++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 thatab>=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).
jis a number between 0 and 3, selecting the seed with that index in +raku.ris an atom with a maximum length of two bytes. This is an internal function of+feisand+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]