# Tagged Questions

A prime number is an integer greater than 1 with no divisors other than itself and 1. Primes and prime products play an important role in public key cryptography.

2k views

### Is it feasible to build an index of prime factors?

Would it be possible to break an RSA key, in for example 1 week of time, if the cracker have already spent X number of years building an index of primes by performing every permutation of existing ...
9k views

### How are primes generated for RSA?

As I understand it, the RSA algorithm is based on finding two large primes (p and q) and multiplying them. The security aspect is based on the fact that it's difficult to factor it back into p and q. ...
36k views

### How can I generate large prime numbers for RSA?

What is the currently industry-standard algorithm used to generate large prime numbers to be used in RSA encryption? I'm aware that I can find any number of articles on the Internet that explain how ...
11k views

### What makes RSA secure by using prime numbers?

I am just learning about the RSA algorithm. Looking at the first two steps: Choose two distinct prime numbers $p$ and $q$. Compute $n = pq$. I have some probably stupid questions: Why do $p$ ...
291 views

### Factors of RSA modulus

In the article A Method for Obtaining Digital Signatures and Public-Key Cryptosystems, the original RSA article, it is mentioned that Miller has shown that n (the modulus) can be factored using any ...
4k views

### Is it possible to validate a Public Key in RSA?

If I have a 1024-bit number, and someone is telling me that it is in fact a valid RSA public key, is there any way I can quickly validate that it is indeed so (without cracking RSA)? (I suppose I am ...
385 views

3k views

### How can I find the prime numbers used in RSA?

I got this question in a local hacking event, but I couldn't solve it. Problem Statement ---- Continuing their snooping habit, NSA kept bugging Alice's communication. Resorting to the age old ...
4k views

### How large should a Diffie-Hellman p be?

In a Diffie-Hellman exchange, the parties need to agree on a prime p and a base g in order to continue. Assuming some ...
1k views

### What is the correct value for “certainty” in RSA key pair generation?

I'm creating an RSA key pair in Bouncy Castle and need to specify an int value for certainty. This Stack Overflow answer says it is a relative test for how prime the values are. There is another ...
906 views

### Quadratic residue problem on composite integers

Its believed that the quadratic residue modulo $n=p·q$ for large primes $p$ and $q$ is intractable, which forms the basis of some cryptosystems. However, it is solvable if the factors of $n$ are know,...
741 views

### Hill cipher key space

Key space is the set of all possible keys that can be used to generate a key. We using the number of valid key to describe it. I've given a hill cipher of block size $k$ over alphabet of size $p$, ...
450 views

### Significance of 3mod4 in squares and square roots mod n?

Why do most literature while discussing squares or square root modulo a prime P, consider P to be congruent to 3 mod 4?
I'm trying to create an algorithm to find the public exponent e given a plain (non-CRT) private key that doesn't include the public exponent, i.e. I've only got $n$ and $d$. A question has already ...
In the key generation step of paillier cryptosystem , In order to satisfy $\gcd(pq,(p-1)(q-1))=1$ , we can take equal length primes. Instead of taking(length as parameter to generate $p,q$) equal ...