Cryptography Reference
In-Depth Information
LINT
root (void) const;
return
the
integer
part
of
the
square root of
a
LINT
root (const LINT& p) const;
return the square root of
a
mod-
ulo an odd prime
p
LINT
root (const LINT& p,
const LINT& q) const;
return the square root of
a
mod-
ulo
p*q
, where
p
and
q
are odd
primes
int
twofact (LINT& odd) const;
return the even part of
a
,
odd
contains the odd part of
a
LINT
xgcd (const LINT& b,
LINT& u, int& sign_u,
LINT& v, int& sign_v)
const;
extended Euclidean algorithm
with return of gcd of
a
and
b
,
u
and
v
contain the absolute
values of the factors of the linear
combination
g = sign_u*u*a +
sign_v*v*b
B.10 Number-Theoretic Friend Functions
LINT
chinrem (unsigned noofeq,
LINT** coeff);
return a solution of a system of si-
multaneous linear congruences.
In
coeff
is passed a vector of
pointers to
LINT
objects as coef-
ficients
a1
,
m1
,
a2
,
m2
,
a3
,
m3
,
...
of the congruence system with
noofeq
equations
x
≡
a
i
mod
m
i
LINT
extendprime (const LINT& pmin,
const LINT& pmax,
const LINT& a,
const LINT& q,
const LINT& f);
return a prime
p
with
pmin
≤
≤
pmax
,with
p
≡
a
mod
q
and
gcd(
p
−
1
,
f
)=1
,
f
odd
p
LINT
extendprime (USHORT l,
const LINT& a,
const LINT& q,
const LINT& f);
return a prime
p
of length
l
bits,
i.e.,
2
l
−
1
≤
p
<
2
l
,with
p
≡
a
mod
q
and
gcd(
p
−
1
,
f
)=1
,
f
odd
