Of Trapdoors and Elliptic Curves and BraidsOctober 17, 2018
So, in our discussion of encryption as it relates to computer networks and the Internet of Things (IoT), we’re dealing with ciphers, not codes.
The idea then is that a message can be converted to a number, and then some math involving the key will be performed on that number to create the encrypted “ciphertext.” Critical for making this work is the existence of an inverse function that’s hard to derive so that a ciphertext can be converted back into plaintext only by someone with the right key.
Messages can be encrypted by a public key for reading after decryption with a private key, or digests can be signed with a private key for validation using a public key.
You might think that every number has a multiplicative inverse, but we’re talking modulo math here, not real number multiplication.
(n) , where n is the modulus we calculated from p and q .
(Or, if you went with 1024 bits, you’d have more security.)
So part of the vetting process for this system has involved finding curves that work well and then standardizing them.
The first has to do with how security is implemented, and it’s generally said that hardware is far more secure than software.
But these keys work only because the private keys are secret.
So next time we’ll look at some of the considerations for protecting those secrets from unauthorized eyes.