🚀 go-pugleaf

How do I solve this expression?  It is part of the RSA public key
encryption algorithm.

The expression is
e*d mod L = 1
in other words
e*d = k*L+1

How do I find d?

I'll back up now and show you what e and L are:

p and q are prime numbers.
L = (p - 1)*(q - 1)
e is any number except for factors of L

N = p * q

To encrypt data m,
m^e mod N = encrypted data c

To decrypt data
m = c^d mod N

So, you see, I need d to decrypt data.

Example:
p = 19, q + 23, N = 437, L = 396, e = 13, d = 61
(but I don't know how d was calculated - that's what I need to know)

Encrypt the number 180
180^13 mod 437 = 208229648656711680000000000000 mod 437 = 329

Decrypt 329
329^61 mod 437
= (a very long number I won't bother to type) mod 437 = 180

Any help gratefully appreciated.

- j