Key Generation Algorithm for Factorization-Based Cryptosystems - Computer Science Assignment Help

Assignment Task

In this exercise, we will highlight the importance of a good key generation algorithm for factorization-based cryptosystems, and study the impact of lattice reduction algorithms on cryptanalysis.

1. Describe the advantages and drawbacks of Paillier encryption [2] with respect to RSA encryption. Evaluate the key generation algorithm proposed by Paillier. We observe that secret keys of factorization-based cryptosystems are rather large compared to elliptic curve-based cryptosystems. We will now try to reduce these keys by using special primes of the form p = xd + 1 with d, x 2 Z+.

2. We first consider numbers of the form n = pq with p = xd1+1, q = xd2+1, some integer x of appropriate size and two integers d1 6= d2. Are these composite numbers hard to factor? If no provide a factorization algorithm and briefly study its complexity; if yes justify your answer. We now suppose n = pq for a random prime number p of the form p = xd + 1 and a “truly” random prime number q. We first consider general factorization algorithms.

3. Discuss the eciency of general factorization algorithms on numbers of this form, depending on d and the respective bit lengths of p and q. Can you think of other potential approaches? After considering these “obvious” general factorization algorithms, we then turn to perhaps less obvious lattice attacks. In fact, the moduli used above remind us of Takagi’s moduli [3] and we know that the last ones can sometimes be factored using lattice reduction algorithms.

This Computer Science Assignment has been solved by Computer Science experts at My Uni Paper. Our Assignment Writing Experts are efficient to provide a fresh solution to this question. We are serving more than 10000+ Students in Australia, UK & US by helping them to score HD in their academics. Our Experts are well trained to follow all marking rubrics & referencing style.
Be it a used or new solution, the quality of the work submitted by our assignment experts remains unhampered. You may continue to expect the same or even better quality with the used and new assignment solution files respectively. There’s one thing to be noticed that you could choose one between the two and acquire an HD either way. You could choose a new assignment solution file to get yourself an exclusive, plagiarism (with free Turnitin file), expert quality assignment or order an old solution file that was considered worthy of the highest distinctio.