No Room In The Innocence
innocence, my long lost friend,
has left me all alone.
now I'm floating in the deep end,
shivering to the bone.
knowledge comes to comfort me,
to warm me with her power,
but she wreaks of poverty,
like a dead or dying flower.
of poverty from joy and peace,
from love and naïveté;
the sweetness of my simple life
now stained by those who stray.
O God, deliver, turn back the clock;
remove me from the fray;
unteach, untouch, unspeak, unhear,
unsee my eyes today.
-Requiem for Innocence, a poem I wrote a couple of years ago
In a cryptographical context, we have this very important concept of "one-way functions". Things that once done are difficult or impossible to undo. Take for instance, cracking open an egg: no matter what you do, there's no getting that egg back to its pre-crack state. Might as well make an omelet or something. But flipping a lightswitch: this is definitely not a one-way function. You turn it on, you turn it off; nothing too difficult about that. Some things in life we wish were one-way functions. Like cleaning your room. That would be a nice, if once cleaned, it was difficult or impossible to unclean it :) Ok, you've got one-way functions down. In cryptography (that is, modern cryptography), we have a nifty little bit of math that works as a one-way function. It all relies on this idea of "modular arithmetic". So stay with me here, this is not entirely difficult. This is easy stuff. We'll walk through it together, and I'll just give you the high-level. You use modular arithmetic nearly every day, I'm sure! See, if it's 11am right now, and I tell you I'll be at your house in 4 hours, you can expect me at exactly...? I hope you said 3pm. Aww :) It will be nice to see you. We can have an afternoon snack and catch up about life and love and everything in between. (If you said, "1500!", then please close this blog right now, get off the computer, and go talk to a human. Golly.)
Ok. So we could have expressed that time question with this equation:
11 + 4 = x (mod 12)
It's (mod 12) because there are 12 numbers on the clock*. In modular arithmetic, once you reach 12, you start counting back at the beginning. Pretty straightforward, right? Just like a circle- like a clock! So 13 = 1 (mod 12), 14 = 2 (mod 12), etc. And 66 = 6 (mod 12). Right? I just had to go around the circle a couple more times on that last one. So you did that all automatically in your head: 11 + 4 is 15, and 15 is 3 (mod 12). 3pm.
And we don't have to stick to (mod 12), of course. I could say, "What's 7 (mod 4)?", and you would just have to picture a clock that only has the numbers 1 through 4 on it. And then you would tell me...? 3?! That's right. 7 = 3 (mod 4). Ok. You've got this down. Easy. Peasy.**
It gets a little trickier when we start talking about exponents. See, computing an exponent in a particular (mod n) is pretty simple:
a^x (mod n)
For instance, 2^3 = 1 mod 7. That's trivial to figure out. But if you only have the *answer* to the problem, you're up a creek, as they say. Suppose I were to give you this:
Find x where 3^x = 15 mod 17.
That's called 'finding the discrete logarithm'. How do you do it?! In this case, it's not terribly tricky to see that the answer is 6 (because 3^6 is 729, which is 15 greater than the last multiple of 17), but imagine if the numbers were huge! Imagine if instead of a 17 up there, it was a number with 170 digits! Things could get dicey. Ok. There's a lot more to this, but if you want to know more, you should just shoot me an email. There's no use boring the other readers with a soliloquy on cryptography.
Anyway. Why am I telling you all this. Right- one-way functions. Modular exponentiation is a one-way function. Easy for me to arrive at the answer, but hard for you to derive the question.
Virginity falls into this "one-way" category as well, as I hope you've deduced. And so also, as I lament in the poem above, does Innocence: once lost, never found. It slips away in a moment, a quick succession of moments; a single splash of mud and the white dress isn't white anymore. You remember Adam and Eve in the garden; their shamelessness, their joy, their freedom. They were naked, but neither of them knew it. So neither of them cared. And then what?! They both ate some hooky fruit, and we've been wearing clothes ever since.*** And if we're not careful, we might throw Sin onto that pile of one-ways... but I hope we both know that although there is no undoing of sin, there is redemption from sin. We crack the egg of our selves into the hot frying-pan of lawlessness and our expected end is to be COOKED. But God gave us this tool to return to our true unbroken selves: teshuva-- repentance.
* Everywhere except Gastonia, I've been told.
** Now go make some lemonade.
*** I mean most of us have, at least.