Decrypting Data with Modular Mathematics

  • Context: Undergrad 
  • Thread starter Thread starter Fiona Rozario
  • Start date Start date
  • Tags Tags
    Mathematics
Click For Summary

Discussion Overview

The discussion revolves around the encryption and decryption of data using modular arithmetic, specifically the operation (data + 203) mod 200. Participants explore the implications of this operation for decrypting the original data.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant describes their encryption method and seeks to understand how to decrypt the data.
  • Another participant explains that the encryption function is not invertible due to multiple possible original values mapping to the same encrypted result.
  • A suggestion is made that if the data is limited to a specific range, decryption might be feasible by adjusting the encrypted value.
  • Participants clarify that the original operation involves adding 203, not 3, and discuss the implications of this on the decryption process.
  • There is confusion regarding the arithmetic involved in reversing the encryption, with one participant questioning the feasibility of certain calculations.
  • Another participant asserts that the arithmetic operations discussed are indeed possible, leading to further clarification on the matter.

Areas of Agreement / Disagreement

Participants express differing views on the invertibility of the encryption function and the feasibility of decrypting the data. There is no consensus on the correct approach to decryption, and confusion remains regarding the calculations involved.

Contextual Notes

The discussion highlights limitations related to the assumptions about the range of data and the nature of the modular arithmetic involved. The specific steps for decryption remain unresolved.

Fiona Rozario
Messages
52
Reaction score
1
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...
 
Physics news on Phys.org
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.
 
data might be limited to a range like [0,199], that would allow decrypting it (simply by taking encrpytedvalue-3 mod 200).
 
Yes, my data has a range from 1 to 200...
 
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?
 
Fiona Rozario said:
i am adding 203 to the data (not 3)
That is the same mod 200.
Fiona Rozario said:
But (153-203) is not possible
Of course it is possible.
 
mfb said:
That is the same mod 200.Of course it is possible.

Yes...got it. Thanks...
 

Similar threads

Undergrad Modulo and Modulus in math and computer programming
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Weighting data based on the errors
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Filling in Missing Values in a string of data
  • · Replies 7 ·
Replies
7
Views
1K
Undergrad Max and min values -- Finding them in a data set
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad What are the commonly used estimators in regression models?
  • · Replies 23 ·
Replies
23
Views
4K
Undergrad How Does the Equation D x E mod Φ(N) = 1 Relate to RSA Encryption?
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Take errors into account for a data fit
  • · Replies 3 ·
Replies
3
Views
2K
MHB Help in identifying why these two calculations have the same result?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Calculate the mean, variance, stdev, and CV with 2 methods: check answers
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad How Should You Approach Fitting Multiple Gaussians to Data with Poisson Errors?
  • · Replies 28 ·
Replies
28
Views
4K