Abstract
We establish new results about the frequency of small gaps between the elements of multiplicative subgroups of finite fields. As an application, we give some rigorous support to uniqueness assumptions of Boneh et al. (Why textbook ElGamal and RSA encryption are insecure, 2000) for solutions to additive and multiplicative subgroup rounding problems. These problems arise during attacks on some careless use of the ElGamal encryption.
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Acknowledgments
The author is very grateful to the referees for many very useful comments. This research was supported by the ARC Grant DP130100237.
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Communicated by D. Panario.
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Shparlinski, I.E. On small gaps between the elements of multiplicative subgroups of finite fields. Des. Codes Cryptogr. 80, 63–71 (2016). https://doi.org/10.1007/s10623-015-0063-9
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DOI: https://doi.org/10.1007/s10623-015-0063-9
Keywords
- Multiplicative subgroups
- Finite fields
- Additive subgroup rounding problem
- Multiplicative subgroup rounding problem