In mathematical cryptography, a '''Kleinian integer''' is a complex number of the form <math>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>\mathbb{Q}(\sqrt{-7})</math>. This ring is a unique factorization domain.
==See also==
*Eisenstein integer *Gaussian integer
==References==
* {{Citation|authorlink=John Horton Conway|last1=Conway|first1=John Horton|last2=Smith|first2=Derek A.|year=2003|title=On Quaternions and Octonions: Their Geometry, Arithmetic, and Symmetry|publisher=A. K. Peters, Ltd.|isbn=978-1-56881-134-5|postscript=<!--none-->}}. ([http://nugae.wordpress.com/2007/04/25/on-quaternions-and-octonions/ Review]). *{{citation|series=Lecture Notes in Computer Science |volume= 4249|year= 2006|pages=445–459 |title=Cryptographic Hardware and Embedded Systems - CHES 2006|chapter=FPGA Implementation of Point Multiplication on Koblitz Curves Using Kleinian Integers |first1=V. S.|last1= Dimitrov|first2= K. U.|last2= Järvinen|first3= M. J.|last3= Jacobson|first4= W. F.|last4= Chan|first5= Z.|last5= Huang|doi=10.1007/11894063_35|isbn=978-3-540-46559-1|doi-access= free}}
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