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2014 Alan Turing Cryptography Day 30th April 2014 School of Mathematics Alan Turing Building Floorplan Mike’s Mall Ellie’s Enclave Staging Area WC Café Lungrem’s Lair Barquith’s Bunker Lunch Area Entrance WC p 42, 7 ÷ 7, 3 + 4, 25, 15 × 3 − 4 × 11 Introduction Hello and welcome to the Alan Turing Building, the home of Math- ematics at The University of Manchester! This booklet contains really useful information about the afternoon's activities and more exciting codes and ciphers for you to try. In fact, we've forgotten how many codes we've packed inside this short pamphlet. Perhaps you can help. How many messages can you track down? Hopefully you are all ready for the challenge. The codes range from easy to extremely tricky, but, as usual, we've tried to make them all fun! Initially, we'll be here in the Alan Turing Building for lunch, crypto- related activities and that chance to meet the people that you have seen posting on the forums, and the CryptoTeam of course. Please try to contain your excitement because other people are still working in the building. Next, we'll have the live crypto-competition!!! People (in teams of at most five) must crack three new codes each located in a different room. Unlike the online competition, you can attack them in any order. The winners will be the first team to hand in the correct answers to all three codes. Be careful though, you get no extra chances. Each team is only allowed to submit one answer sheet, so don't just guess! If all that isn't enough, we will finish with a short lecture and the giving of prizes. So many people wanted to come today that we can't hold everybody in our lecture theatres in the Alan Turing Building. This means that we'll have to walk over to University Place, just next door, for the final events of the day. ÈÊÊÆàÅàâäæÈêÄâ p 100; 60 ÷ 3; 32; 7 × 2; X − V I; 20 × 0:75; −5 × −4; 2 × 32 + 1 Useful Information Locations The activities be.tween 12pm and 2:45pm wi.ll take place on the ground floor of the A.lan Turing Bu.ilding: the. Atrium, the study rooms and G.207. The .lecture, CryptoTeam Question Time and prize-giving will be in Lecture Theatre A in University Place. See maps o.n the back cov.er. The Live Competition If you want to take part in the live. competition (and why wouldn't you?), you must register your team at the regis.tration desk before 1:20pm. The c.ompetition will take place in three different rooms and your team will be given a random starting location. Please make sure that you are all at the starting location by 1:25pm. The challenge is to decrypt three different co.des and then hand in your answer sheet before 2:30pm. The first team to hand. in the corre.ct answer to the desk in the Atrium will be the winners.. Tea.chers can. also take part in separate teachers' teams! We want the competition to be fun for all, so please d. on't cheat, shout out or interfere with other teams. (You c.an use smartphones, but they probably won't help!) We reserve the r.ight to disqualify any teams immediately and without ap. peal if we perceive that th. ey are behaving inappropriately. There are other people working and studying in the building at the same. time, so please don't r.un and keep noise to the minimum. Let's. just keep it fun! CryptoTeam Question Time If you have any questions about cryptography, the competition, or mathematics in general that you'd like CryptoTeam to answer, then leave them at the desk in the Atrium and we'll answer a selection during CryptoTeam Question Time later this afternoon. éàÉÊ2 left space for note followed by magic number Programme 12:00pm Registration Opens 12:10pm Welcome Address 12:15pm Lunch and Crypto-Activities 1:20pm Assemble in designated starting room 1:30pm Live Cryptography Competition 2:30pm End of Live Competition 2:45pm Leave Alan Turing Building 3:00pm Lecture: Enigma Variations 3:30pm CryptoTeam Question Time 3:45pm Prize-giving âàÅáæÇäÊÂÊàëàéÊäÈæÅ ruoF egaP Warm-up exercises Here are a few straightforward codes and ciphers to get you warmed up for the live challenge! Ahf vghqkr gzud khsskd vghqkr, Sgzs eddc nm sgdhq udknbhsx; Zmc jhssjd vghqkr gzud kdrrdq vghqkr, Zmc rn nm sn uhrbnrhsx. | Kdvhr Eqx Qhbgzqcrnm MATHEMATICIANS HAVE TRIED IN VAIN TO THIS DAY TO DISCOVER SOME ORDER IN THE SEQUENCE OF PRIME NUMBERS AND WE HAVE REASON TO BELIEVE THAT IT IS A MYSTERY INTO WHICH THE HUMAN MIND WILL NEVER PENETRATE | LEONHARD EULER plePeo ear allygener terbet adedpersu yb eth onsreas chwhi eyth veha elvesthems vereddisco. | iseBla calPas Rl R whoh qk dwdehj dlqho edurjb pfhmq lko d qekspdji yhdop, gy lropq nshpqrkj wksfi ah: Edp qeh Orhgdjj eymkqehprp ahhj mokuhj? | IdurI Erfahoq Bmm rvpuft gspn nbuifnbujdjbot p 1 + 1; 15 ÷ 3; 8 ÷ 4; 7 + 8; 1448 ÷ 2 Early Cryptography Cryptography pervades many aspects of modern life: from Internet banking to web-based cryptography competitions! But the history, and uses, of cryptography go back thousands of years. The earliest known examples of cryptography were meant not as a way to send secret messages, but instead to make the reader stop and think or to give a sense of importance or dignity to the text. The first recorded example dates from c.1900BC: the tomb of the Egyptian nobleman Khnumhotep II uses some unusual hieroglyphic symbols in place of more ordinary ones to describe his service to the Pharaoh. This is similar to the way that inscriptions on modern statues and monuments are often written in a more formal style. Another example occurs in the Old Testament. In the Old Tes- tament, Jeremiah 25:25 and Jeremiah 51:41 mention \Sheshach" - a place that is not mentioned in any other sources or on any maps. In fact, Sheshach is believed to be Babylon (Babel in ancient He- brew) encoded using the Atbash cipher. The Atbash cipher works by reversing the alphabet: so (in the English alphabet) A becomes Z, B becomes Y, etc. Scholars believe that this (and other sim- ilar instances) is an example of the scribes' interest in word-play and alphabet games. The name Atbash comes from the letters aleph, taw, beth, shin|the first, last, second, and Kviszkh Zgyzhs second-to-last letters of the Hebrew alphabet. hslfow mld yv The first military use of cryptography didn't xzoovw gsv use a substitution cipher such as Atbash, or the Zayb xrksvi? (later) Caesar cipher; instead, it was a transpo- sition cipher using a device known as a scytale. Invented by the Spartans in ancient Greece circa 500BC, a scytale consists of a wooden rod around which a piece of parchment or leather is wrapped. The message is then written on the parchment along the length of the rod. When the parchment is unwrapped, the letters of the message have been re-arranged. Only when the parchment is wrapped around a rod of the same diameter can the original message be easily read. éàÉÊ5 PSaigxe The first text on methods for secure mil- itary communication was written by Aeneas Tacticus in the 4th century BC. An entire chapter of his ‘On the Defence of Fortified Places’ contains descriptions of many different A scytale. methods of encryption, some of which are still used today. For example, he described one method of steganographic cryptography (hiding secret messages in other more innocent mes- sages or pictures) that was very similar to one used by the Germans during both World Wars: namely, pricking holes or dotting letters in a book, pamphlet or newspaper, with the highlighted letters picking out the secret message. Another Greek writer, Polybius, first described another method of encryption that was suggested as being particularly useful for long-distance communication. The letters of the alphabet are ar- ranged in a square with the rows and columns numbered. Each letter can then be enciphered using its co-ordinates (in the example given, ‘h’ would be 2,3 and ‘m’ would be 3,2), which can then be commu- nicated over long distances by, for example, holding the appropriate number of lit torches in each hand. Whilst nowadays we may not use torches to communicate, the princi- 123 4 5 ple behind this method of encryption 1 abc d e lies behind many modern encryption 2 f g h i/j k schemes (as well as in the crossword in 3 lmnop Chapter 2 of this year’s competition). 4 qrs t u It’s not known if the ancient Greeks 5 vwx y z used any of their encryption methods A Polybius square, using militarily. The first known such exam- the English alphabet ple is the Caesar cipher, used by the Roman Emperor Julius Caesar (100BC- 44BC). Whilst itself a simple substitution, other more complicated substitution ciphers such as the Enigma machine, have played a very significant role in cryptography. A comprehensive account of the history of cryptography can be found in David Kahn’s book ‘The Code-breakers’. Strictly speaking the plaintext is not true lk ge an at a n n p ol si ib is y it h l en T VII / n IS AP ZQ VR NM KL MN DB ON RI HJ SH MN PQ ON YA EM ME IJ KL MN D EE UN EA NU MN PQ AB CD UC IT SU MB MN JK LM PQ LI AL RE ER âÇêâæääÊâêëáêãÄÈÄÈàÈâáêàëÊ Qbhf Mjmf A little diversion How many words related to cryptography and the competition can you find in the grid below? D N O I T U T I T S B U S P I G P E N F J M Q Z W C S T E G A N O G R A P H Y E K R I A F Y A L P E O T L N S E R E N E G I V F A L J I O A Q Z W A S R X L I C T G N I R U T E C K E E D O C M B A R Q U I T H M S Q H U A S U M E P R B J I F Q L X E K I M H B O O F H E O N D J E I E T O N W G R C A E S A R R X K S I S Y L A N A K P N W F ÉäÄÁÇÈÊÁÄÅëÄÂÊâãàëëÊÅÉÊ · | | · · | | | · · · | | | | | | | | | Cryptography before the digital age In a substitution cipher, each letter in the plaintext is replaced by another letter in the ciphertext but the substitution used does not change throughout the message.
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