Decrypting Data with Modular Mathematics

[Fiona Rozario]

I have some data which I am encrypting using modulus - (data + 203) mod 200. If the data is 150, I get the result as 153. Is there a way to decrypt and get my data (150) back? I don't know how to calculate inverse of this operation...

 

[Oedipus]

Your encrypting operation is the function ƒ(x)=(x+3) mod 200. For a function ƒ: X→Y to be invertible, for every y∈Y there must be one and only one x∈X so that ƒ(x)=y. In your case, the result 153 can be obtained from multiple data values: 150, 350, 550 and so on. There are multiple x∈X that satisfy ƒ(x)=153, so your operation is not an invertible function. In other words, your decryptor cannot possibly know whether the data was 150,350,550...etc. when it receives the encrypted data 153.

 

[mfb]

data might be limited to a range like [0,199], that would allow decrypting it (simply by taking encrpytedvalue-3 mod 200).

 

[Fiona Rozario]

Yes, my data has a range from 1 to 200...

 

[Fiona Rozario]

Thanks for the help...i am adding 203 to the data (not 3). I tried doing what mfb suggested. But (153-203) is not possible and (203-153) gives 50. 50 mod 200 doesn't give 150...am I going wrong somewhere?

 

[mfb]

i am adding 203 to the data (not 3)

That is the same mod 200.

But (153-203) is not possible

Of course it is possible.

 

[Fiona Rozario]

That is the same mod 200.Of course it is possible.

Yes...got it. Thanks...