Abstract
In this work, we explore a combinatorial optimization problem stemming from the Naccache–Stern cryptosystem. We show that solving this problem results in bandwidth improvements, and suggest a polynomial-time approximation algorithm to find an optimal solution. Our work suggests that using optimal radix encoding results in an asymptotic 50% increase in bandwidth.
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Notes
This can also be described as a modular variant of the “subset product” problem.
In the original NS setting, p would be at least 7, 420, 738, 134, 871.
Indeed, \(p_\text {min}\) is closest to the 75th primorial.
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Géraud, R., Naccache, D. Mixed-radix Naccache–Stern encryption. J Cryptogr Eng 9, 277–282 (2019). https://doi.org/10.1007/s13389-018-0188-7
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DOI: https://doi.org/10.1007/s13389-018-0188-7