Kleinian integer

In mathematical cryptography, a Kleinian integer is a complex number of the form [math]\displaystyle{ m+n\frac{1+\sqrt{-7}}{2} }[/math], with m and n rational integers. They are named after Felix Klein. The Kleinian integers form a ring called the Kleinian ring, which is the ring of integers in the imaginary quadratic field [math]\displaystyle{ \mathbb{Q}(\sqrt{-7}) }[/math]. This ring is a unique factorization domain.

See also

• Eisenstein integer
• Gaussian integer

References

• Conway, John Horton; Smith, Derek A. (2003), On Quaternions and Octonions: Their Geometry, Arithmetic, and Symmetry, A. K. Peters, Ltd., ISBN 978-1-56881-134-5 . (Review).
• Dimitrov, V. S.; Järvinen, K. U.; Jacobson, M. J.; Chan, W. F.; Huang, Z. (2006), "FPGA Implementation of Point Multiplication on Koblitz Curves Using Kleinian Integers", Cryptographic Hardware and Embedded Systems - CHES 2006, Lecture Notes in Computer Science, 4249, pp. 445–459, doi:10.1007/11894063_35, ISBN 978-3-540-46559-1