What if asymmetrical cryptography (RSA) was invented in 1790s?

The math was there. Euler Function etc...
With some random POD it could be done.
Asymmetrical cryptography makes possible secure exchange of information with out shared password.
What it has been invented earlier?

It would not be as strong as with use of computers but on the other hand, the attacker side would have to use hand calculations to do brute forcing.

Ease of use could be enhanced by math tables with exponents and modal divisions.
Base of 26 would be sufficient for a-z plus _ . Exponents of above 5 are impractical. Which leaves you with "1; 2; 3; 5;".
But modular divisions are not impractical especially with math /crypto tables.

For example public key (mod (x) and exponent) could by printed on business cards, in newspapers told by mouth to mouth.

Another approach is binary
How would first mechanical computers affect this? How about famed "differential engine"?
 
on a somewhat related topic, the legal reformer Jeremy Bentham [we think of him as a philosopher] tried to come up with plans to prevent the forgery of bank notes. I think his plan generally involved sending two things through the mail which were put together by the recipient.

In slightly more than a year, from Feb. 1800 to April 1801, more than a hundred persons were executed in England for forgery, and Bentham was a practical-minded reformer.

https://books.google.com/books?id=m...onepage&q=Bentham "bank notes" hanged&f=false
 
Last edited:
The math was there. Euler Function etc...
With some random POD it could be done.
Asymmetrical cryptography makes possible secure exchange of information with out shared password.
What it has been invented earlier?

It would not be as strong as with use of computers but on the other hand, the attacker side would have to use hand calculations to do brute forcing.

Ease of use could be enhanced by math tables with exponents and modal divisions.
Base of 26 would be sufficient for a-z plus _ . Exponents of above 5 are impractical. Which leaves you with "1; 2; 3; 5;".
But modular divisions are not impractical especially with math /crypto tables.

For example public key (mod (x) and exponent) could by printed on business cards, in newspapers told by mouth to mouth.

It's just not feasible before universal computing. You'd have to invent basically the ASCII table, get everyone to agree to it. Plus you plainly state why the method would be impractical in your text. If exponents larger than 5 are impractical, then the whole system is. This would restrict the encryption key and the decryption keys to easily guessable numbers (since they are the exponents).

Not to mention that there is no real need for asymmetric encryption before computing. One time pads are still the best form of encryption today, and are more practical than a non-computer version of RSA.
 
It's just not feasible before universal computing. You'd have to invent basically the ASCII table, get everyone to agree to it. Plus you plainly state why the method would be impractical in your text. If exponents larger than 5 are impractical, then the whole system is. This would restrict the encryption key and the decryption keys to easily guessable numbers (since they are the exponents).

Not to mention that there is no real need for asymmetric encryption before computing. One time pads are still the best form of encryption today, and are more practical than a non-computer version of RSA.

Keys would be limited to few numbers - But still it would have some deterrence factor of reading stuff enlarge.

How about mechanical computers? And Electromechanical ones?
 
The shared ASCII tables are not hard to invent.
What about implications further dawn the line? Even if it is impractical in 1790s what it would do in future?
 
Keys would be limited to few numbers - But still it would have some deterrence factor of reading stuff enlarge.

How about mechanical computers? And Electromechanical ones?

In the 1790s, the Vigenère cipher was considered unbreakable (a substitution cipher with 10 keys) and would be until Babbage cracked in in the mid-19th century. There was no need to invent a new method at the time. Let alone a method that's harder to implement and easier to crack given the constraints of the time. They already had tons of methods to deter people from reading secret messages.

Like I said before, RSA is entirely impractical until universal computing. The 1940s or 1950s would be the earliest times for this to be somewhat useful. Do you know how RSA works?

RSA Algorithm:

First you pick two unique prime numbers: p and q.
Then you multiply them together to get n (your modulus).
Then you pick any prime for the encryption key (e) between 3 to n (not p or q).
Next you calculate the totient, t=(p-1)(q-1).
Then you find the inverse of e in mod t. This is your secret decryption key (d).

You let everyone know n,and e. You must keep t,p,q and d secret. If anyone discovers any of those they will know your secret decryption key.

You encrypt messages by: (message)^(e)
You decrypt by: (enc. message)^(d).

All messages must be vectors of numbers. That's painful to implement by hand all by itself. Then if we can't choose large numbers then the whole encryption is trivial to break.

Example:

Setup:


Let p=3 and q=7
Thus n must be 21.
and t=(3-1)(7-1)=12

We choose 5 as our encryption key, e.
Then d our decryption key must be the inverse of 5 in mod 12. Or 5*d = 1 mod 12. So 5 is our d.

Cracking:

This is trivially easy to guess since everyone knows 3*7 is the prime factorization of 21. Thus we now know t is 12. So we just have to guess d.

Can't be 2 since 5*2 =10
Can't be 3 since 5*3=15= 3 mod 12
Can't be 4 since 5*4=20= 8 mod 12
It's 5 since 5*5=25 = 1 mod 12 since 25=12*2+1.
 
Top