# What cipher(s) did Isaac Newton use?

A number of sources including this one assert that Isaac Newton used encrypted messages to communicate some of his scientific discoveries, and as a way of establishing priority.

What cipher(s) did he use?

What was the ciphertext and what was the plaintext?

What discoveries did he obscure in this way?

• I've found one instance in a 1677 letter from IN to Leibniz: "Data aequatione quotcunque fluentes quantitates involvente, fluxiones invenire; et vice versa. / Given an equation involving any number of fluent quantities to find the fluxions, and vice versa." Anagram "6accdae13eff7i3ℓ9n4o4qrr4s8t12ux" --> a(6)c(2)dæe(13)f(2)i(7)ℓ(3)n(9)o(4)q(4)r(2)s(4)t(8)u/v(12)x
– A E
Commented Dec 17, 2014 at 12:19
• I've found some more here: mathoverflow.net/a/140332 from sp.rpcs.org/faculty/MillerR/towson/Readings/…
– A E
Commented Dec 17, 2014 at 12:34
• Regarding the Comemrcium Epistolicum (dispute N-L) you can see here for an analysis, here for Newton point of view and the "classical" modern reconstruction of A.R.Hall, Philosophers at Wars (1980). Commented Dec 17, 2014 at 18:34

Newton used anagrams which are not the usual ciphers. It is not designed for a secret communication, but only for proving at a later time that you knew something. So nobody is supposed to be able to decode the message until you tell what the message was.

To do this, he used a simple procedure: he wrote a sentence (in Latin) and then just counted letters in it. And the anagram consisted of the list of letters and how many times each letter occurs in the message.

An example of such anagram is given on Math Overflow:

https://mathoverflow.net/questions/140327/arnold-on-newtons-anagram

together with its decoding, according to Newton's later statements. The message was usually sent to some third party (Oldenburg, the secretary of the Royal Society in the case of Newton), who then forwarded a copy to the addressee (Leibniz).

The discoveries Newton wanted to secure this way was essentially "calculus", more precisely power series. There were two coded messages in two different letters to Leibniz via Oldenburg. You can see the exact messages in the MO (link above).

Similar methods were widely used to secure priority in 17-th and 18-th centuries. The last time that I know was in 1918 when Gaston Julia send sealed (not coded) messages to the Academie de Science, and these messages had to be publicly opened and read at some later time on his request, to prove his priority. At that time this practice was already obsolete, and Julia was criticized for using it. However he was able to prove his priority and a Grand Prix of the Academy was awarded to him (for what is known now as "Holomorphic dynamics").

http://www.springer.com/mathematics/history+of+mathematics/book/978-3-642-17853-5

• Nice - it was effectively an early form of hash algorithm rather than encryption per se. Commented Dec 18, 2014 at 7:46