What is the quadratic sieve method?

The quadratic sieve algorithm (QS) is an integer factorization algorithm and, in practice, the second fastest method known (after the general number field sieve). It is still the fastest for integers under 100 decimal digits or so, and is considerably simpler than the number field sieve.

What is the complexity of quadratic sieve?

Complexity. The theoretical time and space complexity of the quadratic sieve is O(exp(sqrt(log n log log n))) where n is an integer. The constant e is usually used as the base of the logarithm.

How does number field sieve work?

The principle of the number field sieve (both special and general) can be understood as an improvement to the simpler rational sieve or quadratic sieve. When using such algorithms to factor a large number n, it is necessary to search for smooth numbers (i.e. numbers with small prime factors) of order n1/2.

What is discrete logarithm in cryptography?

Discrete logarithms are logarithms defined with regard to multiplicative cyclic groups. Discrete logarithm problem is not always hard. The hardness of finding discrete logarithms depends on the groups. For example, a popular choice of groups for discrete logarithm based crypto-systems is Zp* where p is a prime number.

What is a smooth number in C?

A smooth number is a number with only small prime factors. In particular, a positive integer is y-smooth if it has no prime factor exceeding y.

How do you find prime factorization in C?

Step by step descriptive logic to find prime factors.

Input a number from user. Store it in some variable say num .
Run a loop from 2 to num/2 , increment 1 in each iteration. The loop structure should look like for(i=2; i<=num/2; i++) .
Inside the loop, first check if i is a factor of num or not.

What is a 200 sieve?

200) sieve. Gravel: Material passing a 75-mm (3-inch) sieve and retained on a 4.75-mm (No. 4) sieve. Coarse Gravel: Material passing a 75-mm (3-inch) sieve and retained on a 19.0-mm (3/4-inch) sieve. Fine Gravel: Material passing a 19.0-mm (3/4-inch) sieve and retained on a 4.75-mm (No.