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be regarded as a variation of Rainbow using a non-commutative ring. However,
if a non-commutative ring used in the proposed scheme is chosen by the group
ring associated to dihedral group, the speed of the signature generation can be
accelerated by about 50% in comparison with the corresponding Rainbow.
Note that the performance of our designed schemes depend upon the arith-
metic operation of adapted non-commutative rings. Therefore, we plan to find
a specific non-commutative ring for achieving high processing speeds within our
schemes.
Acknowledgements.
This work partially supported by JST Strategic Japanese-
Indian Cooperative Programme on multidisciplinary Research Field, which com-
bines Information and Communications Technology with Other Fields. The first
author is supported by JST A-step feasibility study program, No.AS231Z03613A.
The authors would like to thank Jintai Ding and the anonymous reviewers for
their helpful comments on the draft manuscript.
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