I see two types of cyclic groups are most commonly used in cryptography:

  • modulo multiplicative group of integers with prime order
  • elliptic curves

Are there any other cyclic groups used in cryptography?


1 Answer 1


The multiplicative group $\mathbb{F}_{2^n}^{\ast}$ (which is cyclic) is used in defining LFSR sequences and nonlinearly filtered sequences typically as building blocks of stream ciphers.

This group is part of the picture for block ciphers; most prominently, the field $\mathbb{F}_{2^n}$ is used (for $n=8$) for defining the AES. Boolean functions and vector boolean functions defined over $\mathbb{F}_{2^n}$ also appear.

  • 2
    $\begingroup$ Koblitz curves are also over the field $\mathbb{F}^{*}_{2^n}$. $\endgroup$ Jan 17, 2019 at 21:58

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.