[WSG22] Daily Study Group: Cryptography (begins January 31!)

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A new study group devoted to Cryptography begins next Monday!

I will be leading this group daily, Monday to Friday, over the next three weeks, until February 18. The curriculum follows the upcoming Wolfram U course “Introduction to Cryptography”. A list of daily topics can be found on the Daily Study Groups page. The study group sessions include videos and reading materials for the course and time for discussion and Q&A. After the study group will help you may complete the course quizzes and achieve the “Course Completion” certificate for the “Introduction to Cryptography” .

REGISTER HERE:

Webinar: Daily Study Group: Introduction to Cryptography by Wolfram Research

About This Study Group: Cryptography has existed for thousands of years and currently is a fascinating topic to study because of the close ties it forges between theory and practice. It makes use of bitwise computations, advanced algebra, string operations and everything in between. The Wolfram Language, with functions that provide basic building blocks for modern cryptography, makes a great tool for hands-on understanding of various concepts. In this Study Group, you will follow video lessons from the new Wolfram U course Introduction to Cryptography and learn about the concepts, underlying math and connections to real-world scenarios.

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P.S: Don’t worry if you are unable to attend every session live: the recordings will be sent out to those who registered!

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Looking forward to this!

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Over 200 attendees joined the first session of this study group today. Thanks @Dariia Porechna for your presentation. Thanks to the attendees for remaining engaged throughout the session. Looking forward to the rest of the series.

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Interesting start. Maybe not only I ask myself, where I can see some of these machines. Here is a list of museums with Enigmas Liste der Enigma-Exponate – Wikipedia.

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Interesting historical perspective of cryptography from day 1 - looking forward to the next sessions!

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I was also curious about the lesser-known Lorenz machine:

Not a lot of them still present!

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For anyone interested in seeing actual historical equipment, the NSA runs the National Cryptological Museum in Maryland. It has an amazing collection from ancient times through Cold War to modern times including Enigmas and they have the only surviving Bombe (the machine designed at Bletchley Park to decrypt Enigma – the British destroyed all of theirs and had to rebuild one for their recently opened Bletchley Park museum).

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Ahead of the presentation, I am hopeful that the explanation of RSA will include an examination of its usage in SSL, i.e., how is it employed to exchange the symmetric key?

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This will be covered more ahead in Hybrid Cryptography lesson.

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The “Spy Museum” in Washington DC is also a good place to see an Enigma machine:

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please make test bigger on Zoom lecture now

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YHQL YLGL YLFL = VENI VIDI VICI

“I came, I saw, I conquered”

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It helped to notice that it was three words of four characters that start with the same character (and a lot of “L”). It cannot be “alea iacta est” or “aut Caesar aut nihil” for that reason. :slight_smile:

Though I did a brute force to confirm it.

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As Caesar encrypted with a shift of 3, shifting by 23 will decrypt
CaesarCipher[“yhqlylglylfl”, 23]

Producing a famous quote from Caesars Gallic Wars.

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Table[ResourceFunction[“CaesarCipher”][“yhql ylgl ylfl”, i], {i, 1, 26}]

shows the decrypted message in item 23.

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Here is my more “formal” analysis of this, assuming that the first word should be in Mma’s Latin wordlist.

text = "yhql ylgl ylfl";
alpha = Alphabet\[\];
latinWords = WordList["KnownWords", Language -> "Latin"];
candidates = {StringReplace[text, 
      Thread[Rule[alpha, RotateLeft[alpha, #]]]]} & /@ Range[26];
MemberQ[latinWords, StringSplit[#][[1, 1]]] & /@ candidates;
Pick[candidates, %]

Update: Changed an old “A” to “alpha”. Thanks, Luis!

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Nice, just a corretion in the code (A → alpha)

Thread[Rule[alpha, RotateLeft[alpha, #]]]]} & /@ Range[26];

Update: Code is already corrected in original post.

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Thanks, Luis. I’ve changed it in my post.

The code is based on the one in the “04_Classical_ciphers.nb”, but in the last minute changed “A” to “alpha” since it’s not recommended that variables start with an uppercase. But forgot to change it everywhere. :slight_smile:

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Common words appearing as cypher texts of common words when using Caesar Cyphers

With[{
  alpha = ToUpperCase[Alphabet[]],
  enCommon = Select[
    Union[ToUpperCase[WordList[]]],
    Complement[Characters[#], alpha] == {} &]},
 SortBy[
  Table[
   shift -> Intersection[
     enCommon,
     StringReplace[enCommon, 
      Thread[Rule[alpha, RotateLeft[alpha, shift]]]]
     ],
   {shift, 25}],
  Length[Last[#]] &]]

{5 -> {"FIE", "FIT", "IT", "ITS", "KNEE", "PH", "STY", "UM", "YA"}, 
 21 -> {"ADO", "ADZ", "DO", "DON", "FIZZ", "KC", "NOT", "PH", "TV"}, 
 2 -> {"CUR", "DAG", "ETA", "GAG", "GO", "IQ", "KEG", "ME", "MY", 
   "NAG", "OW", "TAG", "TWO", "URGE"}, 
 24 -> {"ASP", "BYE", "CRY", "EM", "EYE", "GO", "ICE", "KC", "KW", 
   "LYE", "MU", "RUM", "RYE", "SPEC"}, 
 1 -> {"BE", "BEE", "BIB", "BY", "DIBS", "EVE", "FOE", "IF", "IN", 
   "JUT", "KPH", "OFF", "PEE", "PI", "PIN", "PIP", "SIP", "TI", "UFO",
    "UP"}, 
 25 -> {"AD", "ADD", "AHA", "AX", "CHAR", "DUD", "END", "HE", "HM", 
   "ITS", "JOG", "NEE", "ODD", "OH", "OHM", "OHO", "RHO", "SH", "TEN",
    "TO"}, 
 9 -> {"AN", "ANY", "ARENA", "ARK", "ARM", "BRA", "BRAN", "BUNNY", 
   "BURY", "BYRE", "CANT", "CARP", "CRY", "DB", "KHAN", "LARK", "NAN",
    "NAP", "NUT", "PRAM", "RAT", "RUT", "TRY", "URN", "WRY"}, 
 17 -> {"BYRE", "CRIB", "ELK", "ERE", "ERG", "GIRD", "ILK", "IRK", 
   "KIP", "LIE", "NIP", "RE", "REP", "RIB", "RID", "RIVER", "SIR", 
   "SIRE", "SLEEP", "SLIP", "SPIV", "TIP", "TREK", "TRIG", "US"}, 
 11 -> {"ALE", "ALTO", "APE", "AS", "AT", "DALE", "DATE", "DAZE", 
   "DAZED", "DEFY", "ELF", "ELM", "ESPY", "ETA", "EYE", "FA", "IT", 
   "LAP", "LO", "LOO", "LYE", "PI", "SPA", "SPY", "STOP", "TO", "YES",
    "ZOO"}, 
 15 -> {"AD", "ADD", "ANT", "APE", "EX", "HEN", "HEP", "HIDE", "ID", 
   "NTH", "ODD", "PAID", "PAT", "PET", "PH", "PI", "SPAT", "SPIT", 
   "SPOT", "SPOTS", "STUN", "TAB", "TAU", "THEN", "TIP", "TNT", "UP", 
   "XI"}, 
 3 -> {"DOE", "DOS", "DUN", "EH", "ERA", "ERE", "ERG", "ERR", "FROG", 
   "GRUB", "HA", "HOP", "HUH", "ID", "IRE", "IRON", "KHZ", "LOO", 
   "ODE", "ORE", "PH", "PLOW", "PROW", "RUE", "SHH", "SHOW", "SHUN", 
   "SOB", "SUB"}, 
 23 -> {"ALB", "ALP", "ARK", "BE", "BOB", "BOD", "BOO", "BOX", "COLD",
    "DORY", "ELM", "ERE", "EX", "FA", "FOB", "FOLK", "HEW", "ILL", 
   "LAB", "LOB", "ME", "MILT", "MOLT", "ORB", "PEE", "PELT", "PERK", 
   "PLY", "PRY"}, 
 13 -> {"AH", "AHA", "ANT", "BALK", "BAR", "CRAG", "CREEL", "ENVY", 
   "ER", "FLAP", "FUR", "GAG", "GEL", "GNAT", "IRK", "NAG", "NU", 
   "NUN", "ONE", "ONYX", "PENT", "PERRY", "RAIL", "RE", "SHE", "SYNC",
    "TANG", "TNT", "TRY", "VEX"}, 
 7 -> {"AH", "AHA", "ALL", "APTLY", "DOLL", "DOPA", "FLAP", "FLU", 
   "GLIB", "HA", "HE", "HO", "IF", "ILK", "ILL", "JOLLY", "LO", "NUB",
    "OBI", "OH", "OLD", "OPT", "PA", "PILE", "SH", "SHALE", "SHE", 
   "SPA", "SPUR", "THY", "VIP", "WHO", "WHY", "WOLD", "ZOO"}, 
 19 -> {"AH", "AT", "AX", "BED", "BEE", "BY", "CHEER", "EH", "GNU", 
   "HA", "HEW", "HIM", "HUB", "IBEX", "IT", "LA", "LATEX", "LAX", 
   "LINK", "LIT", "MAR", "OBI", "PAH", "PAR", "PHEW", "SHH", "TA", 
   "TAT", "TEE", "TIMER", "WHEE", "WHIT", "YEN", "YETI", "ZEBU"}, 
 8 -> {"AIL", "AWE", "AWL", "BIAS", "BIB", "BIZ", "CAM", "COP", "EM", 
   "EMIT", "EWE", "I", "IF", "ILL", "JIB", "JIG", "MOIL", "MOO", 
   "MOW", "MU", "NIB", "NIL", "OIL", "OW", "OWL", "PI", "PIE", "PIG", 
   "PIX", "RIG", "SPIV", "TI", "TIE", "TWIN", "TWO", "UM", "WE", 
   "WET", "WIN", "XI", "ZIP"}, 
 18 -> {"A", "ADD", "AX", "BAT", "BAY", "EGAD", "EGG", "EGO", "EM", 
   "FAD", "FAT", "GAD", "GO", "GOD", "HA", "HAP", "HAW", "HAY", "JAY",
    "KHAN", "LA", "LAW", "LOAF", "LOG", "ME", "OAF", "OW", "OWL", 
   "PA", "RAH", "SAD", "SOD", "SOW", "TAR", "TASK", "TAT", "UGH", 
   "USE", "WE", "WEAL", "WOW"}, 
 10 -> {"BED", "BONY", "BOON", "BOP", "COD", "COG", "COO", "COWS", 
   "CRED", "DEW", "DRY", "DYED", "GO", "GOD", "GOO", "GOON", "GROG", 
   "KC", "KW", "LEI", "LIDO", "LO", "LOO", "LOOP", "MEN", "MONO", 
   "NOON", "OH", "OW", "OWE", "OX", "POI", "POX", "RED", "ROB", "ROW",
    "SNOW", "UM", "WE", "WEN", "WOOD", "ZED", "ZOO"}, 
 16 -> {"AM", "AS", "BE", "BEE", "BEEF", "BUY", "BYTE", "CEDE", "CUD",
    "DEED", "EM", "EMU", "EN", "EX", "FEN", "FEY", "HEM", "HER", 
   "HUT", "IDEM", "KC", "MEET", "MU", "MUD", "PEE", "PUT", "REDO", 
   "REED", "REF", "RUT", "SEE", "SEMI", "SET", "SEW", "SHUT", "THO", 
   "TOUT", "TUM", "WE", "WEE", "WEED", "WET", "WHEW"}, 
 4 -> {"AIR", "EAR", "EEL", "EH", "EPOCH", "ER", "EX", "FEE", "FER", 
   "FIX", "GET", "HEAR", "HERO", "IQ", "JERK", "KEPI", "KIP", "LEA", 
   "LET", "LIT", "MU", "NIX", "OLD", "PEA", "PEAR", "PEG", "PET", 
   "PIE", "PIER", "PIX", "PSST", "REF", "SAP", "SHH", "STEP", "STIR", 
   "TEA", "TEAR", "TEMP", "TIE", "TIGER", "TYRO", "VET", "VEX", "WEB",
    "WET"}, 
 22 -> {"AAH", "AD", "ALKYD", "AN", "AT", "AWN", "BAA", "BAN", "BET", 
   "CAP", "DANK", "DAWN", "EM", "FANG", "GALE", "GEL", "HAP", "HAW", 
   "HEP", "IQ", "JET", "KHZ", "LAC", "LAP", "LAW", "LAWN", "LEA", 
   "LEAN", "LET", "LOOP", "NAB", "ODD", "OPAL", "OPEN", "OWL", "PAIL",
    "PAW", "PAWN", "PEA", "PECAN", "PUNK", "RAP", "RAT", "SAP", "SAX",
    "WEN"}, 
 12 -> {"AT", "BAP", "BEEF", "BUS", "DAMP", "DUB", "DUN", "FA", "FAB",
    "FAD", "FAY", "FAZE", "HUB", "HUM", "IMP", "IQ", "ME", "MEW", 
   "MIX", "MUD", "MY", "NAB", "NAN", "NAP", "NUN", "OAF", "OAK", "PA",
    "PAPA", "PAS", "PUB", "PUP", "PUS", "RAJ", "RUN", "SANE", "SAP", 
   "SKY", "SURF", "TA", "TAB", "TAN", "TAP", "TUB", "UP", "VAN", 
   "YAP", "YE", "ZAP"}, 
 14 -> {"AIR", "AM", "AS", "ASK", "AWL", "BIB", "BOB", "BOD", "BOP", 
   "COT", "COY", "DID", "DIG", "DIP", "DO", "DODO", "DOG", "FIB", 
   "FOX", "GIFT", "GOBS", "GOD", "GYM", "HIP", "HO", "HOB", "HOD", 
   "HOP", "ID", "JOB", "MOD", "MS", "NOD", "OH", "PIG", "POD", "PSST",
    "RIB", "RIP", "ROAD", "TO", "TOM", "TONS", "TOP", "TOR", "VIA", 
   "VIP", "WAD", "WE"}, 
 6 -> {"AS", "BOG", "CORE", "CORK", "COT", "COTE", "COZY", "CURL", 
   "CUT", "DO", "HAJ", "HALL", "HAM", "HAS", "HAT", "HAY", "HE", 
   "HOT", "HUE", "HUG", "HUH", "HUM", "HUSH", "INGOT", "JAM", "JOT", 
   "JUT", "LAM", "LATTE", "LAX", "LAYOUT", "LOT", "LOX", "MALL", 
   "MARL", "MAT", "MATTE", "MOM", "MOT", "MU", "NAN", "NEST", "NO", 
   "NOB", "NU", "OUT", "OW", "PARE", "POSSE", "PUNT", "RAM", "ROUT", 
   "RUIN", "RUM", "SATIN", "SO", "SOD", "TA", "TAT", "TOR", "TUT", 
   "TUX", "VAT", "WAG", "WAGE", "YAK", "YETI"}, 
 20 -> {"BIN", "BOA", "BOB", "BOG", "BOMB", "BOY", "BUD", "BUFF", 
   "BUG", "BUM", "BUN", "BUS", "BY", "CHAIN", "DIN", "DON", "DUG", 
   "FIN", "FIR", "FUG", "FUNNY", "FUR", "FUSION", "GIG", "GIN", "GO", 
   "GUFF", "GULF", "GUN", "GUNNY", "HI", "HIV", "HO", "HUH", "HYMN", 
   "ION", "IQ", "JIMMY", "JOHN", "JULY", "LION", "LOCH", "LOG", "LUG",
    "MI", "MIX", "MUNCH", "NIL", "NON", "NOR", "NU", "NUN", "PUN", 
   "QUA", "QUAY", "SUE", "SYNC", "UM", "VIA", "WILE", "WILY", "WIN", 
   "WINY", "WITS", "WOLF", "WON", "XI"}}
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I think there was a lot of interest (including my own!) in the Q&A around random number generation now and historically. I decided I will list a few things I’ve come across and welcome any other clever ways you’ve seen to generate real randomness, starting with a relevant crypto-stack-exchange question:
How were one-time pads and keys historically generated?

One of the answers mentions SIGSALY, wherein the US Army awarded Bell Labs (with Alan Turing & Claude Shannon in their employ) a contract to build a system for encrypted radio calls in 1942, using vinyl records of digitized noise as the one-time-key, employing a source of true entropy and making use of the newly invented vo-coder to minimize the data that needed to be encoded, simultaneously inventing voice compression. The podcast “99% Invisible” has a great episode:

The SIGSALY used the heat of giant vacuum tubes as a source of noise, but I’ve also come across how-to guides for using a reverse-biased zener diode to produce “shot noise”, apparently something to do with total, natural randomness of quantum tunneling, don’t ask me!

A talk on squeezing games into the extreme constraints of the 8 bit Nintendo, including some tiny algorithms to introduce a little entropy to make the game a little less predictable (starting at 19:25). Tetris uses xor + shift on a 16 bit fibonacci sequence. Final Fantasy uses a lookup table of 256 precomputed random values. Contra uses spare cpu cycles to increment a variable that is used whenever a random number is desired.

And of course our man Wolfram figured out you can use Cellular Automata as good sources of entropy (default in mathematica) links thanks to Q&A staff (sorry I missed your name!)

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