Introduction

• Suppose Alice wishes to share a string “Quantum” wiht Bob, using a secret key $k$ (a number), such that each alphabet in the string will be shifted by $k$ letters. Consider the case where $k=3$, the encrypted string will be “TXDQWXP”.

• The above described method can be represented as follows :

  $t[i] = (m[i] + k) \% 26$

  where,

  $t[i]$ is the $i^{th}$ character of the transmitted message.

  $m[i]$ is the $i^{th}$ character of the message to be sent.

  and, $k$ is the secret key.

• One-Time Pad Method : Use of a different secret key for each transmission.

• It’s quite evident that it is very easy to decrypt such a message with hit and trial. Thus, due to the encrypted and actual strings being Highly Correlated this message is easily decipherable by an attacker.

One-Time Pad Protocol

• Given, the following (each of length $n$):

  the orignal message, denoted by $T$

  The encrypted message, denoted by $E$

  and, an encryption key, denoted by $K$

• $K$ is generated by tossing a coin $n$ times in order to generate $n$ random bits (say, we map Heads to 1 and Tails to 0, then the outcome HHTTH will give 11001).

• Exchanging messages b/w SENDER & RECEIVER:

  1. Calculate $E = T \oplus K$.

  2. Sender send $E$ via an insecure channel.

  3. Receiver obtains actual message by performing:

     $T = E \oplus K$

• Drawbacks:

  • A different key must be generated each time, because if the same key is used, it can be discovered again through statistical analysis.
  • This method is secure only when the secret key $k$ is uknown to the attacker.

RSA Encryption

<aside> 📌

Based on the idea of generating extremely large numbers which are hard to Factorize. However, later Shor’s Algorithm for Quantum Computing was discovered, which made this problem quite easy.

</aside>

• An encryption scheme, which uses two keys : Public & Private.
• The Private key is used for decryption.
• Steps:
• Solved Example:

Quantum Cryptography

• Uses fundamentals of Quantum Mechanics to generate a secret key. This method is known as Quantum Key Distribution, or simply QKD.
• QKD uses two communication channels:
  • A classical communication Channel: Internet/Cell phone, on which the encrypted messages are sent
  • A Quantum Communication Channel: on which the Quantum Key is distributed.
• This system uses a simple fact for intrusion detection: Measuring a Quantum State distrubs (changes) it. Hence, when the attacker attempts to measure the Key (a Quantum State), Alice & Bob can detect the third party presence.