3
votes
1answer
109 views

Is the strength of RSA over quadratic or other cyclotomic fields as strong as over the integers?

If we assume the strength of RSA is based on the difficulty of factoring (which I know we can't guarantee) and we compose the modulus of some other quadratic ring that is a unique factorization domain ...
1
vote
1answer
83 views

Modular exponentiation with Chinese Remainder Theorem

I'm learning modular exponentiation with Chinese remainder theorem. I found a great answer from below How can I use eulers totient and the chinese remainder theorem for modular exponentiation? But I ...
5
votes
1answer
132 views

Is it possible to fool Miller-Rabin test?

It is well known that it's possible to fool Fermat test with Carmichael numbers. But, is it possible to deliberately fool many-rounded Miller-Rabin test by constructing some special number without ...
2
votes
1answer
139 views

What are the possible cryptographic implications of Zhang's proof of the Twin Prime Conjecture?

Earlier this year, Yitang Zhang published a proof of a weakened form of the Twin Prime Conjecture. I'm wondering if any of the new mathematical machinery he developed has uses in cryptography or could ...
1
vote
0answers
162 views

Can you help me clear a confusion about small subgroup attack on HMQV?

First,i want to show you with a picture how the HMQV works. There are some notations you might not familiar, it doesn't matter. I just want to show you the procedure. Next it's an attack on HMQV ...
1
vote
1answer
229 views

Algorithm for proving Carmichael numbers

I have an application for determining if a number is a prime or not, currently I'm getting a random number, then doing the Fermat primality testing to find out if the number is probably prime (so this ...
2
votes
1answer
166 views

How did they factor RSA-704?

I don't understand the 'Wiedemann algorithm' works. Can someone explain the factoring of RSA-704 in an easy way?
1
vote
1answer
144 views

How to solve the reverse of an equation that uses MOD?

I've been tasked with reverse engineering an unknown crypto function. The function uses the following constants: $a=380951$: I noticed that this is a prime number $b=3182$: I noted that this is a ...
2
votes
1answer
974 views

How can I use eulers totient and the chinese remainder theorem for modular exponentiation?

I'm trying to implement modular exponentiation in Java using Lagrange and the Chinese remainder theorem. The example we've been given is: Let $N = 55 = 5 ยท 11$ and suppose we want to compute ...
1
vote
2answers
320 views

Is there an algorithm for factoring N, which is just as simple as this one, but faster?

I found a simple algorithm for factoring semiprime numbers, you can read about it in Factoring Semiprimes and Possible Implications for RSA. It basically works like this: You reverse the digits in ...
2
votes
1answer
570 views

ABC Conjecture's Impact on RSA Encryption

A recent proof of the ABC Conjecture has been released by one Shinichi Mochizuki. Now, I'm not well versed in mathematics but it would appear that this proof implies that finding prime factors could ...
4
votes
1answer
232 views

How to construct a zero-knowledge proof of a number of the form $n=p^a q^b$

Let $n = p^a$$q^b$ where p and q are distinct primes and a and b are positive integers. How to construct a zero knowledge proof that n is of such form? This is actually a homework problem with a ...
8
votes
3answers
444 views

Is it reasonable to assure that p-1 and q-1 aren't smooth?

I came across the requirement that, in RSA, $p-1$ and $q-1$ shouldn't be smooth, shouldn't consist of lots of small factors. Therefore my question: How complicated is it to check whether $p-1$ is ...
4
votes
1answer
150 views

Is there a group of prime order which could fit the CT-Computational Diffie-Hellman assumption?

I'm trying to choose a group that is hard under the Chosen-Target Computational Diffie-Hellman assumption, according to the definition in this paper, in order to implement the oblivious transfer ...
10
votes
2answers
779 views

Can I select a large random prime using this procedure?

Say I want a random 1024-bit prime $p$. The obviously-correct way to do this is select a random 1024-bit number and test its primality with the usual well-known tests. But suppose instead that I do ...
6
votes
3answers
2k views

What place do prime numbers have in cryptography?

My understanding of hashing and encryption is rather limited. I certainly do not understand the mathematical formulas at play in these algorithms. With that said, what part do prime numbers play in ...
28
votes
4answers
15k 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 ...