Octets and Utilities for Cryptography (Maxima 5.45.0 Manual)

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### 88.5 Octets and Utilities for Cryptography

Function: base64 (arg)

  Returns the base64-representation of arg as a string. The argument arg may be a string, a non-negative integer or a list of octets.

  Examples:

      (%i1) base64: base64("foo bar baz");
      (%o1)                          Zm9vIGJhciBiYXo=
      (%i2) string: base64_decode(base64);
      (%o2)                            foo bar baz
      (%i3) obase: 16.$
      (%i4) integer: base64_decode(base64, 'number);
      (%o4)                       666f6f206261722062617a
      (%i5) octets: base64_decode(base64, 'list);
      (%o5)            [66, 6F, 6F, 20, 62, 61, 72, 20, 62, 61, 7A]
      (%i6) ibase: 16.$
      (%i7) base64(octets);
      (%o7)                          Zm9vIGJhciBiYXo=

  Note that if arg contains umlauts (resp. octets larger than 127) the resulting base64-string is platform dependent. However the decoded string will be equal to the original.

  Categories: Package stringproc

Function: base64_decode
`base64_decode` (base64-string)
`base64_decode` (base64-string, return-type)

  By default `base64_decode` decodes the base64-string back to the original string.

  The optional argument return-type allows `base64_decode` to alternatively return the corresponding number or list of octets. return-type may be `string`, `number` or `list`.

  Example: See base64.

  Categories: Package stringproc

Function: crc24sum
`crc24sum` (octets)
`crc24sum` (octets, return-type)

  By default `crc24sum` returns the `CRC24` checksum of an octet-list as a string.

  The optional argument return-type allows `crc24sum` to alternatively return the corresponding number or list of octets. return-type may be `string`, `number` or `list`.

  Example:

      -----BEGIN PGP SIGNATURE-----
      Version: GnuPG v2.0.22 (GNU/Linux)

      iQEcBAEBAgAGBQJVdCTzAAoJEG/1Mgf2DWAqCSYH/AhVFwhu1D89C3/QFcgVvZTM
      wnOYzBUURJAL/cT+IngkLEpp3hEbREcugWp+Tm6aw3R4CdJ7G3FLxExBH/5KnDHi
      rBQu+I7+3ySK2hpryQ6Wx5J9uZSa4YmfsNteR8up0zGkaulJeWkS4pjiRM+auWVe
      vajlKZCIK52P080DG7Q2dpshh4fgTeNwqCuCiBhQ73t8g1IaLdhDN6EzJVjGIzam
      /spqT/sTo6sw8yDOJjvU+Qvn6/mSMjC/YxjhRMaQt9EMrR1AZ4ukBF5uG1S7mXOH
      WdiwkSPZ3gnIBhM9SuC076gLWZUNs6NqTeE3UzMjDAFhH3jYk1T7mysCvdtIkms=
      =WmeC
      -----END PGP SIGNATURE-----

      (%i1) ibase : obase : 16.$
      (%i2) sig64 : sconcat(
       "iQEcBAEBAgAGBQJVdCTzAAoJEG/1Mgf2DWAqCSYH/AhVFwhu1D89C3/QFcgVvZTM",
       "wnOYzBUURJAL/cT+IngkLEpp3hEbREcugWp+Tm6aw3R4CdJ7G3FLxExBH/5KnDHi",
       "rBQu+I7+3ySK2hpryQ6Wx5J9uZSa4YmfsNteR8up0zGkaulJeWkS4pjiRM+auWVe",
       "vajlKZCIK52P080DG7Q2dpshh4fgTeNwqCuCiBhQ73t8g1IaLdhDN6EzJVjGIzam",
       "/spqT/sTo6sw8yDOJjvU+Qvn6/mSMjC/YxjhRMaQt9EMrR1AZ4ukBF5uG1S7mXOH",
       "WdiwkSPZ3gnIBhM9SuC076gLWZUNs6NqTeE3UzMjDAFhH3jYk1T7mysCvdtIkms=" )$
      (%i3) octets: base64_decode(sig64, 'list)$
      (%i4) crc24: crc24sum(octets, 'list);
      (%o4)                          [5A, 67, 82]
      (%i5) base64(crc24);
      (%o5)                              WmeC

  Categories: Package stringproc

Function: md5sum
`md5sum` (arg)
`md5sum` (arg, return-type)

  Returns the `MD5` checksum of a string, a non-negative integer or a list of octets. The default return value is a string containing 32 hex characters.

  The optional argument return-type allows `md5sum` to alternatively return the corresponding number or list of octets. return-type may be `string`, `number` or `list`.

  Examples:

      (%i1) ibase: obase: 16.$
      (%i2) msg: "foo bar baz"$
      (%i3) string: md5sum(msg);
      (%o3)                  ab07acbb1e496801937adfa772424bf7
      (%i4) integer: md5sum(msg, 'number);
      (%o4)                 0ab07acbb1e496801937adfa772424bf7
      (%i5) octets: md5sum(msg, 'list);
      (%o5)        [0AB,7,0AC,0BB,1E,49,68,1,93,7A,0DF,0A7,72,42,4B,0F7]
      (%i6) sdowncase( printf(false, "~{~2,'0x~^:~}", octets) );
      (%o6)           ab:07:ac:bb:1e:49:68:01:93:7a:df:a7:72:42:4b:f7

  Note that in case arg contains German umlauts or other non-ASCII characters (resp. octets larger than 127) the `MD5` checksum is platform dependent.

  Categories: Package stringproc

Function: mgf1_sha1
`mgf1_sha1` (seed, len)
`mgf1_sha1` (seed, len, return-type)

  Returns a pseudo random number of variable length. By default the returned value is a number with a length of len octets.

  The optional argument return-type allows `mgf1_sha1` to alternatively return the corresponding list of len octets. return-type may be `number` or `list`.

  The computation of the returned value is described in `RFC 3447`, appendix `B.2.1 MGF1`. `SHA1` ist used as hash function, i.e. the randomness of the computed number relies on the randomness of `SHA1` hashes.

  Example:

      (%i1) ibase: obase: 16.$
      (%i2) number: mgf1_sha1(4711., 8);
      (%o2)                        0e0252e5a2a42fea1
      (%i3) octets: mgf1_sha1(4711., 8, 'list);
      (%o3)                  [0E0,25,2E,5A,2A,42,0FE,0A1]

  Categories: Package stringproc

Function: number_to_octets (number)

  Returns an octet-representation of number as a list of octets. The number must be a non-negative integer.

  Example:

      (%i1) ibase : obase : 16.$
      (%i2) octets: [0ca,0fe,0ba,0be]$
      (%i3) number: octets_to_number(octets);
      (%o3)                            0cafebabe
      (%i4) number_to_octets(number);
      (%o4)                      [0CA, 0FE, 0BA, 0BE]

  Categories: Package stringproc

Function: octets_to_number (octets)

  Returns a number by concatenating the octets in the list of octets.

  Example: See number_to_octets.

  Categories: Package stringproc

Function: octets_to_oid (octets)

  Computes an object identifier (OID) from the list of octets.

  Example: RSA encryption OID

      (%i1) ibase : obase : 16.$
      (%i2) oid: octets_to_oid([2A,86,48,86,0F7,0D,1,1,1]);
      (%o2)                      1.2.840.113549.1.1.1
      (%i3) oid_to_octets(oid);
      (%o3)               [2A, 86, 48, 86, 0F7, 0D, 1, 1, 1]

  Categories: Package stringproc

Function: octets_to_string
`octets_to_string` (octets)
`octets_to_string` (octets, encoding)

  Decodes the list of octets into a string according to current system defaults. When decoding octets corresponding to Non-US-ASCII characters the result depends on the platform, application and underlying Lisp.

  Example: Using system defaults (Maxima compiled with GCL, which uses no format definition and simply passes through the UTF-8-octets encoded by the GNU/Linux terminal).

      (%i1) octets: string_to_octets("abc");
      (%o1)                            [61, 62, 63]
      (%i2) octets_to_string(octets);
      (%o2)                                 abc
      (%i3) ibase: obase: 16.$
      (%i4) unicode(20AC);
      (%o4)                                  €
      (%i5) octets: string_to_octets(%);
      (%o5)                           [0E2, 82, 0AC]
      (%i6) octets_to_string(octets);
      (%o6)                                  €
      (%i7) utf8_to_unicode(octets);
      (%o7)                                20AC

  In case the external format of the Lisp reader is equal to UTF-8 the optional argument encoding allows to set the encoding for the octet to string conversion. If necessary see adjust_external_format for changing the external format.

  Some names of supported encodings (see corresponding Lisp manual for more):
  CCL, CLISP, SBCL: `utf-8, ucs-2be, ucs-4be, iso-8859-1, cp1252, cp850`
  CMUCL: `utf-8, utf-16-be, utf-32-be, iso8859-1, cp1252`
  ECL: `utf-8, ucs-2be, ucs-4be, iso-8859-1, windows-cp1252, dos-cp850`

  Example (continued): Using the optional encoding argument (Maxima compiled with SBCL, GNU/Linux terminal).

      (%i8) string_to_octets("€", "ucs-2be");
      (%o8)                              [20, 0AC]

  Categories: Package stringproc

Function: oid_to_octets (oid-string)

  Converts an object identifier (OID) to a list of octets.

  Example: See octets_to_oid.

  Categories: Package stringproc

Function: sha1sum
`sha1sum` (arg)
`sha1sum` (arg, return-type)

  Returns the `SHA1` fingerprint of a string, a non-negative integer or a list of octets. The default return value is a string containing 40 hex characters.

  The optional argument return-type allows `sha1sum` to alternatively return the corresponding number or list of octets. return-type may be `string`, `number` or `list`.

  Example:

      (%i1) ibase: obase: 16.$
      (%i2) msg: "foo bar baz"$
      (%i3) string: sha1sum(msg);
      (%o3)              c7567e8b39e2428e38bf9c9226ac68de4c67dc39
      (%i4) integer: sha1sum(msg, 'number);
      (%o4)             0c7567e8b39e2428e38bf9c9226ac68de4c67dc39
      (%i5) octets: sha1sum(msg, 'list);
      (%o5)  [0C7,56,7E,8B,39,0E2,42,8E,38,0BF,9C,92,26,0AC,68,0DE,4C,67,0DC,39]
      (%i6) sdowncase( printf(false, "~{~2,'0x~^:~}", octets) );
      (%o6)     c7:56:7e:8b:39:e2:42:8e:38:bf:9c:92:26:ac:68:de:4c:67:dc:39

  Note that in case arg contains German umlauts or other non-ASCII characters (resp. octets larger than 127) the `SHA1` fingerprint is platform dependent.

  Categories: Package stringproc

Function: sha256sum
`sha256sum` (arg)
`sha256sum` (arg, return-type)

  Returns the `SHA256` fingerprint of a string, a non-negative integer or a list of octets. The default return value is a string containing 64 hex characters.

  The optional argument return-type allows `sha256sum` to alternatively return the corresponding number or list of octets (see sha1sum).

  Example:

      (%i1) string: sha256sum("foo bar baz");
      (%o1)  dbd318c1c462aee872f41109a4dfd3048871a03dedd0fe0e757ced57dad6f2d7

  Note that in case arg contains German umlauts or other non-ASCII characters (resp. octets larger than 127) the `SHA256` fingerprint is platform dependent.

  Categories: Package stringproc

Function: string_to_octets
`string_to_octets` (string)
`string_to_octets` (string, encoding)

  Encodes a string into a list of octets according to current system defaults. When encoding strings containing Non-US-ASCII characters the result depends on the platform, application and underlying Lisp.

  In case the external format of the Lisp reader is equal to UTF-8 the optional argument encoding allows to set the encoding for the string to octet conversion. If necessary see adjust_external_format for changing the external format.

  See octets_to_string for examples and some more information.

  Categories: Package stringproc

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