4
votes
1answer
71 views

Permutations: If I know $\alpha$ and the cycle structure of $\alpha\beta$, can I find $\gamma$ for which $\gamma\beta$ also has this cycle structure?

Suppose we have two permutations $\alpha$ and $\beta$ (of a set $S$ of size $|S|=n$), and I know $\alpha$ and the cycle structure of $\alpha\beta$. But I don't know $\beta$. Can I find a ...
1
vote
1answer
34 views

Schnorr group membership

Consider the multiplicative group of integers modulo $p$ (where $p$ is prime). Suppose this has a subgroup of order $q$ (where $q$ is prime). (Such a subgroup is known as Schnorr group.) Let $0 < ...
0
votes
2answers
32 views

Requested material on Bilinear Pairing

Bilinear map/pairing is widely used in Pairing based Cryptography. I am new to this area. Can anyone suggest me some good reference on Bilinear pairings? I need at least an example of Bilinear map ...
1
vote
1answer
82 views

ElGamal like encryption

How can I approach the following exercise: Source: An Introduction to Mathematical Cryptography by Hoffstein This exercise describes an approach similar to ElGamal cryptosystem with a numerical ...
1
vote
1answer
84 views

Diffie-Hellman key exchange for three user.

Assume that there are three users that have their own secret key $d_i$ and corresponding public key $Q_i = d_i G$ such that $Q_i$ is a point in an elliptic curve. Now I'm looking for a solution to ...
1
vote
1answer
46 views

Generating a number of a specific order

Here is what I have: select $p$ such that $p - 1$ has a large prime factor $t$: $p - 1 = tu$, where $u$ is a random number $n = p^2 q$, where $q$ is prime pick random $g < n$ and compute $g_p = ...
3
votes
1answer
383 views

Cycle attack on RSA

Let $p$ and $q$ be large primes, $n=pq$ and $e : 0<e<\phi(n), \space gcd(e, \phi(n))=1$ the public encyption exponent, $d : ed \equiv 1 \space (mod \space \phi(n)) $ the private decription ...
7
votes
3answers
1k views

RSA: How Euler's Theorem is used?

I'm trying to understand the working of RSA algorithm. I am getting confused in the decryption part. I'm assuming $$n = pq$$ $$m = \phi(n) = (p - 1)(q - 1)$$ E is the encryption key $\gcd(n, E) = ...
2
votes
2answers
969 views

Primitive root and discrete logarithm

Started studying Diffie Hellman key exchange protocol as part of the course. I dont have much maths knowledge. Can somebody explain in simple terms what is the significance of taking Primitive root in ...
1
vote
1answer
342 views

Breaking RSA in a special case

This is a part of homework assignment, and I am stuck. The RSA signature is being calculated using Chinese Remainder theorem technique. Find the detailed description here. Public and private keys are ...