3d: SHA Hash Family

+shad

Double 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

Half 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

128-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

Salted 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

SHA-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

SHA-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.LvyYT

Discussion

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

Hash 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

SHA-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

SHA-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.HbSpT

Discussion

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

SHA-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.KGkdd

Discussion

SHA-1 is a deprecated function; it is not considered secure.

---

+og

Container 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

Random 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)
7

---

+rads:og

Random 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:rng function call to another in the above example.

---

+raw:og

Random 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

Random 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  (raws:rng 4)
          =^  b  rng  (raws: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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