Humari baat chit kitni surakshit hai?
Aaj ke
digital zamaane mein WhatsApp, Signal, Telegram jaise messaging apps har kisi
ke phone pe hote hain. Lekin, consider karke dekha hai kabhi ki:
"Kya
hamare personal chats, photos, aur calls hackers ya government agencies se
protect ho sakte hain?"
The answer
is — End-to-End Encryption, which is based on a very advanced cryptographic
technique.
🔐 What is End-to-End Encryption?
(E2EE)
"Messages
can only be read by the sender and the recipient; an intermediate party (not
even WhatsApp or a hacker) can't decrypt it."
With
powerful cryptographic techniques, this is possible:
Finite
Fields (Galois Fields)
Modulo
Polynomial Arithmetic
Public-Key
Cryptography (e.g., Diffie-Hellman, Elliptic Curve)
🧠 A Bit of Math: The Powerhouse of
Cryptography
Let's try to
understand a simplified version of mathematics working behind this system:
🔹 1. What Are Finite Fields (GF).
In
Cryptography, instead of using normal numbers:
One uses a
finite set of numbers (for example, 0,1,2,...p−1) under modulo operation.
Ex: GF(2) or
GF(2⁸) — perfect for binary systems.
🔹 2. Polynomial Arithmetic in GF(2ⁿ)
Apps like
WhatsApp use AES (Advanced Encryption Standard), in which:
The data are
processed as binary polynomials.
The
polynomials are combined by XOR (addition) and AND (multiplication).
The result
is then taken modulo an irreducible polynomial
Irreducible
polynomials are used to take modulus of results — just like:
(X^12 + X^7
+ X^2) mod (X^8 + X^4 + X^3 + X + 1)
Inverse aur
Extended Euclidean Algorithm
For safe key
generation AND AES rounds, inverses have to be found.
For inverse
of a polynomial, Extended Euclidean Algorithm is used (mod m(X)).
Whatsapp Encryption: Behind the Scenes
WhatsApp
uses:
·
Signal Protocol
·
Curve25519 Elliptic Curve Cryptography
·
AES-256 for encryption
·
HMAC-SHA256 for integrity
Key Points:
Every user generates a public-private key pair.
Upon sending a message to someone:
App encrypts with the other person's public key.
Only the private key that belongs to her/him can decrypt the message.
AES + HMAC is used to not only encrypt the message, but also make sure
it has not been tampered with.
Meaning: Encrypted data even exists on WhatsApp servers — which cannot
be read even by them!
Conclusion: Cryptography = Digital Shield
End-to-end
encryption on WhatsApp is one solid example of how math + computer science
protect our privacy.
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