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As our society becomes ever more dependent on digital technologies, cryptography becomes increasingly important to secure data while it is being stored, transferred and processed. In the field of cryptography there is a strong crossfertilization between new applications and innovative research results. The 13 contributions in this special issue of ”Recent Trends on Cryptography” encompass a wide range of recent research; we believe that this collection offers an interesting snapshot of research that is appealing to experts in the field but also to a broader audience. Collectively these papers illustrate the diverse range of issues that are presently being investigated in the field of cryptography.
The paper by Michael Scott “Missing a trick: Karatsuba variations” takes the reader for a tour through different versions of Karatsuba multiplication. This is of considerable interest for efficient implementations of public-key cryptography and in particular for Elliptic Curve Cryptography. The author discusses an interesting variant called “arbitrary-degree” Karatsuba (ADK).
In the paper “Backtracking-assisted multiplication”, Houda Ferradi, Remi G ´ eraud, Diana ´ Maimut, David Naccache and Hang Zhou describe a new multiplication algorithm, particularly suited to lightweight microprocessors. This leads to improvements when one of the operands is known in advance.