What sort of mathematical breakthrough would endanger the security of the RSA encryption algorithm?
In an encoding scheme, each letter is replaced as follows: For example, would be encoded as since and
What is the main problem with such a system?
To crack a code, Alice and Bob need to find the product of their secret large primes, and so they each send these primes to each other.
Alice receives and performs , while Bob receives and performs .
What's the main issue with this encryption system?
Suppose Alice and Bob want to establish an encryption key. They start by choosing a large prime , which is shared in public.
Alice secretly picks a large prime , and Bob secretly picks a large prime . Then both Alice and Bob multiply their primes by , so Alice now has and Bob has .
They send and to each other. They then multiply what they receive by what their own secret prime. That is, Alice receives and performs , and Bob receives and performs .
Alice and Bob now have the same number that they can use as their secret key.
Is this encryption system secure?
Suppose a cryptography system included the step where, given and it is necessary to calculate in (That is, first is found, then the value is divided by with the remainder . )
and are going to be shared in public, and it is important that remains a secret.
Which of these circumstances (if known by someone trying to break the code) would easily compromise