Eastern cipher systems – reprint from ‘Findings’

Melakarta.katapayadi.sankhya.72
courtesy of wiki commons. Click for a VERY large version

 

‘Findings’ was a blog where I added posts and jottings which might assist others working on the manuscript.  What follows isn’t an essay but a series of points.

first Published as ‘Eastern cipher methods’, Findings, (Blogger) on Monday, January 30, 2012
At the moment I have a bee in my bonnet about encryption systems east of Suez from the 12thC or earlier, and especially ones based in mathematical values translated/translatable into alphabetical ones.

At that time, I might add, the Katapayadi Shankya had no ‘wikipedia’ article, nor where any of the current diagrams online which can presently been seen, and one of which I have used as a header.
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So far, three encyption systems used east of Suez from the 12thC or earlier have intrigued me:

(i) the Triangle of Yang Hui – 13thC – well before Pascal’s triangle
better illustration of it is in the wiki article – which says (NB):
It is known as Pascal’s triangle in much of the western world, although other mathematicians studied it centuries before him in India, Greece, Iran, China, Germany, and Italy.Interactions during Mongol era see Smith, History of mathematics, Vol.1  p271-3. Also mentions Odoric [of Pordennone] giving his dates in Canton as1286-1331.

——————–

2. An Indian system which .. I won’t try to summarise. See here (The Katapayadi Shankya)

.Intro to that article says.. and note especially the last phrase:

This system of learning was known as the Ka-Ta-Pa-Ya-Di Shankya in Sanskrit and it was also familiar at Kerala and was known as Paralpperu in Malayalam from where it has really originated.

Basically it reduces an abjad/syllabary of 34 parts to notation using nine numbers plus zero.

(see Sanskrit chart on same linked page).

_______

The Paralppery system was used to calculate the calendar- see site here:

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Now, I’m still inclined to see the south arabian minuscule as our closest match for Voynich script, though the Indo-Greek looks very like it, too.

Some have argued seventeen forms for Voynich letters – I’m not going to argue that point, but I suppose that if 34 can be reduced to 9+0 then half as many can be too.

Or one might create an alternative 34: for argument’s sake the 32 points of the compass, and two pole-stars or something of that kind.

It would be a pretty radical change to the order of sounds, fthe original Indian and Malayalam systems following the usual rote order, whereas this couldn’t. Actually the number of points (with the Poles) easily reduces to 9.

___________

  1. Chinese again:  the ‘wandering teacher’ called Chu Shi-ke wrote a book called ‘The Precious Mirror of the Four Elements’ –  a maths text dated to 1303. His name is also romanised as Tchou Che-kie, Chu-Shih-Chieh, and he is sometimes called Chu Sung ting. Zhu Shijie

The wiki article has Zhu Shijie. giving the title of his work as Jade Mirror of the Four Unknowns (四元玉鉴, Siyuan yujian).

rather an impressive person..here his name is given as Chu Shih-Chieh, and the book’s title rendered as

“Siyuan yujian (True reflections of the four unknowns) published in 1303”

He treats polynomial algebra, and polynomial equations, by the “coefficient array method” or “method of the celestial unknown” which had been developed in northern China by the earlier thirteenth century Chinese mathematicians, but up till that time had not spread to southern China.

References

KONANTZ, E.L.:‘The Precious Mirror of the Four Elements’, China Journal of Science and Arts, Vol 2, No 4, 1924.

And here’s an article of interest, I think, though not  Morocco from the eleventh century onwards:
Azizi, Abdelmalek; Azizi, Mostafa, ‘Instances of Arabic Cryptography in Morocco’ Cryptologia, Vol.35, No.1 (Jan 2011) pp.47-57.

Abstract

Cryptography and Steganography were used in the Maghreb and several ideas were introduced before 1600 (Arithmetical cryptography based on the factorisation of integer and the calculus “Hissab Al Jommal”, signature and the use of the ideas of cryptography to insure the security of transactions and inheritance deeds). In this paper, we give an overview of some instances of cryptography which we have found in the Maghreb (from the 11th century to the 17th century): however, there are undoubtedly many other cases to be found in the manuscripts that have not been studied yet.

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One Reply to “Eastern cipher systems – reprint from ‘Findings’”

  1. I find the article about the Indian one extremely interesting. It may not be used in the VM, but might have inspired it.

    The anecdote at the end is the best. It shows how once again the mnemonic methods of the ancients are rediscovered and exploited by those competing in modern memory contests.

    They were much more intuitively familiar with the preferences of the human memory than we are.

    Like

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