Results

**1 - 3**of**3**### Computation of Large Values of

"... bibliography on this topic). From a practical point of view, many tricks can be used to find all primes less than 10 12 in a fast way, as explained for example in [1]. Clearly the enumeration of all the primes less than x cannot have a lower cost than (x). Besides the computation of (x), the numb ..."

Abstract
- Add to MetaCart

bibliography on this topic). From a practical point of view, many tricks can be used to find all primes less than 10 12 in a fast way, as explained for example in [1]. Clearly the enumeration of all the primes less than x cannot have a lower cost than (x). Besides the computation of (x), the number of primes less or equal to x, does not need to find all the primes less than x. This fact is set up by the formula of Legendre, which uses the prime numbers less or equal to p x. Next, the works of Meissel and Lehmer provides more subtle formulae, which reduce the amount of computation. As an example Meissel computed the value of (10 8 ). Nevertheless, these methods all have a cost of O(x 1+" ). Lagarias, Miller, and Odlyzko gave a method which for the fi

### Three Novel Theorems for Applied Cryptography

"... With advancements in computing capabilities public key cryptosystems are going to be more complex yet vulnerable over the modern day‟s computer networks and associated security mechanism, especially those based on novel approaches of applied mathematics. This paper explores three novel theorems deri ..."

Abstract
- Add to MetaCart

With advancements in computing capabilities public key cryptosystems are going to be more complex yet vulnerable over the modern day‟s computer networks and associated security mechanism, especially those based on novel approaches of applied mathematics. This paper explores three novel theorems derived while studying and implementing RSA algorithm, one of the strongest public key cryptosystem. The proposed Theorems are best suited and adequate for RSA algorithm yet being applicable to some of other existing algorithms and theorems of applied mathematics. The first theorem deals with concept of ambiguity while calculating multiplicative inverse of encryption key which in some of instances returns undesirable negative numbers not useful as decryption key. Second theorem deals with unconcealed multiplicative inverses, unconcealed are values which remain unchanged after any mathematical transformations. Concept of unconcealed multiplicative inverses is useful in key generation for RSA cryptosystem. Third theorem deals with the concept of unconcealed exponentiation modulo quite useful in finding unconcealed signature and messages to form

### Under consideration for publication in J. Functional Programming 1 The Genuine Sieve of Eratosthenes

"... A much beloved and widely used example showing the elegance and simplicity of lazy functional programming represents itself as “The Sieve of Eratosthenes”. This paper shows that this example is not the sieve, and presents an implementation that actually is. 1 ..."

Abstract
- Add to MetaCart

(Show Context)
A much beloved and widely used example showing the elegance and simplicity of lazy functional programming represents itself as “The Sieve of Eratosthenes”. This paper shows that this example is not the sieve, and presents an implementation that actually is. 1