3f: Scrambling

+un

Reversible scrambling

A core that contains arms that perform reversible scrambling operations. Used in the @p phonetic base.

Source

++  un
  |%

---

++wren:un

Conceal structure

Scrambles a byte-string pyn by adding the current position to each byte, looking it up in an s-box, and then performing the XOR operation on the result, pushing it forward. The inverse of wred.

Accepts

pyn is an atom.

Produces

An atom.

Source

++  wren
  |=  pyn=@  ^-  @
  =+  len=(met 3 pyn)
  ?:  =(0 len)
    0
  =>  .(len (dec len))
  =+  mig=(zaft (xafo len (cut 3 [len 1] pyn)))
  %+  can  3
  %-  flop  ^-  (list [@ @])
  :-  [1 mig]
  |-  ^-  (list [@ @])
  ?:  =(0 len)
    ~
  =>  .(len (dec len))
  =+  mog=(zyft :(mix mig (end 3 len) (cut 3 [len 1] pyn)))
  [[1 mog] $(mig mog)]

Examples

> `@ux`(wren:un 'testing')
0x30.bf6a.b9fe.7d8f

> `@ux`'testing'
0x67.6e69.7473.6574

> `@da`(wred:un (wren:un ~2001.2.5))
~2001.2.5

---

++wred:un

Restore structure

Unscrambles a byte-string cry by subtracting the current position from each byte, looking it up in an s-box, and performing the XOR operation on the result, pushing it forward. The inverse of wren.

Accepts

cry is an atom.

Produces

An atom.

Source

++  wred
  |=  cry=@  ^-  @
  =+  len=(met 3 cry)
  ?:  =(0 len)
    0
  =>  .(len (dec len))
  =+  mig=(cut 3 [len 1] cry)
  %+  can  3
  %-  flop  ^-  (list [@ @])
  :-  [1 (xaro len (zart mig))]
  |-  ^-  (list [@ @])
  ?:  =(0 len)
    ~
  =>  .(len (dec len))
  =+  mog=(cut 3 [len 1] cry)
  [[1 :(mix mig (end 3 len) (zyrt mog))] $(mig mog)]

Examples

> (wred:un 0x30.bf6a.b9fe.7d8f)
29.113.321.805.538.676

> `@t`(wred:un 0x30.bf6a.b9fe.7d8f)
'testing'

> (wred:un (wren:un 200.038.426))
200.038.426

---

++xafo:un

Add modulo 255

Produces the sum of two atoms modulo 255, encoded as a nonzero byte. The inverse of xaro.

Accepts

a is an atom.

b is an atom.

Produces

An atom.

Source

++  xafo  |=([a=@ b=@] +((mod (add (dec b) a) 255)))

Examples

> (xafo:un 5 6)
11

> (xafo:un 256 20)
21

> (xafo:un 256 (xaro:un 256 20))
20

---

++xaro:un

Subtract modulo 255

Produces the sum of two atoms modulo 255, encoded as a nonzero byte. The inverse of xafo.

Accepts

a is an atom.

b is an atom.

Produces

An atom.

Source

++  xaro  |=([a=@ b=@] +((mod (add (dec b) (sub 255 (mod a 255))) 255)))

Examples

> (xaro:un 17 57)
40

> (xaro:un 265 12)
2

> (xaro:un 256 (xafo:un 256 20))
20

---

++zaft:un

Look up in 255 sub box

Looks up a nonzero byte a in a substitution box with 255 values, producing a unique nonzero byte. The inverse of zart.

Accepts

a is an atom of one byte in length.

Produces

An atom.

Source

++  zaft
  |=  a=@D
  =+  ^=  b
      0xcc.75bc.86c8.2fb1.9a42.f0b3.79a0.92ca.21f6.1e41.cde5.fcc0.
      7e85.51ae.1005.c72d.1246.07e8.7c64.a914.8d69.d9f4.59c2.8038.
      1f4a.dca2.6fdf.66f9.f561.a12e.5a16.f7b0.a39f.364e.cb70.7318.
      1de1.ad31.63d1.abd4.db68.6a33.134d.a760.edee.5434.493a.e323.
      930d.8f3d.3562.bb81.0b24.43cf.bea5.a6eb.52b4.0229.06b2.6704.
      78c9.45ec.d75e.58af.c577.b7b9.c40e.017d.90c3.87f8.96fa.1153.
      0372.7f30.1c32.ac83.ff17.c6e4.d36d.6b55.e2ce.8c71.8a5b.b6f3.
      9d4b.eab5.8b3c.e7f2.a8fe.9574.5de0.bf20.3f15.9784.9939.5f9c.
      e609.564f.d8a4.b825.9819.94aa.2c08.8e4c.9b22.477a.2840.3ed6.
      3750.6ef1.44dd.89ef.6576.d00a.fbda.9ed2.3b6c.7b0c.bde9.2ade.
      5c88.c182.481a.1b0f.2bfd.d591.2726.57ba
  (cut 3 [(dec a) 1] b)

Examples

> (zaft:un 0x12)
42

> (zaft:un 0xff)
204
> `@ux`(zart:un 204)
0xff

> (zaft:un 0x0)
! decrement-underflow
! exit

---

++zart:un

Reverse look up in 255 sub box

Looks up the index of a nonzero byte a in the substitution box with 255 values, producing a unique nonzero byte. The inverse of zaft.

Accepts

a is an atom of one byte in length.

Produces

An atom.

Source

++  zart
  |=  a=@D
  =+  ^=  b
      0x68.4f07.ea1c.73c9.75c2.efc8.d559.5125.f621.a7a8.8591.5613.
      dd52.40eb.65a2.60b7.4bcb.1123.ceb0.1bd6.3c84.2906.b164.19b3.
      1e95.5fec.ffbc.f187.fbe2.6680.7c77.d30e.e94a.9414.fd9a.017d.
      3a7e.5a55.8ff5.8bf9.c181.e5b6.6ab2.35da.50aa.9293.3bc0.cdc6.
      f3bf.1a58.4130.f844.3846.744e.36a0.f205.789e.32d8.5e54.5c22.
      0f76.fce7.4569.0d99.d26e.e879.dc16.2df4.887f.1ffe.4dba.6f5d.
      bbcc.2663.1762.aed7.af8a.ca20.dbb4.9bc7.a942.834c.105b.c4d4.
      8202.3e61.a671.90e6.273d.bdab.3157.cfa4.0c2e.df86.2496.f7ed.
      2b48.2a9d.5318.a343.d128.be9c.a5ad.6bb5.6dfa.c5e1.3408.128d.
      2c04.0339.97a1.2ff0.49d0.eeb8.6c0a.0b37.b967.c347.d9ac.e072.
      e409.7b9f.1598.1d3f.33de.8ce3.8970.8e7a
  (cut 3 [(dec a) 1] b)

Examples

> `@ux`(zart:un 204)
0xff

> `@ux`(zart:un 42)
0x12

> (zaft:un 0x12)
42

---

++zyft:un

Lookup byte in 256 sub box

Looks up a byte a in a substitution box with 256 values, producing a byte. The inverse of zyrt.

Accepts

a is an atom of one byte in length.

Produces

An atom.

Source

++  zyft
  |=  a=@D
  =+  ^=  b
      0xbb49.b71f.b881.b402.17e4.6b86.69b5.1647.115f.dddb.7ca5.
        8371.4bd5.19a9.b092.605d.0d9b.e030.a0cc.78ba.5706.4d2d.
        986a.768c.f8e8.c4c7.2f1c.effe.3cae.01c0.253e.65d3.3872.
        ce0e.7a74.8ac6.daac.7e5c.6479.44ec.4143.3d20.4af0.ee6c.
        c828.deca.0377.249f.ffcd.7b4f.eb7d.66f2.8951.042e.595a.
        8e13.f9c3.a79a.f788.6199.9391.7fab.6200.4ce5.0758.e2f1.
        7594.c945.d218.4248.afa1.e61a.54fb.1482.bea4.96a2.3473.
        63c2.e7cb.155b.120a.4ed7.bfd8.b31b.4008.f329.fca3.5380.
        9556.0cb2.8722.2bea.e96e.3ac5.d1bc.10e3.2c52.a62a.b1d6.
        35aa.d05e.f6a8.0f3b.31ed.559d.09ad.f585.6d21.fd1d.8d67.
        370b.26f4.70c1.b923.4684.6fbd.cf8b.5036.0539.9cdc.d93f.
        9068.1edf.8f33.b632.d427.97fa.9ee1
  (cut 3 [a 1] b)

Examples

> (zyft:un 0x12)
57

> (zyft:un 0x0)
225

> (zyft:un 0xff)
187
> `@ux`(zyrt:un 187)
0xff

---

++zyrt:un

Reverse lookup byte in 256 sub box

Looks up a byte a in a substitution box with 256 values, producing a byte. The inverse of zyft.

Accepts

a is an atom of one byte in length.

Produces

An atom.

Source

++  zyrt
  |=  a=@D
  =+  ^=  b
      0x9fc8.2753.6e02.8fcf.8b35.2b20.5598.7caa.c9a9.30b0.9b48.
        47ce.6371.80f6.407d.00dd.0aa5.ed10.ecb7.0f5a.5c3a.e605.
        c077.4337.17bd.9eda.62a4.79a7.ccb8.44cd.8e64.1ec4.5b6b.
        1842.ffd8.1dfb.fd07.f2f9.594c.3be3.73c6.2cb6.8438.e434.
        8d3d.ea6a.5268.72db.a001.2e11.de8c.88d3.0369.4f7a.87e2.
        860d.0991.25d0.16b9.978a.4bf4.2a1a.e96c.fa50.85b5.9aeb.
        9dbb.b2d9.a2d1.7bba.66be.e81f.1946.29a8.f5d2.f30c.2499.
        c1b3.6583.89e1.ee36.e0b4.6092.937e.d74e.2f6f.513e.9615.
        9c5d.d581.e7ab.fe74.f01b.78b1.ae75.af57.0ec2.adc7.3245.
        12bf.2314.3967.0806.31dc.cb94.d43f.493c.54a6.0421.c3a1.
        1c4a.28ac.fc0b.26ca.5870.e576.f7f1.616d.905f.ef41.33bc.
        df4d.225e.2d56.7fd6.1395.a3f8.c582
  (cut 3 [a 1] b)

Examples

> `@ux`(zyrt:un 57)
0x12

> `@ux`(zyrt:un 225)
0x0

> `@ux`(zyrt:un 187)
0xff
> (zyft:un 0xff)
187

---

+ob

Reversible scrambling, v3

A core for performing reversible scrambling operations for the @p phonetic base.

Source

++  ob
  ~%  %ob  ..ob
    ==
      %fein  fein
      %fynd  fynd
    ==
  |%

---

++fein:ob

conceal structure, v3

+fein conceals planet-sized atoms. The idea is that it should not be trivial to tell which planet a star has spawned under.

Permutes atom pyn which fits into 17 to 32 bits, or if pyn fits into 33 to 64 bits, does the same permutation on the low 32 bits only. Otherwise, passes pyn through unchanged.

Accepts

pyn is an atom.

Produces

An atom.

Source

++  fein
  ~/  %fein
  |=  pyn=@  ^-  @
  ?:  &((gte pyn 0x1.0000) (lte pyn 0xffff.ffff))
    (add 0x1.0000 (feis (sub pyn 0x1.0000)))
  ?:  &((gte pyn 0x1.0000.0000) (lte pyn 0xffff.ffff.ffff.ffff))
    =/  lo  (dis pyn 0xffff.ffff)
    =/  hi  (dis pyn 0xffff.ffff.0000.0000)
    %+  con  hi
    $(pyn lo)
  pyn

Examples

> (fein:ob 111.103)
2.783.373.008

> (fynd:ob 2.783.373.008)
111.103

---

++fynd:ob

Restore structure, v3

Restores obfuscated values that have been enciphered with +fein.

Permutes atom cry that fits into 17 to 32 bits, or permutes the low 32 bits of cry if it fits into 33 to 64 bits. Otherwise, passes the atom through unchanged. The inverse of the one applied by +fein.

Accepts

cry is an atom.

Produces

An atom.

Source

++  fynd
  ~/  %fynd
  |=  cry=@  ^-  @
  ?:  &((gte cry 0x1.0000) (lte cry 0xffff.ffff))
    (add 0x1.0000 (tail (sub cry 0x1.0000)))
  ?:  &((gte cry 0x1.0000.0000) (lte cry 0xffff.ffff.ffff.ffff))
    =/  lo  (dis cry 0xffff.ffff)
    =/  hi  (dis cry 0xffff.ffff.0000.0000)
    %+  con  hi
    $(cry lo)
  cry

Examples

> (fein:ob 111.103)
2.783.373.008

> (fynd:ob 2.783.373.008)
111.103

---

++feis:ob

Four-round generalised Feistel cipher over the domain [0, 2^32 - 2^16 - 1]

See: Black & Rogaway (2002), Ciphers for arbitrary finite domains.

Inverse of +tail.

Accepts

m is an atom.

Produces

An atom.

Source

++  feis
  |=  m=@
  ^-  @
  (fee 4 0xffff 0x1.0000 (mul 0xffff 0x1.0000) eff m)

Examples

> (feis:ob 11)
776.343.932

> (tail:ob 776.343.932)
11

---

++tail:ob

Reverse +feis

Applies the reverse of the Feistel cipher applied by +feis.

Accepts

m is an atom.

Produces

An atom.

Source

++  tail
  |=  m=@
  ^-  @
  (feen 4 0xffff 0x1.0000 (mul 0xffff 0x1.0000) eff m)

Examples

> (feis:ob 11)
776.343.932

> (tail:ob 776.343.932)
11

---

++fee:ob

"Fe" in B&R (2002)

A Feistel cipher given the following parameters:

• r: Number of Feistel rounds.

• a, b: Parameters such that ab >= k.

• k: Value such that the domain of the cipher is [0, k - 1].

• prf: A gate denoting a family of pseudorandom functions indexed by its first argument and taking its second argument as input.

• m: An input value in the domain [0, k - 1].

Accepts

r, a, b, k are an atoms.

prft is a gate: $-([j=@ r=@] @).

m is an atom.

Produces

An atom.

Source

++  fee
  |=  [r=@ a=@ b=@ k=@ prf=$-([j=@ r=@] @) m=@]
  ^-  @
  =/  c  (fe r a b prf m)
  ?:  (lth c k)
    c
  (fe r a b prf c)

---

++feen:ob

Reverse +fee

"Fe^-1" in B&R (2002). Reverses a Feistel cipher constructed with parameters as described in +fee.

Accepts

r, a, b, and k are atoms.

prf is a gate: $-([j=@ r=@] @).

m is an atom.

Produces

An atom.

Source

++  feen
  |=  [r=@ a=@ b=@ k=@ prf=$-([j=@ r=@] @) m=@]
  ^-  @
  =/  c  (fen r a b prf m)
  ?:  (lth c k)
    c
  (fen r a b prf c)

---

+fe:ob

An internal function to +fee.

Note that this implementation differs slightly from the reference paper to support some legacy behaviour.

Accepts

r, a, and b are atoms.

prf is a gate: $-([j=@ r=@] @).

m is an atom.

Produces

An atom.

Source

++  fe
  |=  [r=@ a=@ b=@ prf=$-([j=@ r=@] @) m=@]
  =/  j  1
  =/  ell  (mod m a)
  =/  arr  (div m a)
  |-  ^-  @
  ::
  ?:  (gth j r)
    ?.  =((mod r 2) 0)
      (add (mul arr a) ell)
    ::
    :: Note that +fe differs from B&R (2002)'s "fe" below, as a previous
    :: implementation of this cipher contained a bug such that certain inputs
    :: could encipher to the same output.
    ::
    :: To correct these problem cases while also preserving the cipher's
    :: legacy behaviour on most inputs, we check for a problem case (which
    :: occurs when 'arr' is equal to 'a') and, if detected, use an alternate
    :: permutation instead.
    ::
    ?:  =(arr a)
      (add (mul arr a) ell)
    (add (mul ell a) arr)
  ::
  =/  f  (prf (sub j 1) arr)
  ::
  =/  tmp
    ?.  =((mod j 2) 0)
      (mod (add f ell) a)
    (mod (add f ell) b)
  ::
  $(j +(j), ell arr, arr tmp)

---

++fen:ob

Reverse +fe

This is an internal function to +feen

Note that this implementation differs slightly from the reference paper to support some legacy behaviour.

Accepts

r, a and b are atoms.

prf is a gate: $-([j=@ r=@] @).

m is an atom.

Produces

An atom.

Source

++  fen
  |=  [r=@ a=@ b=@ prf=$-([j=@ r=@] @) m=@]
  =/  j  r
  ::
  =/  ahh
    ?.  =((mod r 2) 0)
      (div m a)
    (mod m a)
  ::
  =/  ale
    ?.  =((mod r 2) 0)
      (mod m a)
    (div m a)
  ::
  :: Similar to the comment in +fe, +fen differs from B&R (2002)'s "fe^-1"
  :: here in order to preserve the legacy cipher's behaviour on most inputs.
  ::
  :: Here problem cases can be identified by 'ahh' equating with 'a'; we
  :: correct those cases by swapping the values of 'ahh' and 'ale'.
  ::
  =/  ell
    ?:  =(ale a)
      ahh
    ale
  ::
  =/  arr
    ?:  =(ale a)
      ale
    ahh
  ::
  |-  ^-  @
  ?:  (lth j 1)
    (add (mul arr a) ell)
  =/  f  (prf (sub j 1) ell)
  ::
  ::  Note that there is a slight deviation here to avoid dealing with
  ::  negative values.  We add 'a' or 'b' to arr as appropriate and reduce
  ::  'f' modulo the same number before performing subtraction.
  ::
  =/  tmp
    ?.  =((mod j 2) 0)
      (mod (sub (add arr a) (mod f a)) a)
    (mod (sub (add arr b) (mod f b)) b)
  ::
  $(j (sub j 1), ell tmp, arr ell)

---

++eff:ob

murmur3-based pseudorandom function.

'F' in B&R (2002).

• j is a number between 0 and 3, selecting the seed with that index in +raku.

• r is an atom with a maximum length of two bytes. This is an internal function of +feis and +tail.

Accepts

j is an atom.

r is an atom.

Produces

An atom.

Source

++  eff
  |=  [j=@ r=@]
  ^-  @
  (muk (snag j raku) 2 r)

Example

> (eff:ob 0 'ab')
1.178.819.349

---

++raku:ob

Key list

Produces a list of arbitrary hexademical keys for use with +eff.

Produces

A list of atoms of aura @ux (hexadecimal).

Source

++  raku
  ^-  (list @ux)
  :~  0xb76d.5eed
      0xee28.1300
      0x85bc.ae01
      0x4b38.7af7
  ==

Examples

> raku:ob
~[0xb76d.5eed 0xee28.1300 0x85bc.ae01 0x4b38.7af7]

---