Coron, Jean-SĂ©bastien; Handschuh, Helena; Naccache, David ECC: Do we need to count? (English) Zbl 0977.94026 Lam, Kwok Yan (ed.) et al., Advances in cryptology - ASIACRYPT ’99. International conference on the theory and application of cryptology and information security, Singapore, November 14-18, 1999. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 1716, 122-134 (1999). Summary: A prohibitive barrier faced by elliptic curve users is the difficulty of computing the curves’ cardinalities. Despite recent theoretical breakthroughs, point counting still remains very cumbersome and intensively time consuming.In this paper we show that point counting can be avoided at the cost of a protocol slow-down. This slow-down factor is quite important (typically \(\cong 500)\) but proves that the existence of secure elliptic-curve signatures is not necessarily conditioned by point counting.For the entire collection see [Zbl 0929.00090]. Cited in 2 Documents MSC: 94A60 Cryptography 14H52 Elliptic curves Keywords:signature; elliptic-curve cryptography; elliptic curve; point counting PDFBibTeX XMLCite \textit{J.-S. Coron} et al., Lect. Notes Comput. Sci. 1716, 122--134 (1999; Zbl 0977.94026)