Perfect Secrecy

1,048,576

The summer I left for Bristol, my mother walked me down Lemon Street to the entropy office and bought us a megabit.

This was four years after the Solver, so I’ll not spend long on what everyone knows. A proof is a proof; the ingenious part was that it was constructive. Every lock that had depended on a problem being hard opened within the same eighteen months — the banks first, then the archives, then the dead. That last part they call the Reading. Every message anyone had ever sent under the old ciphers had been kept by somebody, on the old principle of harvest now, read later, and now it could all be read. My grandmother’s generation learned what their friends had really thought of them, forty years on, with citations.

What survived was the one kind of secrecy that had never depended on anything being difficult. If two people share a string of truly random bits, and spend each bit once, then a message sealed with those bits tells an eavesdropper nothing — not because the eavesdropper lacks the machinery, but because there is nothing in the message for machinery to find. Shannon proved it in 1949, in a paper nobody had needed for a century. Randomness, shared in person, spent once. That was privacy now. All of it.

The clerk sat us on either side of the minting bench, drew the curtain, and let the diode fill two glass tablets with the same 1,048,576 bits. We watched the buffer wiped. Then we fed the coster its codebook — the shared corpus our letters would be compressed against before sealing. Mum brought Dad’s cassettes and nine years of the parish newsletter. I brought the photo captions and the dog.

“That’s you provisioned,” the clerk said. “Most families never spend a tenth of it.”

983,041

There are six years I will not put down here. This page is cleartext; you may have the shape of them but not the middle. We spent freely in the Bristol years — jokes, mostly, sealed for the pleasure of sealing them, because privacy felt renewable then. We could have re-minted any weekend for the price of a train ticket. We did not, because we did not know we were spending down a fixed thing; nobody who can still meet ever knows that.

My father died in the March I turned twenty-four. At the funeral I said a thing. My mother, who had a settler’s licence she had never once mentioned, signed for Arcadia Planitia within the year. The contracts were one-way. They were priced that way on purpose.

From Mars there is no visiting, so there is no re-minting, ever. Radio between worlds is broadcast, and after the Reading nobody pretends otherwise. Which meant the tablet in my drawer stopped being a keepsake. It was the whole of the privacy my mother and I would ever have. A fixed sum, spendable once.

The convention is old and sensible: one party seals from the top of the pad, the other from the bottom, so no bit is ever spent twice. She took the top. I took the bottom. The unspent middle was what we had left to say.

Her first letter cost 509 bits, of which 128 went on the seal proving it was her. Arrived. A third of the gravity. The dog would have hated the dust. — M.

601,772

What the coster teaches you, living with it, is that surprise is the only thing that costs. A message is priced by how unlikely it is, given the codebook and everything already sealed. Words she half-expected cost almost nothing. The dog was nearly free. Kindness, too — kindness is mostly old words in the expected order. Fury is expensive. Fury is always news.

And my new life was news. Ana, the flat in Bedminster, the work — none of it was in the codebook, and every word of it was dear. The economics ran one way: it was always cheaper to write about the past, which we shared, than the present, which we didn’t. For twenty years the pad pushed us gently back towards the house, the cassettes, the captions. I understood, eventually, that this was not a flaw in the scheme. It is what any channel does when the model stops being fed. Estrangement has a unit price, and I paid it by the letter.

You learned thrift from other families’ ruin. The Pascoes, two doors down from the old house, had run their pad round twice — spent every bit a second time rather than go silent. Reused bits leak; that is arithmetic, not misfortune. The Reading took their second decade whole, and afterwards everyone on the terrace knew precisely what Mrs Pascoe thought of everyone on the terrace.

So we rationed. Two letters a month, drafted long, costed, cut. I learned to feel the price of a sentence before the coster gave it. I learned to write to my mother in the idiom of a house that no longer existed, about people who were dead, because those were the words we could afford.

348,160

In the nineteenth year her letters began to shorten, and I thought: she is saving. I priced my worry and did not send it.

Then a letter arrived that had spent 344,064 bits.

She was direct about the reason in the first line — the settlement medics had given her a number, and she meant to spend accordingly. Saved privacy, she wrote, is only secrecy you are keeping from yourself.

I will not quote the rest. It began with the funeral. It answered what I said there, plainly, the way you can only answer a thing you have been drafting for nineteen years against a fixed corpus of everything two people ever shared. It ended with the dog.

She left me 4,096 bits exactly. A round number — she would have had to pad her final block to leave it round, so she had chosen it: enough, if I kept to words we already owned, for about four hundred of them. Answer once, properly, she added in clear, where anyone could read it, or spend it on the weather. Both are good.

4,096

Four hundred words, once. It took me five months.

The coster was honest with me the whole way, and its honesty was an education. My first draft priced at nine thousand and change; it was mostly explanation, and explanation is surprise, and surprise was what I could not afford. Every cut brought the price down and the letter closer to true. What survived the budget was, almost exactly, what I should have said at the graveside — in the language of the house, every word already in the codebook — which is to say, nothing she did not already know. It priced at 4,032 with the seal. I padded the last block, as she had, and spent us to zero. I sent it on a Tuesday and watched the two pointers meet in the middle, and the middle close, and the tablet’s status change to a word I had never seen it use: spent.

0

After that we wrote in clear, the way everyone writes to Mars, and it turns out the clear channel was never the empty one. Weather. The greenhouse rota. A dog at the settlement, not hers, that she fed anyway. Anyone could read it, and I hope someone did, because what we were doing in public those last months was holding hands where people could see.

The registrar posted her death the way everything is posted now. I learned of it in the same minute as anyone who cared to look, which is what it is, these days, to be survived.

The tablet still works. Spent does not mean blind: the pad opens every letter it ever sealed, today, identically, and will tomorrow. That is the property nobody lists in the textbooks, though it is the same theorem wearing its other face: what perfect secrecy protects, it protects for ever. No Solver is coming for her last letter. No Reading will ever hold it. Of everything I have of my mother, those letters are the only things that are safe.

And on a shelf in a settlement store on Arcadia Planitia there is a strip of glass holding 1,048,576 bits of pure noise, agreeing with mine, bit for bit, as it has for thirty years across two worlds. That agreement can never again be used for anything. It was never anything else that we had.