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Chapter 6 · XOR function in cryptography

From the book: Data Encryption at the Intersection of Mathematics and Physics – Comparing Physical Methods of Cryptography

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Chapter 6 · XOR function in cryptography

This chapter focuses on the XOR function as the cryptographic primitive that enables mathematically provable secrecy in the one-time pad. It first explains XOR as a Boolean operation that is easy to implement in digital hardware and central both to encryption and to message-authentication mechanisms.

The chapter then discusses the one-time pad in detail. It explains the three classic conditions for absolute secrecy: the key must be truly random, at least as long as the plaintext, and never reused. Under those conditions, XOR-based encryption is information-theoretically secure. The text also links XOR to MAC constructions that support integrity and authenticity.

A further contribution of the chapter is its treatment of storage encryption. It reviews XTS mode and proposes extensions intended to move storage encryption closer to one-time-pad principles. These variants—XTSO, XTSC, and true OTP mode—are presented as ways to reconcile practical data storage requirements with the security logic of one-time-pad-like processing.

  • Defines XOR as a core logical operation
  • Explains why OTP achieves provable secrecy
  • Connects XOR to integrity and authenticity tools
  • Reviews XTS for storage encryption
  • Introduces OTP-oriented XTS extensions

Suggested citation

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Show BibTeX placeholder 
@incollection{piller_schoelnast_physcrypto_ch1,
  title     = {Introduction},
  author    = {Piller, Ernst and Sch\"olnast, Hubert},
  booktitle = {Data Encryption at the Intersection of Mathematics and Physics},
  publisher = {Springer},
  year      = {2026},
  note      = {Open Access}
}