Many Time Pad Attack

  The many-time pad attack exploits a critical vulnerability of reusing a one-time pad (OTP) key across multiple messages. While the OTP is perfectly secure when a unique key is used for each message, reusing the same key compromises security. Let’s understand why.

Suppose Alice and Bob use the same key $k$ for two distinct plaintext messages $m_1$ and $m_2$. The ciphertexts generated are $c_1=m_1\oplus k$ and $c_2=m_2\oplus k$. An eavesdropper, Eve, intercepting both ciphertexts, can compute their XOR:

$$c_1\oplus c_2=(m_1\oplus k)\oplus (m_2\oplus k)=m_1\oplus m_2$$

This removes the key entirely, leaving Eve with $m_1\oplus m_2$, the XOR of the original plaintexts. Although Eve does not directly see $m_1$ or $m_2$, patterns in natural language (such as common words or phrases) or predictable message structures allow her to deduce the plaintexts. This vulnerability is why reusing keys in an OTP scheme is strictly forbidden.

Stop and think! How does this differ from the original one-time pad approach? The key’s uniqueness is central to the OTP's security. Reusing keys transforms a perfectly secure system into one vulnerable to cryptanalysis.

See attack description here

Disadvantages of One-Time Pad

  While the one-time pad provides perfect secrecy, it comes with significant practical limitations:

• Key Length Requirement: The key must be at least as long as the message to ensure security. For large messages, this makes key management challenging.

• Key Distribution: Both parties must securely exchange the key in advance. If Alice and Bob have never met or cannot share a secret key beforehand, using the OTP becomes infeasible.