Incredibly tough challenges from competitors

I just noticed that the next challenge is TWO WEEKS away. This rightly should be mentioned under the BUGS thread.
Anyway, y’all will probably be bored to tears during the wait, so I will post here an article about Bellaso that
was rejected by the ACA because they said 1. they don’t take anonymous submissions (I refused to give my human
name) and 2. their readers WOULD NOT BE INTERESTED. What?! Yeah, they said that.

The “new” Bellaso cipher
madness
2020-09-17 (and after)

Recently, the original cipher of 1552 by Giovan Battista Bellaso was uncovered in Venice, Italy. It used
the 22-letter Italian alphabet of the time, according to this tableau:

key   plaintext alphabet
   abcdefghilmnopqrstuxyz
 A NOPQRSTUXYZABCDEFGHILM
 E ZNOPQRSTUXYBCDEFGHILMA
 I YZNOPQRSTUXCDEFGHILMAB
 O XYZNOPQRSTUDEFGHILMABC
 U UXYZNOPQRSTEFGHILMABCD
 B TUXYZNOPQRSFGHILMABCDE
 C STUXYZNOPQRGHILMABCDEF
 D RSTUXYZNOPQHILMABCDEFG
 F QRSTUXYZNOPILMABCDEFGH
 G PQRSTUXYZNOLMABCDEFGHI
 H OPQRSTUXYZNMABCDEFGHIL
 L MLIHGFEDCBAZYXUTSRQPON
 M AMLIHGFEDCBYXUTSRQPONZ
 N BAMLIHGFEDCXUTSRQPONZY
 P CBAMLIHGFEDUTSRQPONZYX
 Q DCBAMLIHGFETSRQPONZYXU
 R EDCBAMLIHGFSRQPONZYXUT
 S FEDCBAMLIHGRQPONZYXUTS
 T GFEDCBAMLIHQPONZYXUTSR
 X HGFEDCBAMLIPONZYXUTSRQ
 Y IHGFEDCBAMLONZYXUTSRQP
 Z LIHGFEDCBAMNZYXUTSRQPO

In such a tableau, a plaintext letter is enciphered to the ciphertext letter under it in the row labeled by a
key letter. Key letters are from a keyword, which is the cipher’s key, in a periodic way. We will see an
example shortly, when we encipher a message with a modernized version. Notice that each of the
ciphertext alphabets is reciprocal, i.e., encipherment with any of them is the same as decipherment. The
same is true for each cipher in this paper.

The following year, Bellaso published a revised cipher. He removed the rotated reversed
ciphertext alphabets, leaving eleven. Not to restrict the choice of keyword, he doubled the assignment
of key letters to each alphabet. The new tableau follows.

key    plaintext alphabet                        
    abcdefghilmnopqrstuxyz
A/B NOPQRSTUXYZABCDEFGHILM
C/D TUXYZNOPQRSFGHILMABCDE
E/F ZNOPQRSTUXYBCDEFGHILMA
G/H STUXYZNOPQRGHILMABCDEF
I/L YZNOPQRSTUXCDEFGHILMAB
M/N RSTUXYZNOPQHILMABCDEFG
O/P XYZNOPQRSTUDEFGHILMABC
Q/R QRSTUXYZNOPILMABCDEFGH
S/T PQRSTUXYZNOLMABCDEFGHI
V/X UXYZNOPQRSTEFGHILMABCD
Y/Z OPQRSTUXYZNMABCDEFGHIL

This eleven-alphabet Bellaso cipher of 1553 was incorrectly attributed to Giovanni Battista
della Porta. The modern version, now called the “Porta cipher,” comes in two varieties. Their tableaux
are combined here:

key (version)  plaintext alphabet                       
 1   2  abcdefghijklmnopqrstuvwxyz
A/B A/B NOPQRSTUVWXYZABCDEFGHIJKLM
C/D Y/Z OPQRSTUVWXYZNMABCDEFGHIJKL
E/F W/X PQRSTUVWXYZNOLMABCDEFGHIJK
G/H U/V QRSTUVWXYZNOPKLMABCDEFGHIJ
I/J S/T RSTUVWXYZNOPQJKLMABCDEFGHI
K/L Q/R STUVWXYZNOPQRIJKLMABCDEFGH
M/N O/P TUVWXYZNOPQRSHIJKLMABCDEFG
O/P M/N UVWXYZNOPQRSTGHIJKLMABCDEF
Q/R K/L VWXYZNOPQRSTUFGHIJKLMABCDE
S/T I/J WXYZNOPQRSTUVEFGHIJKLMABCD
U/V G/H XYZNOPQRSTUVWDEFGHIJKLMABC
W/X E/F YZNOPQRSTUVWXCDEFGHIJKLMAB
Y/Z C/D ZNOPQRSTUVWXYBCDEFGHIJKLMA

Let’s work through an example with both versions of the modern Porta cipher. Here is a short
message, which we encipher with the keyword PORTA.

plaintext:   GIOVANNI DELLA PORTA PUBLISHED IN FIFTEEN SIXTY-THREE
key letters: PORTAPOR TAPOR TAPOR TAPORTAPO RT APORTAP ORTAP ORTAP
version 1:   NPGMNGGQ ZRSSV GBKMV GHVSQJUYX QE SPZLNRG LQBGE MPIRY
version 2:   ZOJENHHN URRRS LBLAS LHURNBUXW NJ SOYBVRH MNGGF AZARX

We propose that the original Bellaso 1552 cipher be modernized for use by cryptography
enthusiasts. Expanding the alphabet to include all 26 letters of the modern English alphabet, and
reassigning key letters to the ciphertext alphabets in a methodical order gives us the following tableau.
Notice again how each of the ciphertext alphabets is reciprocal. The full cipher is also reciprocal:
encipherment and decipherment are the same process.

key     plaintext alphabet
   abcdefghijklmnopqrstuvwxyz
 A NOPQRSTUVWXYZABCDEFGHIJKLM
 B ZNOPQRSTUVWXYBCDEFGHIJKLMA
 C YZNOPQRSTUVWXCDEFGHIJKLMAB
 D XYZNOPQRSTUVWDEFGHIJKLMABC
 E WXYZNOPQRSTUVEFGHIJKLMABCD
 F VWXYZNOPQRSTUFGHIJKLMABCDE
 G UVWXYZNOPQRSTGHIJKLMABCDEF
 H TUVWXYZNOPQRSHIJKLMABCDEFG
 I STUVWXYZNOPQRIJKLMABCDEFGH
 J RSTUVWXYZNOPQJKLMABCDEFGHI
 K QRSTUVWXYZNOPKLMABCDEFGHIJ
 L PQRSTUVWXYZNOLMABCDEFGHIJK
 M OPQRSTUVWXYZNMABCDEFGHIJKL
 N MLKJIHGFEDCBAZYXWVUTSRQPON
 O AMLKJIHGFEDCBYXWVUTSRQPONZ
 P BAMLKJIHGFEDCXWVUTSRQPONZY
 Q CBAMLKJIHGFEDWVUTSRQPONZYX
 R DCBAMLKJIHGFEVUTSRQPONZYXW
 S EDCBAMLKJIHGFUTSRQPONZYXWV
 T FEDCBAMLKJIHGTSRQPONZYXWVU
 U GFEDCBAMLKJIHSRQPONZYXWVUT
 V HGFEDCBAMLKJIRQPONZYXWVUTS
 W IHGFEDCBAMLKJQPONZYXWVUTSR
 X JIHGFEDCBAMLKPONZYXWVUTSRQ
 Y KJIHGFEDCBAMLONZYXWVUTSRQP
 Z LKJIHGFEDCBAMNZYXWVUTSRQPO

Here is a short example of the encipherment of a message with this cipher. The keyword is PLAGIA.

plaintext:   BELLASO BEAT YOU TO IT BY ELEVEN YEARS
key letters: PLAGIAP LAGI APL AG IA PL AGIAPL AGIAP
ciphertext:  ATYSSFW QRUB LWF GH NG AJ RSWIKL LYSES

Finally, here are some ciphertexts, in order of increasing difficulty, for interested readers to try
breaking.

CBURTNMJIEUWLLQJIRJAQHXAJFIWNUJHHFNORFTAONJUEQZJJOOXCNPCIWNOKTSNZALPW
PLIXZDWXINAOIGVWSIXIGJASUAMXJKJYIYZAQDGFYJRCGNOIYCTNLTQTAMAEBPAXYHJHH
JMTLNFNUIPZAELTRFPBUNJPNAEODXAXGAOTQEGRMNELLJWOBXAUOTIIWQTYIKTOLXLDGX
BCPARIWDTBSCTNFXLFNMSVEUTHNOKXMNPODACWTBLWUDBSRFNMSXAHOYZOTAGNFTLWNQK
TWJOKXNATUAPWGHAGNYEFFAEUASFLTRJKFAMJNJGRHRZAAGNFEHJASEOUFMDIXKPACJIW
CNURPOSAJ

NQRLBRGNZJRHNADMSJRLVPOGVNFALPLCOKVCRDTHXWFIBITESOSGAPSKCFMKOONNTXRGA
KRCTYUKQCVVLNUBGPBXKKJWXMZZFPNGAZKVLWYGGPHGOQEGRGNDKJCGRBBNAIHLRVBWOA
NSZUPGNQNXNFKIBYBQYAEGFIFHRKSVZGVXTRBKNZVSTOOVFEQONFIGCFSJGJBHSIZWHQB
FBUYBFFBGRRASGDTVHC

NNNNNSTQIZETSOOHNQAGHKHWNQEZPQNEBPIFCWXWEZAPNZTVIFUPDPEBDJGKBURPWAXIR
RAXBYEQJWIRGHSHYRCBYRANGPETNNHQVSJCKDFNINHLVPIFESCZLMCHQRDSTZNDKDUVEW
WCNDASNPMCWZ

AUBGWRVULFIMABSIKJXJFNYJTACHFUQRCFKIATHSFEOYVNQMHUBCRTJRCKKIHGSLRQVHR
SOPXNFTZFIBIBZDAVNFPDOA

TNCTLAIANCNRDIBRRPHUTQBOSGTSKFIARIFABNPCGKJGMXHKCYIRWQGKWTEAPEDYTHYTK
RKJUJEXZAPJEGOLPEWLZQPIXLXFJDFSUBKWTAQMXNDDFKJNLLTPVWLOKDBZAFGJSOMGAP
WNVMRGBFHDBFJOWFUMTIRXIMGKXLTJTPFUANDZBJGMB

References

American Cryptogram Association, The ACA and You, page 68, http://www.cryptogram.org/downloads/aca.info/ciphers/Porta.pdf

Giovan Battista Bellaso, La Cifra del Sig. Giouan Battista Belaso [sic], 1553.

Paolo Bonavoglia, “Bellaso’s 1552 cipher recovered in Venice,” Cryptologia 43:6 (2019) 459-465, doi.org/10.1080/01611194.2019.1596181

Paolo Bonavoglia, “Trithemius, Bellaso, Vigenère: Origins of the Polyalphabetic Ciphers,” Proceedings of the 3rd International Conference on Historical Cryptology, 2020, ep.liu.se/ecp/171/007/ecp2020_171_007.pdf, doi.org/10.3384/ecp2020171007

Augusto Buonafalce, “Bellaso’s Reciprocal Ciphers,” Cryptologia 30:1 (2006) 39-51, doi.org/10.1080/01611190500383581

Johannes Trithemius, Polygraphiae libri sex, Reichenau: Joannis Haselberg de Aia, 1518, http://www.loc.gov/item/32017914

Blaise de Vigenère, Traicté des chiffres ou secrètes manières d’escrire, Paris: Abel l’Angelier, 1586, hdl.handle.net/2027/ien.35552000251008, gallica.bnf.fr/ark:/12148/bpt6k1040608n, gallica.bnf.fr/ark:/12148/bpt6k94009991

NOTE TO HARRY: It should be easy for you to break the ciphertexts, so I don’t need to send the plaintexts.

I’m bored. Here is an interesting cipher:

The Chase cipher is an invention of Pliny Chase from the 1800s. It begins with a 3×10 grid in which
we place the alphabet, mixed perhaps with a keyword. The remaining four spaces are filled with other
symbols; we will use the digits 2, 3, 4, 5 (0 and 1 look too much like O and I).

  0 1 2 3 4 5 6 7 8 9
0 K E Y W O R D 2 A 3
1 B C F G H I J L M 4
2 N P Q S T U V X Z 5

Notice that the table has headings for the 10 digits along the top, and 0, 1, 2 on the side. These are the
coordinates of each character in the grid.

We take our secret message:

THIS MESSAGE WAS ENCRYPTED WITH A CHASE CIPHER

We need to decide on a period. We can take the entire message at one go, or break it into words, or
break it into blocks of the same length. For security, we should either use the entire message at once or
use blocks whose lengths are all the same. For this example, we take blocks of length five, and pad the
last block.

THISM ESSAG EWASE NCRYP TEDWI THACH ASECI PHERX

For each block, we fractionate by writing the coordinates of the letters in two rows, like this:

THISM
21121
44538

We take the bottom row and treat it like an integer; in our case, the integer is 44538. Then we perform
some mathematical operation on that integer. Here there is some flexibility, but both parties to the
message must agree on what operation to use. The only requirement is that it must be reversible, so that
the recipient can decipher the message. For example, we might multiply by 7. Our new set of
coordinates is

021121
311766

Notice that we add a zero to the beginning of the upper row, so that both rows have the same length.
We could add any of 0, 1, or 2, and should choose randomly, for security. The new coordinates are
converted back into characters, according to the table.

021121
311766
WPCLVJ

One possibility for the full ciphertext is

WPCLVJ K3SVAC B3DAP2 BPBDOX Q5EOOI SPGD4M UAPABI B54K35

The Chase cipher is very flexible in how it is set up. The length of the blocks can be changed, as
can the mathematical operation used in the enciphering. With another choice of operation, such as
taking the first few digits of the logarithm after the decimal point, the blocks in the ciphertext can be
the same length as the blocks in the plaintext, rather than requiring the addition of an extra digit, as in
our example.

References

Pliny Earle Chase, “Mathematical Holocryptic Cyphers,” The Mathematical Monthly 1:6 (1859) 194-196,
http://books.google.com/books?id=SVNLAAAAMAAJ&pg=PA194

David Kahn, The Codebreakers: The Story of Secret Writing, New York: Simon & Schuster, 1967,
revised and updated 1996, pages 203-204.

Challenge

This ciphertext was encrypted using multiplication by 7. The leading digit for the top row was always
chosen randomly. Plaintext blocks are 5 letters; ciphertext blocks are 6. I have no idea if it is
possible to break it. If you do it, please report how. All glory to the one who succeeds.

U5EFA3 KEBPU4 AVMIJM KIGBJU UOHKI3 2UUIFE 2AHIUP WTORBU UUJAK4 V5EFA3 2AJTMA DXXLBY
MOIFMC BUTOJM DBTPUP V2BGKI IHQTOR NKODQI DSSGBG ZCALQI UIFMGS NCHTAO GGINIS VOHPIO
ZLIPAR NKODQI ASWFAS JUTAHY TBGNTH DQTBAG GUENJB AEB2NI YJSTBU XTRIQI V2FUBY KEFUWI
AGBPLY JOIG2F DUBINI NRATVM GUGTIF NAJTOH MRAVMA NCBMTR ZOTWHE NAHMSA IQIAYG GTIKIG
VK2PAG GSTBBG SYTNTH VIFUIE WLRUFU WSTPTS ALZIGE 2TRUU4 MIPJUU SENKIG VKINIS GBLAIF
DMNTSL SZIJIG DBMAIF 2AIGDL DWAPTA ZMIVMA JAOTWF OMAHMS WUQINI NBTUHM 2NWREM VITRLM
GPTHMG YINDOT MJDBOE BIWURF GT2COO GHIJFU 2JBUNT VI5INI 2RATSA GNIADA MGJJTY U4OIFS
WOEMJ4 IBTUHM NPLIWU SQINLY GLPCJT YHHTKE NAHMMG AF4OIF SWOCOO WGUQQI AVCLWI IK52NI
IRATSA JPE3EI BMBAHM VEBOLM GUSEKJ ZIVMWU OOLIKT YHNUQM WNLIKT YHJVIF DUIET4 MAIGBG
NAIHIF IUOONF FIUQ2F AUIFAS MUTAGD GBPL2F IAJBPI DZJIOK AWTFIG 2CQIAS YIHRFU TSTKEA
NBKIPI NK4MGD MIGDLS WAK5IF ITRTBU XOIVUR SBHEMM VOQEUP AIBBCD OOLMMC BOEOWU 2JIUQY
TLPCJT JH2KEO THDQIA VMPIMM GLPLIS F4LOCD 2POWIA FYT5IF BEARUI DVINIP ZUOSTH DVINCB
YEHDSA MGFINI GDRTAG VFEACD ASMGFM WFUBIF NAH5IS GFBMUF DUWIUY GLPCNO WMOFUS ZIGURE
KLMBUE AIBKIG ZISMGD TFCEMG TEIBKT YPIV4T UIFBOC WUQIFA VETGBG WTMTDH ITAOIF MIKNIF
SUBUNC KISV5I ORJT2E GLQIOB TUEIEA 2BKIPI ASMGFM TPAEHL AZLUNC ZISV5I MALBCI 2JUGKI
2HVMMG AFINEE NTBFMG MEOBOR TLJEMU YJTGOT VGESTO AMNJTM TFUWLM WNLEME BLILAG ODO5IF
ZEARUI ASMGFM WNCCEH ADSMGD FINLFC WOSTHS SMGFIF ZEDRUI YHFEAC SDWXXV

@Cribbage, all correct; well done. For #3, your method is the same way I do them.