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Computational Complexity

  • Reference work entry
Encyclopedia of Cryptography and Security

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Synonyms

Complexity theory

Related Concepts

Exponential Time; O-Notation; One-Way Function; Polynomial Time; Security (Computational, Unconditional); Subexponential Time

Definition

Computational complexity theory is the study of the minimal resources needed to solve computational problems. In particular, it aims to distinguish between those problems that possess efficient algorithms (the “easy” problems) and those that are inherently intractable (the “hard” problems). Thus computational complexity provides a foundation for most of modern cryptography, where the aim is to design cryptosystems that are “easy to use” but “hard to break” (Security [Computational, Unconditional]).

Theory

Running Time. The most basic resource studied in computational complexity is running time – the number of basic “steps” taken by an algorithm (Other resources, such as space[i.e., memory usage], are also studied, but they will not be discussed here). To make this precise, one needs to fix a model of...

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Recommended Reading

  1. Arora S, Barak B (2009) Computational complexity: a modern approach. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  2. Garey MR, Johnson DS (1979) Computers and intractability: a guide to the theory of NP-completeness. W.H. Freeman and Company, San Francisco

    MATH  Google Scholar 

  3. Goldreich O (2008) Computational complexity: a conceptual perspective. Cambridge University Press, Cambridge

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  4. Goldreich O (2001) Foundations of cryptography: basic tools. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  5. Goldreich O (2004) Foundations of cryptography. Vol II: basic applications. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  6. Sipser M (1997) Introduction to the theory of computation. PWS Publishing, Boston

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Author information

Authors and Affiliations

  1. School of Engineering & Applied Sciences, Harvard University, Maxwell Dworkin 337, 33 Oxford Street, 02138, Cambridge, MA, USA

    Salil Vadhan (Professor)

Authors
  1. Salil Vadhan
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computing Science, Eindhoven University of Technology, 5600 MB, Eindhoven, The Netherlands

    Henk C. A. van Tilborg

  2. Center for Secure Information Systems, George Mason University, Fairfax, VA, 22030-4422, USA

    Sushil Jajodia

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© 2011 Springer Science+Business Media, LLC

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Vadhan, S. (2011). Computational Complexity. In: van Tilborg, H.C.A., Jajodia, S. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-5906-5_442

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