How does tiCrypt compute my private key?

The public key is a fixed exponent e and the product of the primes n = pq.

The private key is d =(p −1)(q −1) /e and n. The public and private keys are opposites of each other: messages encrypted with one have to be decrypted with the other.

Specifically, for m, a message, me mod n is the encrypted message; it can be decrypted by performing d(me) mod n = m mod n. Conversely, dm mod n is a digital signature that can be verified by performing e(dm) mod n = m mod n.