Jarl Van Eycke solves 400 year old longitude message

A Belgian scholar proposed a potentially revolutionary navigation method 400 years ago. He encoded the description. Jarl Van Eycke, who had previously been involved in solving the Zodiac Killer message, was now able to decipher it.

English version (translated with DeepL)

Let me briefly mention at the beginning that the U.S. Cyber Command has published some nice crypto puzzles for Valentine’s Day. There is nothing to win, but at least you can check a found solution immediately. If anyone is into it, feel free to give a short feedback when you get a chance.

The Langrenus method

But now to the actual topic. In 2015, I came across a fascinating crypto puzzle that had not been mentioned in the crypto literature until then. It involves an encrypted text written by the Belgian scholar Michael Florent van Langren (1598-1675).

Van Langren (also known as Langrenus) proposed in 1644 a method by which the crew of a ship at sea could determine longitude. Anyone who has read the book “Longitude” by Dava Sobel knows what this means. While it was already quite easy to determine the latitude of the current position by the position of the sun, the determination of the longitude on the sea was only possible very inaccurately for centuries. This led time and again to catastrophic navigational errors.

The seafaring nations therefore desperately searched for a suitable longitude method and offered high rewards. It was not until the middle of the 18th century that a workable method was finally developed. It required a clock accurate to the second, which could be built for the first time at that time.

Van Langren was also concerned with this issue and proposed at least two methods for determining longitude. The first one dates back to 1644 and is based on a precise observation of the lunar surface. If the method had worked, the Belgian would undoubtedly have gone down in history with it. But it did not, and van Langren merely added to the long list of longitude errors.

Nevertheless, together with his method, van Langren presented the earliest known statistical graph. It shows the distances of various cities between the prime meridian (which at that time ran through Toledo in Spain) and Rome.

Quelle/Source: DataVis

The Langrenus cryptogram

Van Langren’s second method for determining longitude is mentioned on the web page I came across in 2015. Van Langren communicated it to the Spanish royal court in a coded letter (I use the term “Langrenus cryptogram” for it). This letter has been preserved, but it was unsolved until recently.

Quelle/Source: DataVis

Although this is an extremely exciting historical crypto puzzle, it has never been covered in the crypto literature to my knowledge. I admit that I have also only blogged about it twice myself, without really realizing its significance. Actually, this cryptogram should have been on my top 50 list.

Jarl Van Eycke

A few weeks ago I received an email from Jarl Van Eycke. Jarl is one of the three codebreakers who solved the second Zodiac message last year – from my point of view the greatest non-military deciphering success in crypto history.

Quelle/Source: Van Eycke

Jarl Van Eycke (39) comes from Flanders in Belgium. Originally trained as a graphic designer, he now works for a logistics provider, where he mainly deals with the automotive industry. He has been interested in cryptography since 2014, when he first tried to solve the second Zodiac message – which led to success years later. Jarl also holds the world record (along with Louie Helm) for the shortest bigram substitution message solved.

Jarl is also the author of AZdecrypt, a fast and powerful program that solves homophonic encryption. AZdecrypt played an important role in deciphering the said Zodiac cryptogram.

No question, Jarl Van Eycke is a world-class codebreaker.

The solution

Jarl informed me in his mail that he had now also solved the Langrenus cryptogram. His solution was already presented on a Belgian news portal. Thankfully he sent me a detailed description of the solution. My blog is thus the first crypto publication to report on it.

Jarl’s solution path started with a tanscription of the cryptogram:

ImieV9 ap3Apa Ihrr5e tlSmeIf9 5lesEortEr 5e eadnu9c Rtl9e9T omgupea Nſnnd cAlveMa
dfneagL p9rIir5 rEant tdTeo9Im nc5T9t noqCtuN veroQn nnmEef alarRl 9kIe raIman
Me4tn eqtIu u4xV eu ulriqDa ſuVne etſelId ſe5tſ couAu 9ſ9Vldu lir5te Tce4o vEe7oſnE
i5uameg Ebſe lodRa 9ebtſl Sa95u rVcmai AenprIt a9dL3do9 9nRt e3enqQe cun5ef
Etſot dEr 5emus Oeacdſae 5ucſoMe e9lrrI9 acnuoEd umr92 L5d9a5 eI9cnai dnneNt t4pAIeai
gPrmrO e5e VnſzbmF oaenſeS5 uſlOnt teoDe p9noIl l9lo Enen trEge59 cut To 9uned
V9neq ItduLau Deum NamDe nEerEmſ9 9LmdVl eR99mEe e5nOu rdTd9 oOedu
I9oVa5 nqnp ntEaE eerlVrt lLrT9 5etoſ Y9ntl Sfrnae eG9a6 rſaiIau uulAnoTtp 9qVe ruIcſeT
t9pOu erE9 leLſln Ecedo EſrNn eMeſu 3Nove Ar9ſ VmdtS qcVeueEd oVn9nufu R9fenPe
utrTl 5eAten Aftca qTe9u prSa a5trOl rle5ef hRſ95 eDluſ Iert5 eoVa ſ9qc lS u elalet
eſ9Oſd qtuuef eſ9pero tmuaaru mumeuen yſtdm aeeuNr 9tlne eſnmſt pTdaſ 9n3t taMe
qnſutu euDalnſa depesE rſeedtm9 l9tVe5e ſrſaeu H9uia aſnſet tReſrc ſe eomſ9p ſtAle v9du
Qdc95 3dLloe eu5ale uea4Rrfe ſ9l5na4 dAme 5nnr neoeſR nrtcaro oe7uſOn uuoer9r pſtc
tEn9e rnresEa aoplna afrſa lSe9 Eecrſoae nTfſ4l teoolLt 9atlq elnr eeuſlCn elune e3frLo 97mneb
9tE9r teaena aduNue ſ4tſ9Ve ytm ccpaNe ſnled9 lCln ladXedr ſS9eſ tſe5u uepuIſ p9todNo
re9tnl etlpLe eaeſ rqeEurua aeE9alau qCnmu te5Snſ lom9t Ce5em gRoeenr dPl9ea
dNq9 9nTſeos nyMed 4ru9al ec9uoeE Inuold ue uurdeD

Jarl noticed that the words are too long compared to an unencoded text and that the word lengths differ too little. The most likely explanation seemed to him to be that the spaces have no meaning. He therefore omitted the blanks.

Jarl suspected, based on the letter frequencies, that he was dealing with a transposition cipher. He ran tests for periodic transpositions (using trigram frequencies as a criterion), but to no avail.

Jarl now tested whether removing certain symbols improved the trigram statistics. Capital letters proved to be the best candidates. Without spaces and capital letters, the message looked like this:

mie9ap3pahrr5etlmef95lesortr5eeadnu9ctl9e9omgupeaſnndclveadfneagp9rir5r
anttdeo9mnc59tnoqtuveronnnmefalarl9keramane4tneqtuu4xeuulriqaſuneetſeld
ſe5tſcouu9ſ9ldulir5tece4ove7oſni5uamegbſeloda9ebtſla95urcmaienprta9d3do
99nte3enqecun5eftſotdr5emuseacdſae5ucſoee9lrr9acnuodumr925d9a5e9cnaidnn
ett4peaigrmre5enſzbmoaenſe5uſlntteoep9noll9lonentrge59cuto9uned9neqtdua
ueumamenermſ99mdle99mee5nurdd9oedu9oa5nqnpntaeerlrtlr95etoſ9ntlfrnaee9a
6rſaiauuulnotp9qerucſet9puer9leſlncedoſrneeſu3over9ſmdtqceuedon9nufu9fe
neutrl5etenftcaqe9upraa5trlrle5efhſ95eluſert5eoaſ9qcluelaleteſ9ſdqtuuef
eſ9perotmuaarumumeuenyſtdmaeeur9tlneeſnmſtpdaſ9n3ttaeqnſutueualnſadepes
rſeedtm9l9te5eſrſaeu9uiaaſnſetteſrcſeeomſ9pſtlev9dudc953dloeeu5aleuea4r
feſ9l5na4dme5nnrneoeſnrtcarooe7uſnuuoer9rpſtctn9ernresaaoplnaafrſale9ec
rſoaenfſ4lteoolt9atlqelnreeuſlnelunee3fro97mneb9t9rteaenaaduueſ4tſ9eytm
ccpaeſnled9llnladedrſ9eſtſe5uuepuſp9todore9tnletlpeeaeſrqeuruaae9alauqn
mute5nſlom9te5emgoeenrdl9eadq99nſeosnyed4ru9alec9uoenuoldueuurde

Now Jarl found that meaningful words were created by reading only every third letter:

m93h5lflorenc9ouanlangr5nd9ctqvonfa9ra4euxui?e?d5cu9ure4e?5mblabl5cipa3
9teenformedecel9ndr5a9antpim5?mee?to9ller5u9entaume?mem5r9donpart9t9lne
6aultqueprendre3e?ted9fferenceparle?e?to9lle?duf9rmamentautentantquelap
rem95reua?trempl9d5leau4elamnneraouuertnreala?econ4elaqnellef9n9raau??y
candlad9t5e?to9lle?euelqu5l95gedeqnoy49eunleriaprem9er5autemp?dvdepirte
m5ntenmarkantquelquee?to9ll5co7nue?o9taumer9d9enc5tt5ua?5?erauu9d5cinte
grezon5ltenlong9tudedumer9d9endouaqnell5onfa9riunpectu9?con?ormquonueul
tfa9r5lef9le5aquat9quepouruuyderlemp?3antunde?d9te?ui?eece??edc3ouler?5
4ene?tre?urpc9nsonfa9raflotterunuer7etteau49tcel9ndre?upporteparua9antn
oteonla9?seracoududeparte5sted9l9gencefa9raton9ournellement4urantle?u?d
itevoiagede?9rantdon3que?descauo9rcom29ende4arenba?unepo9ntecon9queanm9
l9eude95nterre?trea?auo9r?9elle?euv9dcenu9nt5etquatr5h5ure?cele?te?etau
me?me9n??d9te?ua?esetle?a9ant??o9tvu9de5eaf9nd5ronco7no9?teraparle?e?to
9lle?en3omb9endetemp?elle??euu9denteeqraaume?memer9d9endul9eouue

If you number each letter in the original text (without capital letters and spaces), then the following is the order in which you must put the letters:

1 330 659 2 331 660 3 332 661 4 333 662 5 334 663 6 335 664 7 336 665 8 337 666 9 338 667 10 339 668 11 340 669 12 341 670 13 342 671 14 343 672 15 344 673 16 345
674 17 346 675 18 347 676 19 348 677 20 349 678 21 350 679 22 351 680 23 352 681 24 353 682 25 354 683 26 355 684 27 356 685 28 357 686 29 358 687 30 359 688 31 360 689 32
361 690 33 362 691 34 363 692 35 364 693 36 365 694 37 366 695 38 367 696 39 368 697 40 369 698 41 370 699 42 371 700 43 372 701 44 373 702 45 374 703 46 375 704 47 376 705
48 377 706 49 378 707 50 379 708 51 380 709 52 381 710 53 382 711 54 383 712 55 384 713 56 385 714 57 386 715 58 387 716 59 388 717 60 389 718 61 390 719 62 391 720 63 392
721 64 393 722 65 394 723 66 395 724 67 396 725 68 397 726 69 398 727 70 399 728 71 400 729 72 401 730 73 402 731 74 403 732 75 404 733 76 405 734 77 406 735 78 407 736 79
408 737 80 409 738 81 410 739 82 411 740 83 412 741 84 413 742 85 414 743 86 415 744 87 416 745 88 417 746 89 418 747 90 419 748 91 420 749 92 421 750 93 422 751 94 423 752
95 424 753 96 425 754 97 426 755 98 427 756 99 428 757 100 429 758 101 430 759 102 431 760 103 432 761 104 433 762 105 434 763 106 435 764 107 436 765 108 437 766 109 438 767 110 439
768 111 440 769 112 441 770 113 442 771 114 443 772 115 444 773 116 445 774 117 446 775 118 447 776 119 448 777 120 449 778 121 450 779 122 451 780 123 452 781 124 453 782 125 454 783 126
455 784 127 456 785 128 457 786 129 458 787 130 459 788 131 460 789 132 461 790 133 462 791 134 463 792 135 464 793 136 465 794 137 466 795 138 467 796 139 468 797 140 469 798 141 470 799
142 471 800 143 472 801 144 473 802 145 474 803 146 475 804 147 476 805 148 477 806 149 478 807 150 479 808 151 480 809 152 481 810 153 482 811 154 483 812 155 484 813 156 485 814 157 486
815 158 487 816 159 488 817 160 489 818 161 490 819 162 491 820 163 492 821 164 493 822 165 494 823 166 495 824 167 496 825 168 497 826 169 498 827 170 499 828 171 500 829 172 501 830 173
502 831 174 503 832 175 504 833 176 505 834 177 506 835 178 507 836 179 508 837 180 509 838 181 510 839 182 511 840 183 512 841 184 513 842 185 514 843 186 515 844 187 516 845 188 517 846
189 518 847 190 519 848 191 520 849 192 521 850 193 522 851 194 523 852 195 524 853 196 525 854 197 526 855 198 527 856 199 528 857 200 529 858 201 530 859 202 531 860 203 532 861 204 533
862 205 534 863 206 535 864 207 536 865 208 537 866 209 538 867 210 539 868 211 540 869 212 541 870 213 542 871 214 543 872 215 544 873 216 545 874 217 546 875 218 547 876 219 548 877 220
549 878 221 550 879 222 551 880 223 552 881 224 553 882 225 554 883 226 555 884 227 556 885 228 557 886 229 558 887 230 559 888 231 560 889 232 561 890 233 562 891 234 563 892 235 564 893
236 565 894 237 566 895 238 567 896 239 568 897 240 569 898 241 570 899 242 571 900 243 572 901 244 573 902 245 574 903 246 575 904 247 576 905 248 577 906 249 578 907 250 579 908 251 580
909 252 581 910 253 582 911 254 583 912 255 584 913 256 585 914 257 586 915 258 587 916 259 588 917 260 589 918 261 590 919 262 591 920 263 592 921 264 593 922 265 594 923 266 595 924 267
596 925 268 597 926 269 598 927 270 599 928 271 600 929 272 601 930 273 602 931 274 603 932 275 604 933 276 605 934 277 606 935 278 607 936 279 608 937 280 609 938 281 610 939 282 611 940
283 612 941 284 613 942 285 614 943 286 615 944 287 616 945 288 617 946 289 618 947 290 619 948 291 620 949 292 621 950 293 622 951 294 623 952 295 624 953 296 625 954 297 626 955 298 627
956 299 628 957 300 629 958 301 630 959 302 631 960 303 632 961 304 633 962 305 634 963 306 635 964 307 636 965 308 637 966 309 638 967 310 639 968 311 640 969 312 641 970 313 642 971 314
643 972 315 644 973 316 645 974 317 646 975 318 647 976 319 648 977 320 649 978 321 650 979 322 651 980 323 652 981 324 653 982 325 654 983 326 655 984 327 656 985 328 657 986 329 658 987

Now Jarl replaces the numbers by letters (1=a, 2=b, …, 9=i). Then the following plain text resulted:

michelflorenciouanlangrendictqvonfairadeuxuiſeſdecuiuredeſemblablecipac
iteenformedecelindreaiantpimeſmeeſtoillereuientaumeſmemeridonpartitilne
6aultqueprendreceſtedifferenceparleſeſtoilleſdufirmamentautentantquelap
remiereuaſtremplideleaudelamnneraouuertnrealaſecondelaqnellefiniraauſſy
candladiteeſtoilleſeuelqueliegedeqnoydieunleriapremiereautempſdvdepirte
mentenmarkantquelqueeſtoilleco7nueſoitaumeridiencetteuaſeſerauuidecinte
grezoneltenlongitudedumeridiendouaqnelleonfairiunpectuiſconſormquonueul
tfairelefileeaquatiquepouruuyderlempſcantundeſditeſuiſeeceſſedccoulerſe
deneſtreſurpcinsonfairaflotterunuer7etteauditcelindreſupporteparuaiantn
oteonlaiſseracoududeparteestediligencefairatoniournellementdurantleſuſd
itevoiagedeſirantdoncqueſdescauoircom2iendedarenbaſunepointeconiqueanmi
lieudeienterreſtreaſauoirſielleſeuvidcenuinteetquatreheureſceleſteſetau
meſmeinſſditeſuaſesetleſaiantſſoitvuideeeafinderonco7noiſteraparleſeſto
illeſencombiendetempſelleſſeuuidenteeqraaumeſmemeridiendulieouue

The plaintext

According to Jarl, the plain text says the following:

Michel Florencio van Langren says that one should make two cylindrical copper vessels of equal volume that have a cone-shaped end at the bottom, in which a hole is made in the middle so that when they are filled with seawater, they let a line of water run until they are empty. The stars know in how much time they must be empty.

When this is noted, the first barrel is run at departure, while recording which known star is on the meridian. This vessel will be empty when this star is back on the same Earth meridian, knowing that it is empty in 24 hours of sidereal time. At the same time as when the first vessel stops flowing, the second vessel opens, which will also be empty when the said star is back on the meridian of departure.

This careful operation will be done daily during the voyage mentioned here if one wishes to know how many degrees of longitude one has traveled from the meridian of departure. One has only to determine this difference from the stars in the sky each time one of the vessels is empty. In order not to be surprised, a cylindrical float floating on cork is applied to indicate.

If I understand correctly, two copper vessels are used here, which are filled with water. The vessels each have a hole through which the water can escape. The time that passes until one vessel is empty is used to measure time.

Did I understand this correctly? Can any reader say if this method works?

Another question: are the capital letters just meaningless filler or do they also encode a message?

In any case, I heartily congratulate Jarl on his recent success! I am more than impressed!

Let’s see if historians can also do something with the new findings.

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