gematria

gematria is an efficient criptography tool to aid in the decyphering of cicada 3301's Liber Primus(LP), It's purpose is to process a given string and analyse it into various hash functions and gematria sums. It can process hashes and gematria sums almost instantly.

After processing, gematria will create a file with the results in ./outputs/{string}.txt

Gematria Primus

Gematria Primus, found during the 2013 puzzle, is an alphabet with 29 runes, each with an English equivalent and a numerical value, The numerical values are consecutive prime numbers in ascending order. The runes themselves are the focal point of the current step, Liber Primus.

3301's inclusion of a value for each rune allows for a function to assign a number to any word. This is simply adding the value of each rune - what we call gematria sum. 3301 has used this gematria sum previously, notably in the count command from the onion terminal and with certain phrases throughout the puzzles. Certain phrases include:

• The Instar Emergence: 761 (reflected in the song's file name of 761.mp3, and in the song's length of 167 seconds)
• Patience is a virtue: 761
• Interconnectedness: 772 (not prime, but 277 is, which is the song's length in seconds)
• one of the solved pages contains words in runes within a square of numbers; gematria summing the words completes a magic square
• more sentences than you would expect in the solved pages gematria sum to prime numbers

Gematria Primus Script

By running gematria, it will automatically process the sums and calculte primes and emirps of the Gematria Primus values... Processing order:

1. Whole string
2. Each word in string
3. Each line in string
4. Atbash string
5. Each word in atbash string
6. Each line in atbash string

Example of output:

$ python lib/main.py 'Any Message'

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
   GEMATRIA PROCESSING...
	RUNIC: ᚪᚾᚣ ᛗᛖᛋᛋᚪᚷᛖ
	LATIN: AENY MESSAGE >>> 2023-06-14 11:09:36.018235
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
ᚪᚾᚣ ᛗᛖᛋᛋᚪᚷᛖ
---------------
	GEMATIRA SUM: 654
	IS_PRIME() = False >>> IS_EMIRP() = False

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
   PROCESSING EACH WORD IN "ᚪᚾᚣ ᛗᛖᛋᛋᚪᚷᛖ" >>> 2023-06-14 11:09:36.027583
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
ᚪᚾᚣ
-------
	GEMATIRA SUM: 229
	IS_PRIME() = True >>> IS_EMIRP() = False

ᛗᛖᛋᛋᚪᚷᛖ
-----------
	GEMATIRA SUM: 425
	IS_PRIME() = False >>> IS_EMIRP() = False

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
   PROCESSING EACH LINE IN "ᚪᚾᚣ ᛗᛖᛋᛋᚪᚷᛖ" >>> 2023-06-14 11:09:36.042432
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
ᚪᚾᚣ ᛗᛖᛋᛋᚪᚷᛖ
---------------
	GEMATIRA SUM: 654
	IS_PRIME() = False >>> IS_EMIRP() = False

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
   ATBASH >> GEMATRIA PROCESSING...
	RUNIC: ᚱᛗᚦ ᚾᛁᛈᛈᚱᛟᛁ
	LATIN: ZVMB NVHHZTV >>> 2023-06-14 11:09:36.052845
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
ᚱᛗᚦ ᚾᛁᛈᛈᚱᛟᛁ
---------------
	GEMATIRA SUM: 358
	IS_PRIME() = False >>> IS_EMIRP() = True

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
   PROCESSING EACH WORD IN "ᚱᛗᚦ ᚾᛁᛈᛈᚱᛟᛁ" >>> 2023-06-14 11:09:36.062569
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
ᚱᛗᚦ
-------
	GEMATIRA SUM: 87
	IS_PRIME() = False >>> IS_EMIRP() = False

ᚾᛁᛈᛈᚱᛟᛁ
-----------
	GEMATIRA SUM: 271
	IS_PRIME() = True >>> IS_EMIRP() = False

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
   PROCESSING EACH LINE IN "ᚱᛗᚦ ᚾᛁᛈᛈᚱᛟᛁ" >>> 2023-06-14 11:09:36.077203
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
ᚱᛗᚦ ᚾᛁᛈᛈᚱᛟᛁ
---------------
	GEMATIRA SUM: 358
	IS_PRIME() = False >>> IS_EMIRP() = True

Hashing

In Page 56 of LP a message was deciphered.

Within the deep web, there exists a page that hashes to :

36367763ab73783c7af284446c
59466b4cd653239a311cb7116
d4618dee09a8425893dc7500b
464fdaf1672d7bef5e891c6e227
4568926a49fb4f45132c2a8b4

It is the duty of every pilgrim to seek out this page

The full hash is: (512 bits) 36367763ab73783c7af284446c59466b4cd653239a311cb7116d4618dee09a8425893dc7500b464fdaf1672d7bef5e891c6e2274568926a49fb4f45132c2a8b4

It indicates that there is a onion v2 URL, which when hashed (The hashing algorithm is not known, but potential candidates are SHA-512, BLAKE-512 or BLAKE2b) produces the full hash. The hash can also be a unique file identifier for deep web applications such as Freenet, GnuNET or P2P file sharing systems, which use Distributed Hash Tables.

Hashing Check Script

I made a script that hashes a given string into various 512 bit hashing algorithms and then compares the hex digest into the DWH. This script can be given a .txt file and it will go through every line and hash it

An example of Gematria hashing "xmh57jrknzkhv6y3ls3ubitzfqnkrwxhopf5aygthi7d6rplyvk3noyd.onion":

python lib/main.py xmh57jrknzkhv6y3ls3ubitzfqnkrwxhopf5aygthi7d6rplyvk3noyd.onion
> HASHING "xmh57jrknzkhv6y3ls3ubitzfqnkrwxhopf5aygthi7d6rplyvk3noyd.onion"...
> BLAKE2B   1ed7f0c22b5f0b90db36b120f625034fde7b81055275144ffef65597114c4d29773a114a40a9de8179d3fec16f940696b1f8653dadd8be6a01b42c2b8f936184 | IS_DEEPWEB_HASH() -> False >> d:122
> BLAKE512  050c6418b6a34e5c6d49b268bd9a83bd41d2b840383db3833f3bc7d4305a0d58acaa33e963bddf4e91c65d049a427fa01ba88171151a4ea9884f226becdb3523 | IS_DEEPWEB_HASH() -> False >> d:118
> SHA512    f9f7386ff0abd23d43a58718562be3b9a1c50f135e6080277c91be569ceb09d49e08951b691e66e23f01b028dca5968c2f63e2bc99b582f455d358ffee912b18 | IS_DEEPWEB_HASH() -> False >> d:114
> SHA3      a2e0ff145026a8af2a7592b2e6d9d69d0bd3724c47d76ca643acc4dbf4bc8c62abe6474a6e07ac7a9528da579bd567527cf37a95b16912458e737aa84bd4f1d2 | IS_DEEPWEB_HASH() -> False >> d:118
> WHIRLPOOL cfa22a8e02cb9d0c977dcd43a3d42b80fd381d0520a938097a6dedc29579807e427edc8b328c92b141df75833d1412c434ee4065b883084323932e63c9ec5c54 | IS_DEEPWEB_HASH() -> False >> d:121
> SKEIN512  66f8de627d0177ce0aa64bfa97563c5fdd180cbfcb11aeae275b1a21b041d73328d23b6f8dd0405dda8852e18308c457ca61e752b9ef40d34efd00a298f7ac24 | IS_DEEPWEB_HASH() -> False >> d:114
    ALGO                                                                   HEX-DIGEST                                                               HASH COMPARE             DISTANCE

Where:

ALGO Is the hash function used.

HEX-DIGEST Is the output of the message into the hash function.

HASH COMPARE Is the flag checking if found the DWH.

DISTANCE Is the Hamming distance between HEX-DIGEST and DWH(0 means they are the same, 128 complete opposite)

a tool by lipeeeee