Article · Wikipedia archive · Last revised Jun 1, 2026

Torus-based cryptography

Torus-based cryptography involves using algebraic tori to construct a group for use in ciphers based on the discrete logarithm problem. This idea was first introduced by Alice Silverberg and Karl Rubin in 2003 in the form of a public key algorithm by the name of CEILIDH. It improves on conventional cryptosystems by representing some elements of large finite fields compactly and therefore transmitting fewer bits.

Last revised
Jun 1, 2026
Read time
≈ 1 min
Length
134 w
Citations
2
Source
Wikipedia ↗

Torus-based cryptography involves using algebraic tori to construct a group for use in ciphers based on the discrete logarithm problem. This idea was first introduced by Alice Silverberg and Karl Rubin in 2003 in the form of a public key algorithm by the name of CEILIDH. It improves on conventional cryptosystems by representing some elements of large finite fields compactly and therefore transmitting fewer bits.12

See also

See also

References

References

  1. Rubin, Karl; Silverberg, Alice (2003). Boneh, Dan (ed.). "Torus-Based Cryptography". Advances in Cryptology - CRYPTO 2003. Berlin, Heidelberg: Springer: 349–365. doi:10.1007/978-3-540-45146-4_21. ISBN 978-3-540-45146-4.
  2. Gorla, Elisa (2025), "Torus-Based Cryptography", Encyclopedia of Cryptography, Security and Privacy, Springer, Cham, pp. 2632–2634, doi:10.1007/978-3-030-71522-9_481, ISBN 978-3-030-71522-9, retrieved 2026-02-03{{citation}}: CS1 maint: work parameter with ISBN (link)
External links