I attempted a new operation similar to division, on natural numbers to encode and covert them to another natural number; and also invented inverting the new converted natural number to the original number.
Right now I am accurately encoding numbers below hundred.
The encoding and decoding is explained below:
The new division operation to encode the number always has number '2' as a divisor. For convenience let us call this operation as 'special division(SD)'.
1]Obtaining encoded number: While performing the 'SD' operation divide the number by '2' in such a way that the first digit in division must be less than 1 of the correct division digit; further division process is same as regular division. e.g. The encoded number obtained by SD operation for number 58 is 119.
2]Inverting the encoded number to original number: Add multiplication of first digit in the original number and '9' to the sum of digits of the number obtained by multiplying 2 with the new converted number . And we will get back the original number. e.g. Considering the prior example where we encoded 58 to 119; let us invert the conversion 119 to 58. Multiplying 119 by 2 we get 238. If we add all the digits in 238 we get number 13. Adding 13 with the multiplication of first digit in original number and 9 we get, 13 + (9*5) = 13 + 45 = 58.
Can this algorithm be useful in cryptography?
I am afraid this question is a bit too broad to be answered negatively with any degree of certainty. However, if we consider instead the following question then the answer is probably not:
In cryptography, a common assumption is that security cannot rely on the adversary not knowing the scheme (otherwise it's known as security through obscurity https://en.wikipedia.org/wiki/Security_through_obscurity). Since there is no secret key used to decode, an adversary therefore has as much information as the intended recipient.
If you were to use this scheme outside of crypto, where security through obscurity is acceptable (say if you were designing a puzzle or wanted to exchange messages with a friend), then you would run into frequency analysis attacks (https://en.wikipedia.org/wiki/Frequency_analysis), since each letter -once encoded into a number- would always be 'encoded' by the same number.
I would recommend looking at other esoteric bijection with easy encoding and decoding (such as quaterimaginary base $2i$ or base $-1\pm i$ https://en.wikipedia.org/wiki/Complex-base_system#Base_%E2%88%921_%C2%B1_i), and see if they have been used.