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

        > (shad 11)
        \/20.519.637.820.582.103.109.435.907.615.585.653.479.776.629.591.855.451.248.\/
          718.295.626.625.655.417.234
    

    ++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                                                ::  half sha-256
          |=  [sal=@ ruz=@]
          =+  haz=(shas sal ruz)
          (mix (end 7 1 haz) (rsh 7 1 haz))
    

    Examples

        > (shaf 17 8)
        52.667.672.807.485.289.251.324.336.639.183.409.041
    
        > `@ub`(shaf 17 8)
        \/0b1011.1111.1101.0110.1110.1000.0100.1110.1100.1000.0010.0100.1111.0001.0010.0010\/
          .0100.1110.1110.0011.1100.1111.0001.1101.1101.1100.1110.1111.0100.0101.0001.0100
        \/
    

    ++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)
            (rep 6 (turn (rip 6 hax) net))
          =+  ^=  wox
              =+  dux=(cut 10 [i 1] ful)
              =+  wox=(rep 6 (turn (rip 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

        > (shal 1 'hello')
        \/7.956.615.373.791.575.273.027.009.123.631.914.645.972.441.264.528.176.292.399.908\/
          .424.469.676.078.106.561.839.264.176.650.109.335.825.608.088.511.266.620.100.157.
          847.055.280.028.606.252.747.432.021.213.474
        \/
    
        > (shal 1 'hello')
        \/7.956.615.373.791.575.273.027.009.123.631.914.645.972.441.264.528.176.292.399.908\/
          .424.469.676.078.106.561.839.264.176.650.109.335.825.608.088.511.266.620.100.157.
          847.055.280.028.606.252.747.432.021.213.474
        \/
    

    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.


    ++sham

    128-bit noun hash

    Produces a 128-bit atom by hashing a noun yux with the shah 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

    An atom.

    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
    

    ++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

        > (shan 'hello')
        975.987.071.262.755.080.377.722.350.727.279.193.143.145.743.181
    

    Discussion

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


    ++shas

    Salted hash

    Produces an atom by using SHA-256 plus a salt input. The bitwise XOR is performed on sal and the product of 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
          |=  [sal=@ ruz=@]
          (shax (mix sal (shax ruz)))
    

    Examples

        > (shas 12.845 6)
        \/111.115.941.493.032.291.043.932.789.632.248.509.108.945.255.494.251.860.287\/
          .707.279.709.200.349.471.936
        \/
    

    ++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
    

    ++shax

    SHA-256

    Produces an atom by hashing an atom ruz with SHA-256.

    Sources

        ++  shax
              ~/  %shax
              |=  ruz=@  ^-  @
              (shay [(met 3 ruz) ruz])
    

    Examples

        > (shax 'hello')
        \/16.552.786.619.039.860.277.601.417.878.457.384.195.409.020.923.835.016.617.984.82\/
          0.774.431.701.725.740
        \/
    

    ++shay

    SHA-256 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.

    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)
            (rep 5 (turn (rip 5 hax) net))
          =+  ^=  wox
              =+  dux=(cut 9 [i 1] ful)
              =+  wox=(rep 5 (turn (rip 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

        > (shay 1 'hello')
        \/16.144.219.278.061.159.438.339.586.294.967.166.038.336.988.797.862.808.055.174.98\/
        7.398.597.302.069.674
        \/
    
        > (shay 2 'hello')
        \/100.467.333.538.737.303.691.714.735.404.408.035.555.613.179.595.938.688.113.300.8\/
          01.974.878.934.544.183
        \/
    

    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.


    ++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

        > (shaz 'hello')
        \/3.548.533.422.469.437.734.729.094.584.175.910.682.076.656.883.559.953.324.378.007\/
          .735.849.386.038.666.450.748.109.671.344.747.196.048.200.348.948.408.339.256.384.
          360.070.359.656.053.016.948.640.159.265.179
        \/
    

    ++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=@  ^-  @
            =+  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

    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 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 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.