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26 April 2022

Summary

By now we have seen general techniques in constructing \(\ECM^+\) secure signature schemes. The roadmap is summarised below. Arrows represent direct implications.

Although theoretically satisfactory, this is not the end of the story. In the remaining chapters we will study more concrete \(\ECM^+\) secure schemes that aim at improving performance and/or providing new features. In particular we investigate two genres:

• Schemes that directly root in the RSA assumption and bypass the chain of transformations we have developed. They run much faster and also significantly reduce signature lengths.
• Schemes based on the so-called “Diffie-Hellman assumption” and an algebraic structure named “pairings”. These schemes are rather efficient, and enable aggregating/verifying multiple signatures in a large batch.

Our exposition will shift to a less formal (but still rigorous) language and focus on the gist.