Cryptology: Asymmetric Flashcards
What is the main idea behind asymmetric cryptology?
Asymmetric cryptology utilises complex mathematical problems to hide information (in plain sight). In its essence asymmetric crypto uses more than one key, often referred to as public and private, to secure communication. One major advantage with asymmetric crypto is lack of having to establish a shared secret between two entities looking to communicate securely, which is one of the most important downsides of symmetric crypto. One major drawback with public key cryptography is the computational complexity involved in the utilised algorithms. Consequently, not all devices are powerful enough to utilise this kind of cryptography.
Name some of the more important methods for finding large prime numbers
- Sieve of Eratosthenes - Determinstic but slow
- Fermat test - Use Formats principle a number of times to find the probability of a given number to be prime
- Rabin-Miller - Same as Fermat
What is RSA and how does it work?
RSA is one of the most widely known crypto algorithms which enables public key cryptography. In its essence, RSA takes advantage of the difficulty in factorising large numbers into its base prime number components.
The two keys used are two large prime numbers p & q. Their product is n=p*q. Through using the Euler totient function and the Euclidean algorithm we can use p and q as keys for encrypting messages.
What is Diffie-Hellman used for and how does it work?
Diffie-Helmann is an asymmetric crypto algorithm used for setting up a shared key (to be used in symmetric crypto).
The two nodes need two global parameter q and alpha. From this each node generates a random number x or y in the interval <1, q-1>. Then each node calculates X = alpha ^ x mod q. Next, each node sends their result to the other. The node which created X can from this derive the symmetric key through
K=X ^ y mod q.
And the one that sent y will find the same K through:
K=Y ^ x mod q
What are some of the other use cases of asymmetric crypto besides securing communication?
One of the key benefits of asymmetric crypto is the integrity it provides. If some message has been signed with a private key we can be very confident that the message was not spoofed by someone else.
One common method of checking for integrity is to first find the hash of the message, encrypt the hash, and append it to the end of the message. When the message has been received, the recipient can easily check the integrity of the message by decrypting the appended hash of the message, calculate the hash of the message, and comparing the two hashes. If they are similar, we know that the hash was encrypted with the senders private key which is a strong indication of integrity.
