3d: SHA Hash Family
+shad
+shadDouble SHA-256
Produces an atom that is twice-hashed with +shax, the SHA-256 cryptographic hash algorithm.
Accepts
ruz is an atom.
Produces
An atom.
Source
++ shad |=(ruz=@ (shax (shax ruz)))Examples
> `@uw`(shad 11)
0w2Rt.J1gzO.JjsQc.0Komy.DYUUO.27koh.QxwE0.Qgwt7.EPGCi+shaf
+shafHalf SHA-256
Produces a 128-bit atom by performing the bitwise XOR on the first and last halves of the 256-bit salted hash +shas.
Accepts
sal is an atom.
ruz is an atom.
Source
++ shaf
|= [sal=@ ruz=@]
=+ haz=(shas sal ruz)
(mix (end 7 haz) (rsh 7 haz))Examples
> `@uw`(shaf 17 8)
0wD.DSP0L.WUuQg.-A765.4RY-h+sham
+sham128-bit noun hash
Produces a 128-bit atom by hashing a noun yux with the +shaf function. If that noun is a cell, then it is passed to the +jam function to produce an atom to be hashed.
Accepts
yux is a noun.
Produces
A @uvH.
Source
++ sham
|= yux=* ^- @uvH ^- @
?@ yux
(shaf %mash yux)
(shaf %sham (jam yux))Examples
> (sham [2 4])
0v3.71s52.4bqnp.ki2b8.9hhsp.2ufgg
> (sham "hello")
0v1.hg8mv.t7s3f.u4f8a.q5noe.dvqvh+shas
+shasSalted hash
Produces an atom by using SHA-256 plus a salt input. The bitwise XOR is performed on salt +sal and the product of atom ruz hashed with SHA-256. The product of that logical operation is then itself hashed with SHA-256.
Accepts
sal is an atom.
ruz is an atom.
Source
++ shas
~/ %shas
|= [sal=@ ruz=@]
(shax (mix sal (shax ruz)))Examples
> `@uw`(shas 1 1)
0w5hZ.Gim4L.9xKlU.jJJQr.2Bgi~.RHd5s.IwXuV.p43at.ZdsTY+shax
+shaxSHA-256
Produces an atom by hashing an atom ruz with SHA-256.
Sources
++ shax
~/ %shax
|= ruz=@ ^- @
(shay [(met 3 ruz) ruz])Examples
> `@uw`(shax 'foo')
0waXD.pCa8n.EHVEb.-3p70.JgxcQ.gj0tf.4mr-o.~6~Sx.HJ2oI+shay
+shaySHA-256 with length
Produces an atom by hashing an atom ruz with SHA-256. Another atom, len, is the byte-length of the theoretical buffer represented by the atom.
Accepts
len is an atom.
ruz is an atom.
Source
++ shay
~/ %shay
|= [len=@u ruz=@] ^- @
=> .(ruz (cut 3 [0 len] ruz))
=+ [few==>(fe .(a 5)) wac=|=([a=@ b=@] (cut 5 [a 1] b))]
=+ [sum=sum.few ror=ror.few net=net.few inv=inv.few]
=+ ral=(lsh [0 3] len)
=+ ^= ful
%+ can 0
:~ [ral ruz]
[8 128]
[(mod (sub 960 (mod (add 8 ral) 512)) 512) 0]
[64 (~(net fe 6) ral)]
==
=+ lex=(met 9 ful)
=+ ^= kbx 0xc671.78f2.bef9.a3f7.a450.6ceb.90be.fffa.
8cc7.0208.84c8.7814.78a5.636f.748f.82ee.
682e.6ff3.5b9c.ca4f.4ed8.aa4a.391c.0cb3.
34b0.bcb5.2748.774c.1e37.6c08.19a4.c116.
106a.a070.f40e.3585.d699.0624.d192.e819.
c76c.51a3.c24b.8b70.a81a.664b.a2bf.e8a1.
9272.2c85.81c2.c92e.766a.0abb.650a.7354.
5338.0d13.4d2c.6dfc.2e1b.2138.27b7.0a85.
1429.2967.06ca.6351.d5a7.9147.c6e0.0bf3.
bf59.7fc7.b003.27c8.a831.c66d.983e.5152.
76f9.88da.5cb0.a9dc.4a74.84aa.2de9.2c6f.
240c.a1cc.0fc1.9dc6.efbe.4786.e49b.69c1.
c19b.f174.9bdc.06a7.80de.b1fe.72be.5d74.
550c.7dc3.2431.85be.1283.5b01.d807.aa98.
ab1c.5ed5.923f.82a4.59f1.11f1.3956.c25b.
e9b5.dba5.b5c0.fbcf.7137.4491.428a.2f98
=+ ^= hax 0x5be0.cd19.1f83.d9ab.9b05.688c.510e.527f.
a54f.f53a.3c6e.f372.bb67.ae85.6a09.e667
=+ i=0
|- ^- @
?: =(i lex)
(run 5 hax net)
=+ ^= wox
=+ dux=(cut 9 [i 1] ful)
=+ wox=(run 5 dux net)
=+ j=16
|- ^- @
?: =(64 j)
wox
=+ :* l=(wac (sub j 15) wox)
m=(wac (sub j 2) wox)
n=(wac (sub j 16) wox)
o=(wac (sub j 7) wox)
==
=+ x=:(mix (ror 0 7 l) (ror 0 18 l) (rsh [0 3] l))
=+ y=:(mix (ror 0 17 m) (ror 0 19 m) (rsh [0 10] m))
=+ z=:(sum n x o y)
$(wox (con (lsh [5 j] z) wox), j +(j))
=+ j=0
=+ :* a=(wac 0 hax)
b=(wac 1 hax)
c=(wac 2 hax)
d=(wac 3 hax)
e=(wac 4 hax)
f=(wac 5 hax)
g=(wac 6 hax)
h=(wac 7 hax)
==
|- ^- @
?: =(64 j)
%= ^$
i +(i)
hax %+ rep 5
:~ (sum a (wac 0 hax))
(sum b (wac 1 hax))
(sum c (wac 2 hax))
(sum d (wac 3 hax))
(sum e (wac 4 hax))
(sum f (wac 5 hax))
(sum g (wac 6 hax))
(sum h (wac 7 hax))
==
==
=+ l=:(mix (ror 0 2 a) (ror 0 13 a) (ror 0 22 a)) :: s0
=+ m=:(mix (dis a b) (dis a c) (dis b c)) :: maj
=+ n=(sum l m) :: t2
=+ o=:(mix (ror 0 6 e) (ror 0 11 e) (ror 0 25 e)) :: s1
=+ p=(mix (dis e f) (dis (inv e) g)) :: ch
=+ q=:(sum h o p (wac j kbx) (wac j wox)) :: t1
$(j +(j), a (sum q n), b a, c b, d c, e (sum d q), f e, g f, h g)Examples
> `@uw`(shay 1 'hello')
0w2eN.jupNe.OyGTU.-l0Co.SWSGS.fFD9k.HPHg1.-AYmg.CgaCG> `@uw`(shay 2 'hello')
0wdUu.vKccX.fhjYt.tY2a4.B~sqA.KWNOM.1TnEu.8sQd8.LvyYTDiscussion
Because byte-strings can have leading zeros, but atoms cannot, we use len as a way of saying that the atom ruz is shorter than its representative byte-string.
+shaw
+shawHash to nbits
Produces an atom of len random bits by hashing ruz with the salted SHA-256 hash algorithm, where sal is the cryptographic salt.
Accepts
sal is an atom.
len is an atom.
ruz is an atom.
Produces
An atom.
Source
++ shaw
|= [sal=@ len=@ ruz=@]
(~(raw og (shas sal (mix len ruz))) len)Examples
> `@ub`(shaw 3 6 98)
0b11.0111
> `@ub`(shaw 2 6 98)
0b11+shaz
+shazSHA-512
Produces an atom by hashing an atom ruz with SHA-512.
Accepts
ruz is an atom.
Produces
An atom.
Source
++ shaz
|= ruz=@ ^- @
(shal [(met 3 ruz) ruz])Examples
`@uw`(shaz 'hello')
0w1.3MdWY.sS~QT.zFsbB.N7oQo.cSImU.56Xcu.DMtMq.mrSsc.z8WsY.pNABZ.Z~ySG.Ecysb.XCP5P.fuHjq.Jimnn.zPoHQ.AQD6r+shal
+shalSHA-512 with length
Produces an atom by hashing an atom ruz with SHA-512. Another atom, len, is the byte-length of the theoretical buffer represented by the atom.
Accepts
len is an atom.
ruz is an atom.
Produces
An atom.
Source
++ shal
~/ %shal
|= [len=@ ruz=@] ^- @
=> .(ruz (cut 3 [0 len] ruz))
=+ [few==>(fe .(a 6)) wac=|=([a=@ b=@] (cut 6 [a 1] b))]
=+ [sum=sum.few ror=ror.few net=net.few inv=inv.few]
=+ ral=(lsh [0 3] len)
=+ ^= ful
%+ can 0
:~ [ral ruz]
[8 128]
[(mod (sub 1.920 (mod (add 8 ral) 1.024)) 1.024) 0]
[128 (~(net fe 7) ral)]
==
=+ lex=(met 10 ful)
=+ ^= kbx 0x6c44.198c.4a47.5817.5fcb.6fab.3ad6.faec.
597f.299c.fc65.7e2a.4cc5.d4be.cb3e.42b6.
431d.67c4.9c10.0d4c.3c9e.be0a.15c9.bebc.
32ca.ab7b.40c7.2493.28db.77f5.2304.7d84.
1b71.0b35.131c.471b.113f.9804.bef9.0dae.
0a63.7dc5.a2c8.98a6.06f0.67aa.7217.6fba.
f57d.4f7f.ee6e.d178.eada.7dd6.cde0.eb1e.
d186.b8c7.21c0.c207.ca27.3ece.ea26.619c.
c671.78f2.e372.532b.bef9.a3f7.b2c6.7915.
a450.6ceb.de82.bde9.90be.fffa.2363.1e28.
8cc7.0208.1a64.39ec.84c8.7814.a1f0.ab72.
78a5.636f.4317.2f60.748f.82ee.5def.b2fc.
682e.6ff3.d6b2.b8a3.5b9c.ca4f.7763.e373.
4ed8.aa4a.e341.8acb.391c.0cb3.c5c9.5a63.
34b0.bcb5.e19b.48a8.2748.774c.df8e.eb99.
1e37.6c08.5141.ab53.19a4.c116.b8d2.d0c8.
106a.a070.32bb.d1b8.f40e.3585.5771.202a.
d699.0624.5565.a910.d192.e819.d6ef.5218.
c76c.51a3.0654.be30.c24b.8b70.d0f8.9791.
a81a.664b.bc42.3001.a2bf.e8a1.4cf1.0364.
9272.2c85.1482.353b.81c2.c92e.47ed.aee6.
766a.0abb.3c77.b2a8.650a.7354.8baf.63de.
5338.0d13.9d95.b3df.4d2c.6dfc.5ac4.2aed.
2e1b.2138.5c26.c926.27b7.0a85.46d2.2ffc.
1429.2967.0a0e.6e70.06ca.6351.e003.826f.
d5a7.9147.930a.a725.c6e0.0bf3.3da8.8fc2.
bf59.7fc7.beef.0ee4.b003.27c8.98fb.213f.
a831.c66d.2db4.3210.983e.5152.ee66.dfab.
76f9.88da.8311.53b5.5cb0.a9dc.bd41.fbd4.
4a74.84aa.6ea6.e483.2de9.2c6f.592b.0275.
240c.a1cc.77ac.9c65.0fc1.9dc6.8b8c.d5b5.
efbe.4786.384f.25e3.e49b.69c1.9ef1.4ad2.
c19b.f174.cf69.2694.9bdc.06a7.25c7.1235.
80de.b1fe.3b16.96b1.72be.5d74.f27b.896f.
550c.7dc3.d5ff.b4e2.2431.85be.4ee4.b28c.
1283.5b01.4570.6fbe.d807.aa98.a303.0242.
ab1c.5ed5.da6d.8118.923f.82a4.af19.4f9b.
59f1.11f1.b605.d019.3956.c25b.f348.b538.
e9b5.dba5.8189.dbbc.b5c0.fbcf.ec4d.3b2f.
7137.4491.23ef.65cd.428a.2f98.d728.ae22
=+ ^= hax 0x5be0.cd19.137e.2179.1f83.d9ab.fb41.bd6b.
9b05.688c.2b3e.6c1f.510e.527f.ade6.82d1.
a54f.f53a.5f1d.36f1.3c6e.f372.fe94.f82b.
bb67.ae85.84ca.a73b.6a09.e667.f3bc.c908
=+ i=0
|- ^- @
?: =(i lex)
(run 6 hax net)
=+ ^= wox
=+ dux=(cut 10 [i 1] ful)
=+ wox=(run 6 dux net)
=+ j=16
|- ^- @
?: =(80 j)
wox
=+ :* l=(wac (sub j 15) wox)
m=(wac (sub j 2) wox)
n=(wac (sub j 16) wox)
o=(wac (sub j 7) wox)
==
=+ x=:(mix (ror 0 1 l) (ror 0 8 l) (rsh [0 7] l))
=+ y=:(mix (ror 0 19 m) (ror 0 61 m) (rsh [0 6] m))
=+ z=:(sum n x o y)
$(wox (con (lsh [6 j] z) wox), j +(j))
=+ j=0
=+ :* a=(wac 0 hax)
b=(wac 1 hax)
c=(wac 2 hax)
d=(wac 3 hax)
e=(wac 4 hax)
f=(wac 5 hax)
g=(wac 6 hax)
h=(wac 7 hax)
==
|- ^- @
?: =(80 j)
%= ^$
i +(i)
hax %+ rep 6
:~ (sum a (wac 0 hax))
(sum b (wac 1 hax))
(sum c (wac 2 hax))
(sum d (wac 3 hax))
(sum e (wac 4 hax))
(sum f (wac 5 hax))
(sum g (wac 6 hax))
(sum h (wac 7 hax))
==
==
=+ l=:(mix (ror 0 28 a) (ror 0 34 a) (ror 0 39 a)) :: S0
=+ m=:(mix (dis a b) (dis a c) (dis b c)) :: maj
=+ n=(sum l m) :: t2
=+ o=:(mix (ror 0 14 e) (ror 0 18 e) (ror 0 41 e)) :: S1
=+ p=(mix (dis e f) (dis (inv e) g)) :: ch
=+ q=:(sum h o p (wac j kbx) (wac j wox)) :: t1
$(j +(j), a (sum q n), b a, c b, d c, e (sum d q), f e, g f, h g)Examples
> `@uw`(shal 1 'hello')
0w2.nWO0R.zMAzH.OSWU1.apOje.19Mta.RE24o.4u~MB.wQuj4.NDdG6.0QZA0.w21Br.yQVhu.pFBII.Cdgvd.WT-bH.g51Yu.fL44y> `@uw`(shal 2 'hello')
0w1.r3W4g.hae37.8YUFp.ntryr.DsQuY.rPsdm.p3Xjv.rayLz.DslEc.Lxvll.OJUc3.tZeLZ.TjUnu.XMyGr.82qPA.zl1y0.HbSpTDiscussion
Because byte-strings can have leading zeros, but atoms cannot, we use len as a way of saying that the atom ruz is shorter than its representative byte-string.
+shan
+shanSHA-1
Produces an atom by hashing an atom ruz with SHA-1.
Accepts
ruz is an atom.
Produces
An atom.
Source
++ shan
|= ruz=@
=+ [few==>(fe .(a 5)) wac=|=([a=@ b=@] (cut 5 [a 1] b))]
=+ [sum=sum.few ror=ror.few rol=rol.few net=net.few inv=inv.few]
=+ ral=(lsh [0 3] (met 3 ruz))
=+ ^= ful
%+ can 0
:~ [ral ruz]
[8 128]
[(mod (sub 960 (mod (add 8 ral) 512)) 512) 0]
[64 (~(net fe 6) ral)]
==
=+ lex=(met 9 ful)
=+ kbx=0xca62.c1d6.8f1b.bcdc.6ed9.eba1.5a82.7999
=+ hax=0xc3d2.e1f0.1032.5476.98ba.dcfe.efcd.ab89.6745.2301
=+ i=0
|-
?: =(i lex)
(rep 5 (flop (rip 5 hax)))
=+ ^= wox
=+ dux=(cut 9 [i 1] ful)
=+ wox=(rep 5 (turn (rip 5 dux) net))
=+ j=16
|- ^- @
?: =(80 j)
wox
=+ :* l=(wac (sub j 3) wox)
m=(wac (sub j 8) wox)
n=(wac (sub j 14) wox)
o=(wac (sub j 16) wox)
==
=+ z=(rol 0 1 :(mix l m n o))
$(wox (con (lsh [5 j] z) wox), j +(j))
=+ j=0
=+ :* a=(wac 0 hax)
b=(wac 1 hax)
c=(wac 2 hax)
d=(wac 3 hax)
e=(wac 4 hax)
==
|- ^- @
?: =(80 j)
%= ^$
i +(i)
hax %+ rep 5
:~
(sum a (wac 0 hax))
(sum b (wac 1 hax))
(sum c (wac 2 hax))
(sum d (wac 3 hax))
(sum e (wac 4 hax))
==
==
=+ fx=(con (dis b c) (dis (not 5 1 b) d))
=+ fy=:(mix b c d)
=+ fz=:(con (dis b c) (dis b d) (dis c d))
=+ ^= tem
?: &((gte j 0) (lte j 19))
:(sum (rol 0 5 a) fx e (wac 0 kbx) (wac j wox))
?: &((gte j 20) (lte j 39))
:(sum (rol 0 5 a) fy e (wac 1 kbx) (wac j wox))
?: &((gte j 40) (lte j 59))
:(sum (rol 0 5 a) fz e (wac 2 kbx) (wac j wox))
:(sum (rol 0 5 a) fy e (wac 3 kbx) (wac j wox))
$(j +(j), a tem, b a, c (rol 0 30 b), d c, e d)Examples
> `@uw`(shan 'hello')
0waH.QNxTs.NuyyS.HXu3P.J8bdC.KGkddDiscussion
SHA-1 is a deprecated function; it is not considered secure.
+og
+ogContainer arm for SHA-256-powered random-number generation. Its sample .a is an atom that is used as a seed for the hash.
Accepts
.a is an atom.
Produces
A core.
Source
++ og
~/ %og
|_ a=@Examples
> ~(. og 919)
<4.wmp {a/@ud <54.tyv 119.olq 31.ohr 1.jmk $143>}>Discussion
Note that the product is deterministic; the seed will produce the same result every time it is run. Use eny, 256 bits of entropy, for a non-deterministic product.
+rad:og
+rad:ogRandom in range
Produces a random number that is within the range of first .b whole numbers, starting at 0.
Accepts
.b is an atom.
Produces
An atom.
Source
++ rad
|= b=@ ^- @
~_ leaf+"rad-zero"
?< =(0 b)
=+ c=(raw (met 0 b))
?:((lth c b) c $(a +(a)))Examples
> (~(rad og 5) 11)
4
> (~(rad og 758.716.593) 11)
2
> (~(rad og 1) 100.000)
71.499
> (~(rad og eny) 11) :: `eny` acts as a random sample
7+rads:og
+rads:ogRandom continuation
Produces a cell. The head of the cell is a random number that is within the range of first .b whole numbers, starting at 0. The tail is a new core produced from hashing the parent core with (rad b).
Accepts
.b is an atom.
Produces
A cell.
Source
++ rads
|= b=@
=+ r=(rad b)
[r +>.$(a (shas %og-s (mix a r)))]Examples
> (~(rads og 4) 10)
[2 <4.wmp {a/@ <54.tyv 119.olq 31.ohr 1.jmk $143>}>]
> =/ rng ~(. og 7)
=^ a rng (rads:rng 10)
=^ b rng (rads:rng 10)
[a b]
[2 8]Discussion
Since everything in Hoon is a pure function, we need to use tricks like this to generate separate random values from the same seed. Notice how we jump from one +rads function call to another in the above example.
+raw:og
+raw:ogRandom bits
Produces an atom with a bitwidth .b that is composed of random bits.
Accepts
.b is an atom.
Produces
An atom.
Source
++ raw
~/ %raw
|= b=@ ^- @
%+ can
0
=+ c=(shas %og-a (mix b a))
|- ^- (list [@ @])
?: =(0 b)
~
=+ d=(shas %og-b (mix b (mix a c)))
?: (lth b 256)
[[b (end [0 b] d)] ~]
[[256 d] $(c d, b (sub b 256))]Examples
> `@ud`(~(raw og 27) 4)
0b1001
> `@ub`(~(raw og 27) 3)
0b0
> `@ub`(~(raw og 11) 4)
0b1111
> `@ub`(~(raw og 11) 3)
0b100+raws:og
+raws:ogRandom bits continuation
Produces a cell. The head of the cell is an atom with a bitwidth .b that is composed of random bits. The tail is a new core produced from hashing the parent core with (raw b).
Source
++ raws
|= b=@
=+ r=(raw b)
[r +>.$(a (shas %og-s (mix a r)))]Examples
> `[@ub _og]`(~(raws og 7) 4)
[0b1100 <4.wmp {a/@ <54.tyv 119.olq 31.ohr 1.jmk $143>}>]
> =/ rng ~(. og 7)
=^ a rng (rads:rng 4)
=^ b rng (rads:rng 4)
[`@ub`a `@ub`b]
[0b10 0b1]Discussion
Since everything in Hoon is a pure function, we need to use tricks like this to generate separate random values from the same seed. Notice how we jump from one +raws function call to another in the above example.
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