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P packet Flooding Attack Network Bandwidth Denial of Service (DoS) Packet-Dropping AttackBog'liq gu2011 AQLLI SHAHAR, TEST, 1-мактаб тўгарак жадвал, BUYRUQ. YASIN BREND, TAQRIZ YANGI, 2, Tarjima SPLINES, DIFFERENTIAL EQUATIONS, AND OPTIMAL, (11-ozbetinshe K.U.A)Q.Zafar, APPLIKATSIYADA QIRQISHNI HAR HIL USULLARINI BAJARISH, EDUCATION SYSTEM OF UZBEKISTON, O’zbekistonning va jahon hamjamiyati, OCHILOVA NIGORANING, 7 yosh inqirozi uning sabablari va alomatlari, TEXNIKA MADANIYATI, AAASupersingular curves
If E is a supersingular curve, then it has embedding degree
k
∈ {, , , , }. In contrast to ordinary elliptic curves with
embedding degree k
> , supersingular curves have the
advantage that they have so-called distortion maps, which
is a desirable feature in some pairing-based applications, as
this allows the use of symmetric pairings. A discussion of
the cases k
= , , and follows.
Embedding degree
k
= . The case of embedding
degree k
= can be realized both over prime fields and
Pairing-Friendly Elliptic Curves. Table Bit sizes of curve
parameters and corresponding embedding degrees to obtain
commonly desired levels of security
Security Subgroup Extension
level
size
field size
Embedding degree
k
(in bits)
r (in bits)
q
k
(in bits)
ρ
≈
ρ
≈
−,
−
∗
,
−
,
−,
−
−
,
−,
−
−
,
−,
−
−
,
−,
−
−
non-prime fields, using supersingular elliptic curves with
q
+ F
q
-rational points.
If q is a prime with q
≥ , supersingular curves over
F
q
can be obtained as follows: given a subgroup size r, let
h such that q
= hr − is prime and q /≡ (mod ) (this
latter assumption is only for the sake of simplicity). If q
≡
(mod ), then let
E
/F
q
: y
+ y = x
+ ax
where a
∈ F
×
q
such that
−a /∈ (F
×
q
)
. If q
≡ (mod ) let
E
/F
q
: y
+ y = x
+ b
for any b
∈ F
q
. This construction allows to choose r and h
almost arbitrarily, so one can make choices such that r and
q have low Hamming weight or some other special form.
In addition, the above curves both have automorphisms
defined over
F
q
, which yields easy-to-compute distortion
maps.
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