Montgomery reduction: Difference between revisions

Content added Content deleted
m (→‎{{header|Phix}}: replaced with gmp version)
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=={{header|Phix}}==
=={{header|Phix}}==
{{trans|D}}
{{trans|D}}
{{libheader|mpfr}}
<lang Phix>include builtins\bigint.e
<lang Phix>include mpfr.e

function bitLength(bigint v)
if bi_sign(v)=-1 then v = bi_neg(v) end if
integer result = 0
⚫
while bi_compare(v,0)!=0 do
⚫
{v,?} = bi_div3(v, 2)
result += 1
end while
return result
end function
enum BASE, BITLEN, MODULUS, RRM
enum BASE, BITLEN, MODULUS, RRM

function reduce(sequence mont, bigint a)
function reduce(sequence mont, mpz a)
integer n = mont[BITLEN]
integer n = mont[BITLEN]
bigint m = mont[MODULUS]
mpz m = mont[MODULUS],
r = mpz_init_set(a)
for i=1 to n do
for i=1 to n do
if bi_mod(a,2)=BI_ONE then -- odd
if mpz_odd(r) then
a = bi_add(a,m)
mpz_add(r,r,m)
end if
end if
{a,?} = bi_div3(a,2)
{} = mpz_fdiv_q_ui(r,r,2)
end for
end for
if bi_compare(a,m)>=0 then a = bi_sub(a,m) end if
if mpz_cmp(r,m)>=0 then mpz_sub(r,r,m) end if
return a
return r
end function
end function

function Montgomery(bigint m)
function Montgomery(mpz m)
if bi_sign(m)=-1 then crash("must be positive") end if
if mpz_sign(m)=-1 then crash("must be positive") end if
if bi_mod(m,2)!=BI_ONE then crash("must be odd") end if
if not mpz_odd(m) then crash("must be odd") end if
integer n = bitLength(m)
integer n = mpz_sizeinbase(m,2)
bigint rrm = bi_mod(bi_shl(1,n*2),m)
mpz rrm = mpz_init(2)
mpz_powm_ui(rrm,rrm,n*2,m)
return {2, -- BASE
return {2, -- BASE
n, -- BITLEN
n, -- BITLEN
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end function
end function
bigint m = bi_new("750791094644726559640638407699"),
mpz m = mpz_init("750791094644726559640638407699"),
x1 = bi_new("540019781128412936473322405310"),
x1 = mpz_init("540019781128412936473322405310"),
x2 = bi_new("515692107665463680305819378593");
x2 = mpz_init("515692107665463680305819378593"),
t1 = mpz_init(),
t2 = mpz_init()
sequence mont = Montgomery(m)
sequence mont = Montgomery(m)
bigint t1 = bi_mul(x1,mont[RRM]),
mpz_mul(t1,x1,mont[RRM])
t2 = bi_mul(x2,mont[RRM]),
mpz_mul(t2,x2,mont[RRM])
r1 = reduce(mont,t1),
mpz r1 = reduce(mont,t1),
r2 = reduce(mont,t2),
r2 = reduce(mont,t2),
r = bi_shl(1,mont[BITLEN])
r = mpz_init()
mpz_ui_pow_ui(r,2,mont[BITLEN])
printf(1,"b : %d\n", {mont[BASE]})
printf(1,"b : %d\n", {mont[BASE]})
printf(1,"n : %d\n", {mont[BITLEN]})
printf(1,"n : %d\n", {mont[BITLEN]})
printf(1,"r : %s\n", {bi_sprint(r)})
printf(1,"r : %s\n", {mpz_get_str(r)})
printf(1,"m : %s\n", {bi_sprint(mont[MODULUS])})
printf(1,"m : %s\n", {mpz_get_str(mont[MODULUS])})
printf(1,"t1: %s\n", {bi_sprint(t1)})
printf(1,"t1: %s\n", {mpz_get_str(t1)})
printf(1,"t2: %s\n", {bi_sprint(t2)})
printf(1,"t2: %s\n", {mpz_get_str(t2)})
printf(1,"r1: %s\n", {bi_sprint(r1)})
printf(1,"r1: %s\n", {mpz_get_str(r1)})
printf(1,"r2: %s\n", {bi_sprint(r2)})
printf(1,"r2: %s\n", {mpz_get_str(r2)})
printf(1,"\n")
printf(1,"\n")
printf(1,"Original x1 : %s\n", {bi_sprint(x1)})
printf(1,"Original x1 : %s\n", {mpz_get_str(x1)})
printf(1,"Recovered from r1 : %s\n", {bi_sprint(reduce(mont,r1))})
printf(1,"Recovered from r1 : %s\n", {mpz_get_str(reduce(mont,r1))})
printf(1,"Original x2 : %s\n", {bi_sprint(x2)})
printf(1,"Original x2 : %s\n", {mpz_get_str(x2)})
printf(1,"Recovered from r2 : %s\n", {bi_sprint(reduce(mont,r2))})
printf(1,"Recovered from r2 : %s\n", {mpz_get_str(reduce(mont,r2))})
printf(1,"\nMontgomery computation of x1 ^ x2 mod m :")
printf(1,"\nMontgomery computation of x1 ^ x2 mod m :")
bigint prod = reduce(mont,mont[RRM]),
mpz prod = reduce(mont,mont[RRM])
base = reduce(mont,bi_mul(x1,mont[RRM])),
mpz_mul(r,x1,mont[RRM])
mpz base = reduce(mont,r),
expn = x2;
expn = mpz_init_set(x2)
while bitLength(expn)>0 do

⚫
if bi_mod(expn,2)=BI_ONE then -- odd
⚫
while mpz_cmp_si(expn,0)!=0 do
⚫
prod = reduce(mont,bi_mul(prod,base))
⚫
if mpz_odd(expn) then
mpz_mul(prod,prod,base)
⚫
prod = reduce(mont,prod)
end if
end if
{expn,?} = bi_div3(expn,2)
{} = mpz_fdiv_q_ui(expn,expn,2)
base = reduce(mont,bi_mul(base,base))
mpz_mul(base,base,base)
⚫
base = reduce(mont,base)
end while
end while
printf(1,"%s\n",{bi_sprint(reduce(mont,prod))})
printf(1,"%s\n",{mpz_get_str(reduce(mont,prod))})
printf(1,"\n alternate computation of x1 ^ x2 mod m :");
printf(1," alternate computation of x1 ^ x2 mod m :")
mpz_powm(r,x1,x2,m)
printf(1,"%s\n",{bi_sprint(bi_mod_exp(x1, x2, m))})</lang>
printf(1,"%s\n",{mpz_get_str(r)})</lang>
{{out}}
{{out}}
<pre>
<pre>
Retrieved from "https://rosettacode.org/wiki/Montgomery_reduction"