Sentence examples for a prime order from inspiring English sources
Choose an additive group G with a prime order q and a generator P∈G defined on an elliptic curve.
Also, we ensure that the selected elliptic curve has a prime order, in order to comply with the appropriate security standards [9, 10].
CLS.Setup algorithm generates a master key and public system parameters as follows: Choose an additive group G with a prime order q and a generator P∈G defined on an elliptic curve.
Let G be an additive group with a prime order q and P∈G, where G consists of points on an elliptic curve and P is a generator of G. lABE.Setup algorithm generates lABE parameters as follows: 1. Choose a random (s in Z_{q}^) as the attribute master secret key and computes the corresponding public key PK=s·P.
Before starting these processes, the server generates a cyclic group G, of a large prime order q with generator g.
It first chooses a group G 1 of prime order p, a generator P ∈ G 1.
We refer to [113] (the second part) for the explicit determination of the loci of stable curves admitting an action by a cyclic group of prime order, especially those contained in the boundary (partial overline{{mathfrak {M}}_g}).
The scheme is based on the Sphinx blinding logic (cf. [59] and [60]): Instead of sending r shared secrets, a single element e of a cyclic group of prime order (satisfying the decisional Diffie-Hellman assumption) is used at each hop to derive the individual secrets.
The scheme is based on exponentiation of block matrices over a finite field of prime order, and its security is claimed to rely in the hardness of a discrete logarithm problem in a subgroup of GLn(p).
In fact, for ( g ge 4), the locus ( Sing (mathfrak M_g) ) is the locus of curves admitting a nontrivial automorphism, so this locus is the locus of curves admitting a nontrivial automorphism of prime order.
To determine when this happens is an interesting question, fully answered by Cornalba in the case where G is a cyclic group of prime order [127] (this result is the key to understanding the structure of the singular locus ({{mathrm{text {Sing}}}}( mathfrak M_g))).
