Mehdi Tibouchi

238 reputation

	238 reputation	bio	website	normalesup.org/~tibouchi	visits	member for	1 year, 5 months
24 badges		location			seen	Jun 3 at 2:12

4 Comments

Feb 22	comment	Standardized parameters for elliptic curve cryptography One can infer that indeed, but on the other hand, the Digital Signature Standard says that NIST-approved curves are randomly generated (and even “provably” so!) in the sense that the curve coefficients are chosen using a hash function (even though the base fields are quite special). So it seems difficult to tell what exactly randomly generated means in this context.
Feb 22	comment	Standardized parameters for elliptic curve cryptography Very useful, thanks.
Jan 18	comment	Pairing-friendly curves in small characteristic fields I should perhaps note, however (and sorry for commenting twice), that in principle, it might be possible to construct pairing-friendly curves over extension fields of a form like $\mathbb{F}_{p^2}$ with the CM method (see e.g. the discussion in 4.1 of Barreto and Naehrig's paper). But $p$ still has to be large and you cannot fix it in advance, so it doesn't solve the problem in small characteristic.
Jan 18	comment	Pairing-friendly curves in small characteristic fields If you check the output of Algorithms 4.2 and 5.1 in Freeman's paper, you'll find that all of his curves (and hence their Jacobians) are defined over prime fields. The $J(\mathbb{F}_{q^k})$ in the abstract is about finding where the full r-torsion of the Jacobian in contained.