We show that it is not possible to compute any information on the generator g regardless of the number of public keys observed.
In the case of elliptic curves E(GF(p)) or E(GF(2^n)) on short Weierstrass form, or E(K) on Edwards form, twisted Edwards form or Montgomery form, where K is a non-binary field, we show how to compute the domain parameters excluding the generator from four keys on affine form.
Hence, if the domain parameters excluding the generator are to be kept private, points may not be transmitted on affine form. It is an open question whether point compression is a sufficient requirement.
Regardless of whether points are transmitted on affine or compressed form, it is in general possible to create a distinguisher for the domain parameters, excluding the generator, both in the case of the elliptic curve groups previously mentioned, and in the case of multiplicative subgroups of GF(p).
We propose that a good method for preventing all of the above attacks may be to use blinding schemes, and suggest new applications for existing blinding schemes originally designed for steganographic applications.Category / Keywords: public-key cryptography / ECC, elliptic curve, domain parameters, discrete logarithm, Diffie-Hellman Date: received 10 Sep 2015 Contact author: martin ekera at mil se Available format(s): PDF | BibTeX Citation Version: 20150913:192013 (All versions of this report) Short URL: ia.cr/2015/879 Discussion forum: Show discussion | Start new discussion