Izvorni znanstveni članak
https://doi.org/10.21857/y54jofkjqm
A note on Low Order assumptions in RSA groups
István András Seres
; Faculty of Informatics, 3in Research Group, ELTE Eötvös Loránd University, 1117 Budapest, Hungary
Péter Burcsi
; Faculty of Informatics, 3in Research Group, ELTE Eötvös Loránd University, 1117 Budapest, Hungary
Sažetak
In this short note, we show that substantially weaker Low Order assumptions are sufficient to prove the soundness of Pietrzak’s protocol for proof of exponentiation in groups of unknown order. This constitutes the first step to a better understanding of the asymptotic computational complexity of breaking the soundness of the protocol. Furthermore, we prove the equivalence of the (weaker) Low Order assumption(s) and the Factoring assumption in RSA groups for a non-negligible portion of moduli. We argue that in practice our reduction applies for a considerable amount of deployed moduli. Our results have cryptographic applications, most importantly in the theory of recently proposed verifiable delay function constructions. Finally, we describe how to certify RSA moduli free of low order elements.
Ključne riječi
Verifiable delay functions; Low Order assumption; RSA
Hrčak ID:
261465
URI
Datum izdavanja:
25.8.2021.
Posjeta: 664 *