# Polyphonic Substitution in Italian Numerical Ciphers

A polyphonic substitution cipher uses a single symbol for more than one plaintext letters. This means a plaintext letter is not uniquely determined for a given symbol and it would seem that even an authentic recipient has difficulty in deciphering. This is in contrast to homophonic substitution, which provides more than one cipher symbols for one plaintext letter and thus makes it harder for a third party to decipher without a key but leaves no ambiguity for the proper addressee who has the key.

Despite such an apparent disadvantage, many polyphonic substitution ciphers are recorded in the 16th-century Italian ciphers, in particular, papal numerical ciphers (Meister p.47, p.57 etc.). Polyphonic substitution is seen as early as 1538-1542 (Meister p.176) and as late as 1585 (Meister p.345). At least two were given out in June 1585 by Giovanni Battista Argenti (Meister p.345, 350; the latter provides for dots for avoiding ambiguity; see the next section), cipher secretary of Sixtus V from April 1585 to April 1591 (Meister p.51). It appears the polyphonic cipher fell into disuse soon after Argenti came into office. The ciphers sent by Argenti subsequently were regular homophonic substitution ciphers (ibid. p.353, 358, 361, 365, 369, 370, 375, 379, etc.).

The present article presents some examples of such polyphonic substitution ciphers. (For other historical examples of polyphonic ciphers, see another article.)

## Distinction by Diacritics

Meister describes that some ciphers employed by Gianbattista Argenti under Pope Sixtus V (1585-1590) avoided ambiguity by use of diacritics (Meister p.71-72). (That is, it is not truly polyphonic.) In particular, when a figure is used without a mark, the more frequent letter is meant, while the less frequent letter is indicated by the figure with a mark (a dot over or below the figure).

 Null: 9 ad ef ig op ut sr lm nb cxz 1 3 4 2 5 6 7 8 0
(In the following, the apostrophe (') indicates a dot over the preceding digit.) 4792'12'1952739'028636'516'397192'1039584536'6177'385'3932'36'3
91'3641'36'190395'55'49742'6'48042'471028636'548292'36'98'3833'45'
4292'58'7402

PLAINTEXT
Il papa vole conservare la pace universalmente e per[o] desidera c[h]e t[u][t]ti li principi la conservino per benefitio publico

DUMP
4(i) 7(l) 9(-) 2'(p) 1(a) 2'(p) 1(a) 9(-) 5(u) 2(o) 7(l) 3(e) 9'(-) 0(c) 2(o) 8(n) 6(s) 3(e) 6'(r) 5(v) 1(a) 6'(r) 3(e) 9(-) 7(l) 1(a) 9(-) 2'(p) 1(a) 0(c) 3(e) 9(-) 5(u) 8(n) 4(i) 5(u) 3(e) 6'(r) 6(s) 1(a) 7(l) 7'(m) 3(e) 8(n) 5'(t) 3(e) 9(-) 3(e) 2'(p) 3(e) 6'(r) 3(e[o])
9(-) 1'(d) 3(e) 6(s) 4(i) 1'(d) 3(e) 6'(r) 1(a) 9(-) 0(c) [h] 3(e) 9(t) 5'([u]) 5([t]) 5'(t) 4(i) 9(-) 7(l) 4(i) 2'(p) 6'(r) 4(i) 8(n) 0(c) 4(i) 2'(p) 4(i) 7(l) 1(a) 0(c) 2(o) 8(n) 6(s) 3(e) 6'(r) 5(u) 4(i) 8(n) 2(o) 9(-) 2'(p) 3(e) 6'(r) 9(-) 8'(b) 3(e) 8(n) 3(e) 3'(f) 4(i) 5'(t) 4(i) 2(o) 9(-) 2'(p) 5(u) 8'(b) 7(l) 4(i) 0(c) 2(o)

Meister p.350-352 provides a full version of this cipher with a nomenclator (i.e., a code portion or vocabulary portion) consisting of three-figure symbols. One of the two examples given in the cipher --7(m)2(o)8(n)6(r)3(e)1(a)7(l)3(e)-- uses dots under figures for "m" and "r" to indicate the less frequent letter. In the other example, dots over figures are used to indicate that the following three figures form a symbol of the nomenclator (see another article for such a usage of dots).

## True Polyphonic Ciphers

Even when diacritics are not used, it appears care was taken so that one of the letters represented by a figure is a frequently used one. In particular, vowels are always represented by different figures.

### Anonymous (1586?)

One of the simplest is as follows (Meister p.255).

 at ef ig ol up bdz mhq ncx rs 6 1 3 2 4 5 7 9 8

As the instruction for this cipher notes, "putato" is enciphered as "44666."

4286868339283632486838376868681843665374696276927695662

PLAINTEXT
Vostra Signoria illustrissima sara servita di quanto m[i] [h]a comandato

DUMP
4(u) 2(o) 8(s) 6(t) 8(r) 6(a) 8(s) 3(i) 3(g) 9(n) 2(o) 8(r) 3(i) 6(a) 3(i) 2(l) 4(u) 8(s) 6(t) 8(r) 3(i) 8(s) 3(i) 7(m) 6(a) 8(a) 6(a) 8(r) 6(a) 8(s) 1(e) 8(r) 4(u) 3(i) 6(t) 6(a) 5(d) 3(i) 7(q) 4(u) 6(a) 9(n) 6(t) 2(o) 7(m) 6(a) 9(c) 2(o) 7(m) 6(a) 9(n) 5(d) 6(a) 6(t) 2(o)

### Bishop of Fano (1550)

That a polyphonic cipher was actually used without diacritics can be seen in letters of Pietro Bertano, Bishop of Fano, to Antoine Perrenot de Granvelle, bishop of Arras and a trusted adviser for Emperor Charles V, dated Rome, 14 November and 11 December 1550 (Bertomeu Masiá (2009) p.165). The following is from the postscript of the first letter. (A letter of 22 January 1551 of the same correspondents used a different key not yet reconstructed (Bertomeu Masiá p.166).)

tt36133743224568318341568633916336839325653111[.........]
155636637432922328214114961pp332825613417292132819[......]
24543822127633415643329833441916414566137639483[.........]
565313711384914tt314523747831161281282212538432254[......]
19823256542114163ttpp149614354554112834622693395314[........]
6613391621395238232382329137374322369139123742494[.....]
377332937126294pp8417213721271122316141914212374547tt[........]
3162312568392698392222432952263391621413ttpp
678311612547695415314pp812822125382926692186676924[.....]
8611221286368814226294t37414967656913et....

PLAINTEXT (largely based on Bertomeu Masiá (2009))
Circa le cose di Parma et di Piac[e]nza non manc[h]o di far[e] tu[tti quelli]
ufficii che conosco poter[e] venir[e] a comodita et honor com[m]un[e della]
Sede Apostolica et di Sua Mta Cesarea con pace et quiete di Italia ne ma[ncharo mai]
di far[e] altr[i]mente.
Credo che [i]l partito proposto da me a V.S.Rma de[bba, con]
un poco di destrez[z]a, venire ad effetto ma bisogna andare [piano per]
gir[e] acquistando a poco a poco qualche cosa, intanto che se ne [venga]
alla conclusione.
Per hora ho voluto scriver[e] questo che del [restante]
avisaro di mano in mano V.S.Rma secondo si acquist[a]ra.
Il partito del infeudare proposto da Monsignor Pighino e [stato]
piu tosto mia impressione che venghi di qua, et ....

DUMP
tt(-) 3(c) 6(i) 1(r) 3(c) 3(a) 7(l) 4(e) 3(c) 2(o) 2(s) 4(e) 5(d) 6(i) 8(p) 3(a) 1(r) 8(m) 3(a) 4(e) 1(t) 5(d) 6(i) 8(p) 6(i) 3(a) 3(c) [e] 9(n) 16(z) 3(a) 36(non) 8(m) 3(a) 9(n) 3(c) [h] 2(o) 5(d) 6(i) 5(f) 3(a) 1(r) [e] 1(t) 1(u) [...]
1(u) 5(f) 5(f) 6(i) 3(c) 6(i) 6(i) 3(c) 7(h) 4(e) 3(c) 2(o) 9(n) 2(o) 2(s) 3(c) 2(o) 8(p) 2(o) 1(t) 4(e) 1(r) [e] 1(v) 4(e) 9(n) 6(i) 1(r) [e] pp(-) 3(a) 3(c) 2(o) 8(m) 2(o) 5(d) 6(i) 1(t) 3(a) 4(e) 1(t) 7(h) 2(o) 9(n) 2(o) 1(r) 3(c) 2(o) 8(m) [m] 1(u) 9(n) [...]
2(s) 4(e) 5(d) 4(e) 3(a) 8(p) 2(o) 2(s) 1(t) 2(o) 7(l) 6(i) 3(c) 3(a) 4(e) 1(t) 5(d) 6(i) 43(Sua Mta Cesarea) 3(c) 2(o) 9(n) 8(p) 3(a) 3(c) 4(e) 4(e) 1(t) 9(q) 1(u) 6(i) 4(e) 1(t) 4(e) 5(d) 6(i) 6(i) 1(t) 3(a) 7(l) 6(i) 3(a) 9(n) 4(e) 8(m) 3(a) [...]
5(d) 6(i) 5(f) 3(a) 1(r) [e] 3(a) 7(l) 1(t) 1(r) 3[i?] 8(m) 4(e) 9(n) 1(t) 4(e) tt(-) 3(c) 1(r) 4(e) 5(d) 2(o) 3(c) 7(h) 4(e) [i] 7(l) 8(p) 3(a) 1(r) 1(t) 6(i) 1(t) 2(o) 8(p) 1(r) 2(o) 8(p) 2(o) 2(s) 1(t) 2(o) 5(d) 3(a) 8(m) 4(e) 3(a) 22(V.S.Rma) 5(d) 4(e) [...]
1(u) 9(n) 8(p) 2(o) 3(c) 2(o) 5(d) 6(i) 5(d) 4(e) 2(s) 1(t) 1(r) 4(e) 16(z) [z] 3(a) tt(-) pp(-) 1(v) 4(e) 9(n) 6(i) 1(r) 4(e) 3(a) 5(d) 4(e) 5(f) 5(f) 4(e) 1(t) 1(t) 2(o) 8(m) 3(a) 4(b) 6(i) 2(s) 2(o) 6(g) 9(n) 3(a) 3(a) 9(n) 5(d) 3(a) 1(r) 4(e) [...]
6(g) 6(i) 1(r) [e] 3(a) 3(c) 9(q) 1(u) 6(i) 2(s) 1(t) 3(a) 9(n) 5(d) 2(o) 3(a) 8(p) 2(o) 3(c) 2(o) 3(a) 8(p) 2(o) 3(c) 2(o) 9(q) 1(u) 3(a) 7(l) 3(c) 7(h) 4(e) 3(c) 2(o) 2(s) 3(a) 6(i) 9(n) 1(t) 3(a) 9(n) 1(t) 2(o) 3(c) 7(h) 4(e) 2(s) 4(e) 9(n) 4(e) [...]
3(a) 7(l) 7(l) 3(a) 3(c) 2(o) 9(n) 3(c) 7(l) 1(u) 2(s) 6(i) 2(o) 9(n) 4(e) pp(-) 8(p) 4(e) 1(r) 7(h) 2(o) 1(r) 3(a) 7(h) 2(o) 1(v) 2(o) 7(l) 1(u) 1(t) 2(o) 2(s) 3(c) 1(r) 6(i) 1(v) 4(e) 1(r) [e] 9(q) 1(u) 4(e) 2(s) 1(t) 2(o) 3(c) 7(h) 4(e) 5(d) 4(e) 7(l) tt [...]
3(a) 1(v) 6(i) 2(s) 3(a) 1(r) 2(o) 5(d) 6(i) 8(m) 3(a) 9(n) 2(o) 6(i) 9(n) 8(m) 3(a) 9(n) 2(o) 22(V.S.Rma) 2(s) 4(e) 3(c) 2(o) 9(n) 5(d) 2(o) 2(s) 6(i) 3(a) 3(c) 9(q) 1(u) 6(i) 2(s) 1(t) 4[a?] 1(r) 3(a) tt(-) pp(-)
6(i) 7(l) 8(p) 3(a) 1(r) 1(t) 6(i) 1(t) 2(o) 5(d) 4(e) 7(l) 6(i) 9(n) 5(f) 4(e) 1(u) 5(d) 3(a) 1(r) 4(e) pp(-) 8(p) 1(r) 2(o) 8(p) 2(o) 2(s) 1(t) 2(o) 5(d) 3(a) 8(m) 2(o) 9(n) 2(s) 6(i) 6(g) 9(n) 2(o) 1(r) 8(p) 6(i) 6(g) 7(h) 6(i) 9(n) 2(o) 4(e) [...]
8(p) 6(i) 1(u) 1(t) 2(o) 2(s) 1(t) 2(o) 8(m) 6(i) 3(a) 6(i) 8(m) 8(p) 1(r) 4(e) 2(s) 2(s) 6(i) 2(o) 9(n) 4(e) t(-) 3(c) 7(h) 4(e) 1(v) 4(e) 9(n) 6(g) 7(h) 6(i) 5(d) 6(i) 9(q) 1(u) 3(a) et ....

A cipher given to the Bishop of Fano, nuncio to the Emperor, and the Bishop of Aiaccio is similar to this cipher (Meister p.178).

### Camillo Capozucca in Flanders (1579)

(Meister p.296)

 ab em id of ul ng mp rt szc Nulla 0 2 7 3 5 9 4 8 6 1 qua que qui quo che chi non 50 30 40 29 28 02 03
858871306871434557172677280931...

PLAINTEXT
Tutti questi populi desiderano [ritornare alla ubidienza et in breve restaranno tutte queste piazze nette.]

8(t)5(u)8(t)8(t)7(i)1(-)30(que)6(s)8(t)7(i)1(-)4(p)3(o)4(p)5(u)5(l)7(i)1(-)7(d)2(e)6(s)7(i)7(d)2(e)8(r)0(a)9(n)3(o)1(-)...

### Cardinal Savello (1)

The following is a cipher of Cardinal Savello (Meister p.200).

### Cardinal Savello (2)

The following is another cipher of Cardinal Savello (Meister p.200).

57736881838146s1170663466

PLAINTEXT
Il Cardinale si aspetta a Roma.

DUMP
57(il) 7(C) 36(ar) 8(d) 8(i) 18(na) 38(le) 14(si) 6(a) s(9) 11(p) 7(e) 0(t) 6(a) 6(a) 34(Ro) 6(m) 6(a)

### Cardinal Savello (3) (1583)

The following is part of a cipher (Meister p.297) given to Costa, Inquisitor in Malta , by the order of Cardinal Savello in Rome in 1583.

An example in this cipher is as follows.

(In the following, the apostrophe (') indicates a dot over the preceding letter.)
170748295827449'906.6859727994075638264975644170128274'29665
52749855.6149825294'670443752848670596018670456329364+98274859
174'9656671644998'83.64140'380682749951826470094995906629841'2.7560
08416259274143.6

PLAINTEXT
Sono arivato qui in Malta ali oto di Novembre dove son stato ricevuto dal Gran Mastro et da tuti con molta acoglienza con le prime daro aviso dele cose di qua a V.S. Illma et non mancaro di usare ogni diligentia perche Nostro Signore venga servito et V.S.Illma.

DUMP
1(s) 7(o) 0(n) 7(o) 4(-) 8(a) 2(r) 9(i) 5(u) 8(a) 2(t) 7(o) 4(-) 4(-) 9'(qui) 9(i) 0(n) 6.6(Malta) 8(a) 5(l) 9(i) 7(o) 2(t) 7(o) 9(d) 9(i) 4(-) 0(n) 7(o) 5(u) 6(e) 3(m) 8(b) 2(r) 6(e) 4(-) 9(d) 7(o) 5(u) 6(e) 4(-) 4(-) 1(s) 7(o) 0(n) 1(s) 2(t) 8(a) 2(t) 7(o) 4'(-) 2(r) 9(i) 6(c) 6(e) 5(u) 5(u) 2(t) 7(o) 4(-) 9(d) 8(a) 5(l) 5.6(Gran Mastro) 1(et) 4(-) 9(d) 8(a) 2(t) 5(u) 2(t) 9(i) 4'(-) 6(c) 7(o) 0(n) 4(-) 4(-) 3(m) 7(o) 5(l) 2(t) 8(a) 4(-) 8(a) 6(c) 7(o) 0(g) 5(l) 9(i) 6(e) 0(n) 1(z) 8(a) 6(c) 7(o) 0(n) 4(-) 5(l) 6(e) 3(p) 2(r) 9(i) 3(m) 6(e) 4+(-) 9(d) 8(a) 2(r) 7(o) 4(-) 8(a) 5(u) 9(i) 1(s) 7(o) 4'(-) 9(d) 6(e) 5(l) 6(e) 6(c) 7(o) 1(s) 6(e) 4(-) 4(-) 9(d) 9(i) 8'(qua) 8(a) 3.6(V.S.Illma) 4(-) 1(et) 4(-) 0'(non) 3(m) 8(a) 0(n) 6(c) 8(a) 2(r) 7(o) 4(-) 9(d) 9(i) 5(u) 1(s) 8(a) 2(r) 6(e) 4(-) 7(o) 0(g) 0(n) 9(i) 4(-) 9(d) 9(i) 5(l) 9(i) 0(g) 6(e) 6[n?] 2(t) 9(i) 8(a) 4(-) 1'(perche) 2.7(Nostro Signore) 5(u) 6(e) 0(n) 0(g) 8(a) 4(-) 1(s) 6(e) 2(r) 5(u) 9(i) 2(t) 7(o) 4(-) 1(et) 4(-) 3.6(V.S.Illma)

### Cardinal Savello (4) (1585)

The following is part of a cipher (Meister p.298) prepared for the Inquisitor succeeding Costa by the order of Cardinal Savello in 1585.

An example in this cipher is as follows.

(In the following, the apostrophe (') indicates a dot over the preceding letter. £ and ρ are not-very-close approximate symbols.)
6'5619.086316473160956064833656393603125809424894600145240
54631£4234536701417739414'845658647017508417070931336563936038
4'190660941270928456584565536704ρ45102041409489562041025744'456
5164953131£23908017.410.4039394604

PLAINTEXT
Qui in Malta le cose caminano felicemente, vi trovo molta divotione et obedienza, et spero che ogni cosa sia per passare felicemente. non mancaro usare ogni diligenza, et di tuto daro minuto aviso per ogni corriere che vera a Roma. Il Turco teme molto.

6'(qui) 5(i) 6(n) 1(-) 9.0(Malta) 8(-) 6(l) 3(e) 1(-) 6(c) 4(o) 7(s) 3(e) 1(-) 6(c) 0(a) 9(m) 5(i) 6(n) 0(a) 6(n) 4(o) 8(-) 3(f) 3(e) 6(l) 5(i) 6(c) 3(e) 9(m) 3(e) 6(n) 0(t) 3(e) 1(-) 2(u) 5(i) 8(-) 0(t) 9(r) 4(o) 2(u) 4(o) 8(-) 9(m) 4(o) 6(l) 0(t) 0(a) 1(-) 4(d) 5(i) 2(u) 4(o) 0(t)
5(i) 4(o) 6(n) 3(e) 1(-) £(et) 4(o) 2(b) 3(e) 4(d) 5(i) 3(e) 6(n) 7(z) 0(a) 1(-) 4(et) 1(-) 7(s) 7(p) 3(e) 9(r) 4(o) 1(-) 4'(che) 8(-) 4(o) 5(g) 6(n) 5(i) 8(-) 6(c) 4(o) 7(s) 0(a) 1(-) 7(s) 5(i) 0(a) 8(-) 4(per) 1(-) 7(p) 0(a) 7(s) 0(a) 9(r) 3(e) 1(-) 3(f) 3(e) 6(l) 5(i) 6(c) 3(e) 9(m) 3(e) 6(n) 0(t) 3(e) 8(-)
4'[non?] 1(-) 9(m) 0(a) 6(n) 6(c) 0(a) 9(r) 4(o) 1(-) 2(u) 7(s) 0(a) 9(r) 2[e?] 8(-) 4(o) 5(g) 6(n) 5(i) 8(-) 4(d) 5(i) 6(l) 5(i) 5(g) 3(e) 6(n) 7(z) 0(a) 4ρ(et) 4(d) 5(i) 1(-) 0(t) 2(u) 0(t) 4(o) 1(-) 4(d) 0(a) 9(r) 4(o) 8(-) 9(m) 5(i) 6(n) 2(u) 0(t) 4(o) 1(-) 0(a) 2(u) 5(i) 7(s) 4(o) 4'(per) 4(o) 5(g) 6(n)
5(i) 1(-) 6(c) 4(o) 9(r) 5(i) 3(e) 1[r?] 3(e) 1(-) £(che) 2(u) 3(e) 9(r) 0(a) 8(-) 0(a) 1(-) 7.4(Roma) 1(-) 0.4(Il Gran Turco) 0(t) 3(e) 9(m) 3(e) 9(m) 4(o) 6(l) 0(t) 4(o)

## References

María José Bertomeu Masiá (2009). La guerra secreta de Carlos V contra el Papa: La cuestion de Parma y Piacenza en la correspondencia del cardenal Granvela

Aloys Meister (1906), Die Geheimschrift im Dienste der Papstlichen Kurie von ihren Anfangen bis zum Ende des XVI. Jahrhunderts

S. Tomokiyo, "A Polyphonic Substitution Cipher of the Catholic League (1592-1593)" (Another article) features a polyphonic cipher of the Catholic League in France used in 1592-1593 and also gives other historical examples of polyphonic ciphers.

©2017 S.Tomokiyo
First posted on 13 March 2017. Last modified on 31 December 2019.
Articles on Historical Cryptography