22 August 2015

Significant Digits, Chapter Eighteen: Contras

Significant Digits, Chapter Eighteen: Contra

Glewlwyd Gavaelvawr bringt the wægnwright before Merlin, and the man prostravit.
“Wo,” said the wægnwright.  “Þere is a greet vates in my village, and he hath foretold that my wyf will become the wyf of Thegn Edmund the Black.  How meahte this be prevented?  How meahte this be stoppjed?”
Merlin was greatly wroth, and seiden, “Stopje þy spittle!  Know you not that alle prophetie is true, ac it be seied to be unsure?  Time hath but a single þraw for alle its span.  Et quod dicitur erit quod do not differ by even so much as a grain of sand.  Mannfully þou must endure þy fate, and do not clamour, lest þee hasten it.”

                Harry Lowe, The Transmygracioun, passus decimus



Harry Potter-Evans-Verres, Percy Weasley, Haddad, Podrut, and Mafalda Hopkirk relaxed.  Amelia Bones, Cedric Diggory, Hedley Kwannon, Simon Smith, and Alastor Moody did not.

Harry sighed.  “If it’s all secure, and it was just students trying to Gryffindor their way into someplace secure, then let’s finish up here.  We were talking about the Seyhan thing.”

Diggory handed his bubbler to Auror Kwannon, gesturing with his other hand at the door.  “Keep tabs on things, and let me know if they need help sorting through the backlog in Receiving.  Oh, and have someone notify the Headmistress, since it’s students.  This is happening too often.”  She nodded and spent a few moments dispelling the wards on the door until she was able to quietly exit, small mirror in hand.

Everyone else sat down around the meeting table again, gathering up parchments where they’d been scattered.  Harry tapped his finger thoughtfully, and said, “All right… so Moody will take the lead in planning out how to handle this -- the logistics of the fake body.  This could badly hurt us if it gets out, increasing the paranoia and driving even more people into the Independents, so not a word about this outside of this room.”

He turned to regard Simon Smith.  “That means with Hermione, too.  I’ll discuss it with her the next time I see her -- tonight, I think -- and we’ll work out how to handle this with the Returned.”  He wasn’t actually worried about any leaks from them; the loyalty and security of the Returned was so absolute in its nature that it approached the surety of magical vows.  It wasn’t quite a cult, but something about the nature of their suffering and redemption instilled in them an otherworldly certainty in Hermione’s judgment and goodness.  “And I’ll also work out with her how to put some distance between you guys and the Tower.”

Smith nodded.  “She will also want to talk with Madame Bones,” he said.  “Charlevoix has received word from Ministre Isidore about a possible pen for Dementors in Siberia.  We understand that there could be political consequences when we crush it, and we want to minimize that.”

“We might be able to use that, actually,” said Madame Bones, wrinkling her smooth brow thoughtfully.  She lifted a hand to curtail Smith before he could object, adding, “Although I know you won’t delay in acting by even one minute, of course.  Nor should you.”

She turned to Harry.  “Things are coming to a turning point, I think, Harry.  Draco and Narcissa are pushing their treaty with as much energy as they can muster, warning that every state must choose between us and them.  Well, not ‘them’ in as many words -- they’re saying it’s the only way to prevent invasion.  Your ‘bend like the willow’ strategy may be reaching the end of its usefulness… I say we start pushing back a little more.  We can’t let the Malfoys define us in the eyes of world powers.  And if Hermione is going to back off on her tours and advocacy, then it’s especially important that we speak for ourselves.”

“She’s right, Potter,” said Moody, scratching the scalp of today’s body.  “The time for the soft sell is over, especially if you can’t have the Goddess out there selling us to the world.  You’ve been telling us you have some ‘breakthroughs’ that will end Malfoy’s little rebellion for years, and in the meantime the blonde little nit has become a hundredfold more threatening to your goals.”

“Let’s cut off distribution of Malfoy’s newsletter, at least,” chimed in Diggory.  “He uses our Vanishing Rooms to trans-ship to the Americas, Eastern Europe, Africa, and the Ten Thousand.  If we just cut off those lines, then it’s going to be bloody hard for him to get his nonsense out there.  He’ll be back to the old ways.  Even you’ve called this a war… let’s really get our army moving!”

“I wouldn’t rely too much on Vanishing Rooms staying our own exclusive property,” said Harry.  “Plenty of people have all kinds of opportunity to examine the Rooms in other states, and it wasn’t that much of a leap from Vanishing Cabinets.  A few tweaks to the Passus and they’ve got it -- assuming they haven’t stolen the incantations already.”

Moody harrumphed his agreement.  “At least twelve questionable researchers on staff in Extension Establishment and Pairing Partnership alone.”  He pointed a crooked finger at Mafalda Hopkirk.  “The Unspeakables leak like a sieve.”  She scowled, cheeks flushing, but Moody was already turning back to Harry.  “And you have that Umbridge toad in and out of here like she owns the place!  I don’t know what you’re doing with all that Muggle rubbish in Pairing Partnership, churning out reams of squiggly lines while casting first-year cantrips, but if it’s important enough for you to be researching yourself, then Umbridge shouldn’t be allowed anywhere near it.  She shouldn’t even know it exists!”

“You don’t know her value,” said Harry.  “I do.  She and the other people you suspect -- suspect, since you don’t have a shred of evidence or you’d already have told me -- are all essential.  The risk to operational security is outweighed by our need for speed… they have to work all the harder to make themselves useful to me, after all.  In a month, we’ll be able to put the sliceboxes to use properly, and that’s only because of the help of some of your ‘questionable researchers.’ ”  He turned back to Diggory.  “And you’re not cutting off freedom of the press, either.  Everyone gets to say whatever they want.”

“That doesn’t stop us from replying, at least,” said Diggory.  A frown appeared on his ridiculously handsome face.

He cut off the train of thought before it could proceed much further.  “Fair point.  We have regular announcements and releases in The Prophet, but it might shift the Overton window more if we also had our own newsletter.  Percy, maybe you could come up with a few names on who might head that up?”

Weasley nodded, making notes on the parchment in front of him.  “I have a few people in mind.”

“Thank Merlin for small favors,” groused Bones.  “I’d like one of my people on that, too.”

“Malfoy’s fired off two bombs just last month, and this one’s talking about ‘freedom of the press,’ “ muttered Moody, disgruntled with where they’d left the topic.  “Going to need metal detectors on the Tower entrance, soon.  Not a bad thought, actually… we can do that, now, with that Loony Leaf...” He trailed off, thinking.

Harry glanced at the agenda in front of him.  “Moving on, the Westphalians are asking for us to publicly cut all financial ties with Cyprus -- I’m guessing that would be to impress Cappadocia with their clout, for whatever reason -- and for ‘equality in trade.’ ”

“In other words, we drop all tariffs and pressure others to do so, as well,” said Bones.  “Old hat from them.  They’ve been demanding it for a century.”

“Yes, and it would be a huge victory if Hig got us to agree to that… it would put the Treaty over the top with them, and increase his personal prestige.  If we’re cultivating him, that would make sense,” mused Weasley.  “A big hit to your own popularity here at home, but it would be in sectors where we can afford the loss.”

“He also wants us to send them some arithmancers to train them in progressive taxation,” said Harry, smiling.  “The secret to our wealth.  But if we agree to that… well, Hig has laid that out as non-negotiable before they’ll recommend the Treaty.”

“Once they recommend it, it’s as good as passed in the United States and Canada,” commented Haddad.  The Chief Goldsmith pulled an ornate snuffbox from a small pocket in his jacket, loading the crook of his index finger with a pinch.  “Probably a few other countries in the Americas, as well.”

“Yes, it’s common knowledge they own the north, sure enough,” said Bones, thoughtfully.  “But Dumbledore thought -- and I agree with him -- that they could swing almost all of the Americas around like a toy kneazle.  He was uncomfortable with that aspect of American affairs, even as he needed to work with their people in the Confederation to keep things in check.”

“Yes, I’m inclined to agree.  I think we should make the deal, if we can.  We’ll get on the wing to other major signatories, and make sure we have a majority in favor, though,” Harry said.  “If we jump on this, it might forestall them using the Independent situation even more to their advantage.  I honestly still think they could go either way.  We need to lock the Council down… their intelligence operation is invaluable.  Particularly given our current situation.  We can worry about dismantling it after we understand what we’re up against.”

“Even with the mysterious ‘Three’ in play,” asked Moody, “they’d still consider staying neutral?”

“There are some people in the Council who like the idea of three world coalitions -- Independents, Health and Life, and Westphalia.  Councilor Strongbound has been trying to put together enough votes to get Westphalia to reject any motion to endorse us, playing it as another move by imperialist Britain to take control.  He’s echoing a lot of Malfoy talk.”  Harry said.  “Hig leads the majority there, but he doesn’t own the Council of Westphalia as thoroughly as they own the politics of the States.  He’s with us, I think, but he’s not everyone.”

One of the doors opened, and Kraeme entered the room, Pip at her side.  He had a slip of parchment in hand.  “Sir?  We thought you should see this.  One of the intruders today had it, but it doesn’t appear to be any language we recognize.”

“A code, or just another part of the prank meant to look like a code,” added Kraeme.  “They had a sackful of transfigured doxies and a transfigured Vanishing Cabinet, too.  And one of these,” she said, holding up a small wooden abacus.

“Someone’s in trouble,” said Harry, whistling and raising his eyebrows.  “Okay, they got my attention.  Bring them in here, and ask the Headmistress to join us if she’s free.”  He glanced around.  “I think we’ve covered nearly everything -- everything high-security, anyway.  Percy will have some owls out to everyone about a few more things, but it’s nothing we can’t solve later or at a distance.  Bones, you’ll be in Norden for a week from tomorrow, yes?”  She nodded as she got to her feet, shuffling parchments into a pile.  “I’ll owl you about some things, then.”

Everyone departed their separate ways, exchanging cordial pleasantries as they did so.  Most headed to the entrance to the Tower, so they could get a portkey out of Hogwarts, while Podrut went back to Material Methods.  Moody stayed behind long enough to kill a fly he’d noticed in the room with a well-placed curse, then went to check out the situation in the Receiving Room.

While Kraeme and Pip went to go bring in the students that had been taken prisoner -- placed under arrest?  what was the proper terminology? -- Harry examined the slip of parchment.


Could he take the time to break this?  It would be fun, but he hadn’t done cryptography for years… not since he and Draco had come up with the codes for the Bayesian Conspiracy, really.  He smiled at the thought.  The smile faltered as he glanced at his watch.  Not much time left before he needed to get to the clinic and finish off the Transfigurations that were in progress or in holding.  The patients might mostly be in magical sleep, unconscious of the passage of time, but the healers on duty were not so lucky.  Clinic time was starting to dominate his daily schedule… they were going to have to change protocol, and figure out some way for him to multitask.  The Stone required no concentration or effort from him, after all.

Giving the Stone to someone else -- anyone other than Hermione -- was an impossibility, of course.

Well, he had a few minutes, anyway.  He took a mechanical pencil from his pocket, turned his agenda over to use as scrap paper, and got to work.

The opening digits were clearly significant in some way.  Was it a Caesar cypher, rotating through the alphabet 33 letters (i.e. 7 letters) one way or another?  That would be easy almost beyond belief, but this was Magical Britain, and maths hadn’t yet penetrated very deep.  Easy enough to check.

abjjuptlj… no, that wasn’t it, clearly.  The other way didn’t yield up anything intelligible, either.

He counted the letter frequency.  Every letter in the alphabet appeared at least once in the 156-letter message, which reduced the likelihood that it was a rotation cypher or a simple substitution.  If there were spacing between letters, he could have picked out the single-letter words to help rule out some possibilities, but this was just an unbroken string -- no punctuation, either.

He mapped ETAOIN onto the message’s six most common letters, but again there was no discernable pattern.

Harry paused for a moment.  What were some other novice codes?  Or should he take a different tact and assume this was someone who knew what they were doing?  He’d once thought about making a magical Enigma machine, using custom-enchanted quills -- the theory behind giving quills specific instructions for behavior predicated on outside input was voluminous, and it had intrigued him with the possibilities of magical computing, once.  Harry strained to remember… had he ever discussed it with Draco?

No, this was found on students.  Even if someone skilled at cryptography had designed this code, it was probably still simple enough for a student to decipher with materials at hand.  A one-time pad was a good possibility, given the digits at the start of the code.  In that case, the code was unbreakable without the thirty-third sheet from the necessary pad.  He’d assume that wasn’t the case for now, though.  More fun this way.

A book cipher?  The Bible would normally be the obvious choice -- Genesis 3:3 would be the place to start -- but that was unlikely in a magical society, where religion had limited currency.

Harry wasn’t as well-equipped in the magical culture department as most other wizards, but a few alternatives sprang to mind: The Tales of Beedle the Bard, Goshawk’s Book of Spells, Lowe’s The Muggle Conspiracy, or something by Bagshot… there were a variety of books that had been bestsellers for so long they’d become ubiquitous.  In that case, 33 might be the page number or the paragraph used for the encoding.

The door opened, and Harry looked up to see the pair of aurors back, three children floating along behind them.  A healer came just behind, wand resting firmly on the chest of one of the airborne students.  Harry felt a little unhappy with himself, even though he knew that was silly.  He’d eliminated several possibilities, and it was clear the cryptogram was sufficiently sophisticated that he shouldn’t have expected to break it with pencil and paper in only a few minutes.  Still, he’d been expecting some… flash of insight.  He sighed and put down the pencil, pulling on his fingerless gloves.

Kwannon was also dragging the burlap sack filled with dead doxies, which she left on the floor.  She put an abacus and three wands on the table.  “Left the Cabinet back in the Receiving Room… Chief Moody insisted,” she said.

Harry nodded, approaching the third child.  He rested a hand on the boy’s leg, examining him.  “He was injured?” he asked the healer.

“Yes,” replied the man, a tall and slender fellow with a beaky nose.  “Tears along the ligamentum teres hepatis and mesentery, cardiac contusions, pulmonary contusions, multiple fractures, and e-ax bleed.  Fixed the brain, then got him trip-R, and everything bagged again.  Trauma was all severe but typical.  Subsumed some nodules on the thyroid, too, so he’ll leave here with some salt.  Kid’s been stepped down for about... five minutes.”

Harry nodded.  Serious injuries from blunt trauma, including a ruptured liver, damaged intestine, bruising of the heart, and bleeding in the brain… the boy was lucky that the Tower and Safety Sticks existed.  He probably wouldn’t have died under Madame Pomfrey’s care, but he’d probably have suffered brain damage.

He studied the boy’s face, and then the faces of the two other students, but didn’t recognize them.  Hm.

“Auror Kwannon, were all four things -- abacus, doxies, Vanishing Cabinet, and the note -- found on the same student?”

The auror nodded.  “Yes.  The injured one, here.  The other two seem to have just been the ones to break the Stick and bring him to the Receiving Room.”  She paused, lowering her head in thought until her shoulder-length black hair swung forward to cover her face, and then looked up again, asking, “How could this work, as an attack?  The doxies are clever -- you’re stunned, and they revert to their native Form and go on the attack for a few minutes, until they drop dead -- but if you’ve figured out that much, you should also have figured out that the Vanishing Cabinet would also revert, and that you wouldn’t be able to smuggle it into the Tower.”

Harry couldn’t repress a slight smile.  He smelled a clever plot from a novice plotter.

He lifted his hand from the injured boy.  “You can go, Galen.  Thank you.”

The healer lifted his wand from the boy and put it in his sleeve.  “Certainly.”  He paused.  “I know this one, by the way.  The patient.  He came in with his brother, once.  He’s Sammy Meroveni-Bowles.”


Harry raised his eyebrows in surprise.  “Scarlett Meroveni-Bowles is this boy’s mother?”

“Yes,” said the healer, as he headed out the door.  “The one always ranting about the Treaty in letters to The Prophet.”

“She is famous for being a bit of a crackpot about that, isn’t she?  Hm.  Wait, Galen… would you mind asking someone on the door to get me whichever Arithmancy books available in the library on cryptography?”  Harry paused.  “There should be at least… two, if I remember correctly.  Although there might have been new acquisitions.”


As it happened, the books were unnecessary.  By the time Pip appeared at the door with four books in hand, fifteen minutes later, the puzzle was solved.

Harry was able to draw the square from memory: the tabula recta, one of the most basic and famous ways to use a running-key cipher.  It was almost five hundred years old, and fairly famous among cryptographers: a table that was 26 letters tall and 26 letters long, with each row and column beginning one letter further in the alphabet (the first row started A, B, C … , the second column was B, C, D …, etc).  It was a simple and elementary way to use a specific key to encode your text.

There was no 33rd part to the Treaty for Health and Life, and so Harry guessed that the third part of the third section -- that is, 3.3 -- was the indicated key.  It took less than a minute to verify with the first six letters of the cryptograph, moving letter by letter through the key.  He looked in the tabula recta for the A row, then located the cyphertext letter T in that row.  That T was in column T, and so the first decoded letter was T.  Next he found the coded U in row N, resulting in an H.



It only took three letters to know he was correct, as the message began:


“Sir?  Galen said you asked for these?” asked Pip.  He frowned as he entered the room.  “Lawrence Bradwian and Annabeth Dankgesang… I hope they’re not in trouble, sir?”

“Well...” answered Harry, moving his finger up and down the table of letters.


“...I think they’re in a great deal of trouble, indeed.”


  1. I just wanted to say that this is getting interesting and I'm glad this story exists

  2. the cup is not enough. we must add to our collection. i believe that many items of great power are held in the tower. prepare the plan we spoke about before and we will communicate with the abacus.