrial applications, especially for mobile health monitoring and diagnostic services in Japan. Designed for hardware and software implementations, and is resistant to differential and linear cryptanalysis. LED is designed for RFID tags, sensor networks, and other applications with devices constrained by memory or compute power.

## RSA brushes off crypto research findings that RSA algorithm is flawed

Salsa20 uses a pseudorandom function based on bit whole word addition, bitwise addition XOR , and rotation operations, aka add-rotate-xor ARX operations. Salsa20 uses a bit key although a bit key variant also exists. In , Bernstein published ChaCha , a new family of ciphers related to Salsa SEED : A block cipher using bit blocks and bit keys. Simon and Speck : Simon and Speck are a pair of lightweight block ciphers proposed by the NSA in , designed for highly constrained software or hardware environments.

While both cipher families perform well in both hardware and software, Simon has been optimized for high performance on hardware devices and Speck for performance in software. Both are Feistel ciphers and support ten combinations of block and key size:. Skipjack : SKC scheme proposed, along with the Clipper chip , as part of the never-implemented Capstone project.

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Although the details of the algorithm were never made public, Skipjack was a block cipher using an bit key and 32 iteration cycles per bit block. Capstone, proposed by NIST and the NSA as a standard for public and government use, met with great resistance by the crypto community largely because the design of Skipjack was classified coupled with the key escrow requirement of the Clipper chip.

## The RSA algorithm (or how to send private love letters)

TEA was originally developed in , and employed a bit key, bit block, and 64 rounds of operation. TWINE's design goals included maintaining a small footprint in a hardware implementation i. There are several other references that describe interesting algorithms and even SKC codes dating back decades. Savard's albeit old A Cryptographic Compendium page. Public key cryptography has been said to be the most significant new development in cryptography in the last years. Their paper described a two-key crypto system in which two parties could engage in a secure communication over a non-secure communications channel without having to share a secret key.

PKC depends upon the existence of so-called one-way functions , or mathematical functions that are easy to compute whereas their inverse function is relatively difficult to compute. Let me give you two simple examples:. While the examples above are trivial, they do represent two of the functional pairs that are used with PKC; namely, the ease of multiplication and exponentiation versus the relative difficulty of factoring and calculating logarithms, respectively.

The mathematical "trick" in PKC is to find a trap door in the one-way function so that the inverse calculation becomes easy given knowledge of some item of information. Generic PKC employs two keys that are mathematically related although knowledge of one key does not allow someone to easily determine the other key. One key is used to encrypt the plaintext and the other key is used to decrypt the ciphertext. The important point here is that it does not matter which key is applied first , but that both keys are required for the process to work Figure 1B.

Because a pair of keys are required, this approach is also called asymmetric cryptography.

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In PKC, one of the keys is designated the public key and may be advertised as widely as the owner wants. The other key is designated the private key and is never revealed to another party. It is straight-forward to send messages under this scheme. Suppose Alice wants to send Bob a message. Alice encrypts some information using Bob's public key; Bob decrypts the ciphertext using his private key.

This method could be also used to prove who sent a message; Alice, for example, could encrypt some plaintext with her private key; when Bob decrypts using Alice's public key, he knows that Alice sent the message authentication and Alice cannot deny having sent the message non-repudiation. Public key cryptography algorithms that are in use today for key exchange or digital signatures include:.