All Questions
Tagged with prime-factorization cryptography
7
questions with no upvoted or accepted answers
2
votes
0
answers
50
views
The number of integers less than x that have at least two distinct prime factors of bit size greater than one-third the bit size of x
Sander came out with a paper describing how to generate what he calls an RSA-UFO. Anoncoin then utilizes this and mentions that the paper proves that the probability that a randomly generated integer, ...
- 123
2
votes
0
answers
144
views
Factor base for RSA cryptosystem
In RSA crptosystem, we choose two big primes $p,q$ and set $n=pq$. $n$ is public and roughly, the aim is factorize $n$ to decrypt the encrpyted message.
A method to attack the system is the following:...
- 2,807
2
votes
0
answers
273
views
In the General Number Field Sieve, can we estimate the size of the matrix in terms of the number being factored?
One of the last steps of GNFS is to solve a large matrix-vector equation (usually using the Block Lanczos algorithm or the Block Wiedemann algorithm). The matrix for the most recent RSA number ...
- 1,068
2
votes
0
answers
505
views
Using factorization to solve modulo arithmetic involving big numbers.
In one of my classes, the following approach was shown to solve modulo operations involving huge numbers:
Problem to solve:
49 10 mod 187.
Approach taken:
Prime factorize $187$. It's factors are ...
- 141
2
votes
0
answers
2k
views
Discrete Logarithm vs Integer Factorization
Can anyone please tell me if finding discrete logarithm is considered more difficult than integer factorization?
We have very advanced methods to find factors of large composite numbers like Number ...
- 305
1
vote
0
answers
204
views
Understanding the ramifications of Riemann Hypothesis
Proving Riemann Hypothesis is a million dollar problem, but I am more interested in understanding its ramifications in the practical world.
According to many sources, one such effect will be ...
- 395
1
vote
0
answers
347
views
Is it difficult to factor a product of many large primes?
It's well known that it is difficult to factor a product of two large primes, and this fact is used in cryptography.
Is it also difficult to factor a product of $n$ large primes?
- 57