Skip to main content
Engineering LibreTexts

1: One-Time Pad

  • Page ID
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)

    Communication is the act of conveying information from a sender to a receiver. Secure communication refers to the problem of making the communication unavailable to anyone except the desired receiver. Secure communication is the oldest application of cryptography, and remains the centerpiece of cryptography to this day. After all, the word cryptography means “hidden writing” in Greek. So, secure communication is a natural place to start our study of cryptography.

    History provides us with roughly 2000 years of attempts to secure sensitive communications in the presence of eavesdroppers. Despite the many brilliant minds that lived during this period of time, almost no useful concepts remain relevant to modern cryptography. In fact, it was not clear how to even formally define the goal of secure communication until the 1940s. The two modern definitions in use today were identified only in 1982 and 1990.

    The only cryptographic method developed before 1900 that has stood the test of time is the one-time pad, which appears in some form in essentially every modern encryption scheme. In this chapter, we introduce the one-time pad and discuss its important characteristics. Along the way, we will start to get acclimated to cryptographic security definitions.

    • 1.1: Syntax and Correctness for Encryption
      The cryptographic approach to secure communication is a tool known as encryption. Before discussing the specifics of one-time pad, we will first define what pieces comprise an encryption scheme in general.
    • 1.2: One-Time Pad
      Now with a clear definition of encryption syntax, we can give the specifics of one-time pad (OTP)encryption. The idea of one-time pad had historically been attributed to Gilbert Vernam, a telegraph engineer who patented the scheme in 1919. In fact, one-time pad is sometimes called “Vernam’s cipher.” However, an earlier description of one-time pad was recently discovered in an 1882 text on telegraph encryption by banker Frank Miller.
    • 1.3: Properties
      A general-purpose security definition for encryption will be discussed in the next chapter. For now, we will show a simple but important property that one-time pad satisfies, and argue that it has some relevance to secure communication.
    • 1.4: Exercises

    1: One-Time Pad is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Mike Rosulek.

    • Was this article helpful?