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"Introduction to Siribhūvalaya" - Talk at Jain Academy of Scholars

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Anil Jain

"Siribhūvalaya" is one of its kind mind-boggling creations in the whole world. This grand poetry has been crafted by Ācārya Kumudēndu in Numeral Script in 9th century. It is a treasure house of knowledge and encompasses verses in many languages.

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Siribhūvalaya : An Introduction Virtual Talk at Jain Academy of Scholars 27th February 2024 by Er. Anil Kumar Jain FIETE, FIE(I), SMCSI, LM-ISCA email: jain.anilk@gmail.com Siri Bhūvalaya Śōdha evam Praśikșaṇa Kēndra Kundakunda Jñānapīṭha Shri Digambar Jain Udasin Ashram Trust 584, M. G. Road, Indore - 452001
Siribhūvalaya : Key Historic Transitions ProCreation Period : 9th Century (about 1200 years ago) Setting : Ancient Karnataka, Near Bengaluru Focal Characters : Acārya Kumudendu - Outstanding inimitable Genius who scripted this inimitable epic. Mahāmata Mallikabbe - Ardent Benefactor who distributed copies of Siribhūvalaya – one of these survived to be rediscovered in twentieth century. Long Intermission: Wonderful Masterpiece laid into oblivion for next 1000 years due to complexity in deciphering it. Resurrection : In early 20th Century By Paņdit Yellappā Śāstrī (The arduous Redeemer who strived resurrection efforts till his death )2
One Cakra from Original Manuscript in Aṅka-Lipi 3
Transliteration by Paņdit Yellappā Śāstrī (Preserved at National Archives of India, N. Delhi) 4
First Chakra of Siribhūvalaya 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 1 59 23 1 16 1 28 28 1 1 56 59 4 56 1 1 47 16 34 1 7 16 1 1 7 56 1 60 2 53 54 47 28 1 47 45 28 7 4 59 41 4 45 1 30 47 47 45 42 53 28 51 1 52 1 1 3 1 22 1 30 2 1 2 55 30 1 7 45 47 52 1 4 1 47 1 1 1 1 53 1 52 59 52 4 59 30 2 55 55 13 16 2 53 60 1 4 16 47 48 45 16 56 56 43 45 1 56 1 4 1 13 5 47 45 1 1 22 30 51 1 2 56 38 30 4 1 1 56 1 1 16 1 57 7 56 56 1 22 1 6 54 52 52 45 1 7 55 48 1 58 52 35 28 55 1 38 45 30 55 4 47 7 45 38 45 38 1 7 1 1 1 28 13 56 55 51 54 1 1 1 1 42 2 4 4 1 43 16 47 7 1 13 4 51 4 8 28 53 47 22 8 1 53 59 38 7 43 40 1 52 59 54 30 1 45 16 1 28 23 50 7 43 43 9 1 2 45 51 30 1 52 58 48 59 47 54 4 4 1 47 45 47 56 28 1 45 1 13 7 7 7 10 55 1 53 47 56 1 1 7 1 1 2 60 48 56 1 1 16 1 1 54 1 52 17 30 54 45 45 11 59 56 52 1 45 1 55 28 52 28 1 2 1 52 54 4 43 60 48 28 1 16 23 8 53 7 1 12 2 1 53 52 43 23 2 4 16 52 44 54 1 2 42 7 1 7 47 30 28 48 47 1 54 52 16 13 45 54 23 4 28 45 45 30 1 59 1 56 28 2 54 53 38 2 2 1 28 55 40 60 4 50 28 14 2 13 47 1 1 4 17 45 1 56 1 52 56 51 1 47 55 55 45 7 2 54 1 56 7 1 1 15 23 4 53 54 59 48 13 56 1 47 23 1 2 55 16 1 1 47 40 54 16 52 1 47 60 43 60 16 45 16 43 1 7 47 1 7 1 4 54 54 1 43 28 28 7 1 2 7 52 30 1 4 47 4 13 17 42 1 54 13 1 28 1 45 42 5 48 56 1 1 1 52 54 7 1 1 2 56 56 2 43 1 1 18 56 43 22 45 56 43 2 2 56 1 8 48 59 59 7 16 53 55 53 48 1 1 46 2 30 53 1 19 47 45 1 2 54 56 56 2 55 51 4 16 7 13 30 16 1 1 4 52 52 4 54 47 2 38 1 20 1 54 60 56 54 1 60 1 1 16 40 38 17 1 47 56 33 55 1 1 59 48 1 53 7 1 1 21 1 52 16 1 60 1 30 53 30 7 47 13 13 22 8 13 45 59 54 1 2 42 54 47 53 52 53 22 16 30 1 4 52 47 56 1 28 16 1 22 59 51 1 1 7 28 53 60 7 1 16 16 1 1 58 23 4 53 56 1 52 2 13 52 38 30 45 7 1 30 56 16 1 1 1 30 48 56 54 54 55 28 45 24 1 47 47 1 28 22 1 47 1 1 45 46 1 1 47 53 55 52 1 1 7 43 2 1 1 1 43 25 1 4 53 1 45 43 16 55 52 4 47 55 45 22 51 56 1 38 13 30 2 28 56 13 56 28 55 26 4 16 46 1 1 16 1 1 1 1 1 47 59 4 8 38 58 1 1 48 1 7 22 1 1 1 60 27 52 4 30 56 53 52 54 1 30 52 1 16 54 7 58 1 30 54 1 56 51 53 56 57 56 4 60 5 IMPORTANT : Aṅka-Lipi (Numeral Script) allowed efficient implementation of Transposition and Substitution Ciphers (Cryptographic Mechanisms) by Acārya Kumudendu.
Partitioning of 27x27 Matrix of Cakra into Nine 9x9 Sub-Matrices Sub-Matrix 3 Sub-Matrix 2 Sub-Matrix 1 Sub-Matrix 4 Sub-Matrix 9 Sub-Matrix 5 Sub-Matrix 6 Sub-Matrix 8 Sub-Matrix 7 6
Substitution Cipher Key (KCT) for different scripts क ु मुदेन्दु कोड सारणी में देवनागरी, कन्नड़ एवं ब्राह्मी लिलि क े ध्वन्याक्षर 7
Conversion of a Word into Numbers (Encoding) शब्द वर्ण ववच्छे द अङ्क-विवि भूविय भ् ऊ व् अ ि् अ य् अ 51-8-56-1-55-1-53-1 ज्ञानिीठ ज् ञ् आ न् अ ि् ई ठ् अ 35-37-2-47-1-48-5-39-1 लक्षलिश्री क ् ष् इ ि् इ श् र् ई 28-58-4-43-4-57-54-5 8 This is an example of Alphabetic Writing System which represent the phonological structure of the language. Vowels and Consonants have equal status and are presented in a sequence. This type of writing system is in contrast with Abugida (Alphasyllabary), in which a single symbol denotes the combination of one consonant and one vowel. Example - Most of the European Scripts - which are descendents of Latin and Greek writing systems.
Conversion of Numbers into Word (Decoding) अङ्क-विवि वर्ण प्रस्थािन शब्द 59. 4. 54. 4. 51. 8। 56. 1. 55. 1. 53. 1 स् इ र् इ भ् ऊ व् अ ि् अ य् अ विरि भूविय 1. 58. 38. 1. 52. 1. 60. 2. 48. 54. 2. 43. 4. 60. 2. 54. 53. 1 अ ष् ट् अ म् अ ह् आ ि् र् आ ि् इ ह् आ र् य् अ अष्ट महाप्रविहायण 9 An Abugida (Alphasyllabary) is a writing system in which Consonant- Vowel sequences are written as units; each unit is based on a Consonant, and Vowel notation is secondary, like a diacritical mark. Example - Scripts used in Indian Subcontinent. Another Important Characteristics of Aṅka-Lipi Aṅka-Lipi (Numeral Script) allows transliteration in any of the Script of choice, without any need to know any other script.
10 अ ष् ट् अ म् अ ह् आ ि् र् आ ि् इ ह् आ र् य् अ व् अ य् भ् अ व् अ द् इ न् द् अ अ ष् ट् अ ग् उ ण् अ न् ग् अ ळ ओो ळ ओो म् द् अ म् स् र् ष् ट् इ ग् ए म् अ न् ग् अ ळ अ ि् अ र् य् आ य् अ द् इ न् इ ि् अ अ ष् ट् अ म् अ ज् इ न् अ ग् ए र् अ ग् उ व् ए न् उ ||1|| 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 ||𑀅|| ಅ ಷ್ ಟ್ ಅ ಮ್ ಅ ಹ್ ಆ ಪ್ ರ್ ಆ ತ್ ಇ ಹ್ ಆ ರ್ ಯ್ ಅ ವ್ ಅ ಯ್ ಭ್ ಅ ವ್ ಅ ದ್ ಇ ನ್ ದ್ ಅ ಅ ಷ್ ಟ್ ಅ ಗ್ ಉ ಣ್ ಅ ನ್ ಗ್ ಅ ಳ್ ಓ ಳ್ ಓ ಮ್ ದ್ ಅ ಮ್ ಸ್ ರ್ ಷ್ ಟ್ ಇ ಗ್ ಎ ಮ್ ಅ ನ್ ಗ್ ಅ ಳ್ ಅ ಪ್ ಅ ರ್ ಯ್ ಆ ಯ್ ಅ ದ್ ಇ ನ್ ಇ ತ್ ಅ ಅ ಷ್ ಟ್ ಅ ಮ್ ಅ ಜ್ ಇ ನ್ ಅ ಗ್ ಎ ರ್ ಅ ಗ್ ಉ ವ್ ಎ ನ್ ಉ ||೧|| a ṣ ṭ a m a h ā p r ā t i h ā r y a v a y bh a v a d i n d a a ṣ ṭ a g u ṇ a n g a ḷ ō ḷ ō m d a m s r ṣ ṭ i g ē m a n g a ḷ a p a r y ā y a d i n i t a a ṣ ṭ a m a j i n a g ē r a g u v ē n u ||1|| Easy Transliteration of Aṅka-Lipi into various scripts
Conjoining Mūla Varṇās into words, phrases results in Padas and Ślōkas 11
स्तम्भ-काव्य युक्ति िे प्रकट अन्ति-िावहत्य सक्रमवर्त्ती - प्राक ृ ि अट्टववहकम्म ववयिा वर्वट्टय कज्जा िर्ट्टिंिािा । वदट्ट ियित्थ िािा विक्तिआ विक्तिम् मम वदिन्तु ।।1।। अक्रमवर्त्ती - संस्क ृ ि ओकािम् विन्दु िंयुिं वनत्यम् ध्यायक्तन्त योविनः। कामदं मोक्षदम् चैव ओंकािाय नमो नमः ।।1।। 12
Khaṇḍa / Volumes of Siribhūvalaya Entire content of Siribhūvalaya is segmented into nine divisions called Khaṇḍa and each of Khaṇḍas is further divided into Adhyāyas. Each Adhyāya is constituted with a number of related Cakras. These Khaṇḍas (Volumes) have been named by Acārya Kumudendu as: 13
Basic Elements of Siribhūvalaya - 1 Cakra : One Cakra is an encrypted arrangement of integer numbers (in range 1 to 64) in a matrix of 27 rows and 27 columns. Transcript of the first Cakra from the first Adhyāya of Siribhūvalaya is shown in a previous slide. This Cakra will be referred as an example for explanation of cryptographic mechanisms in Siribhūvalaya. Upa-Cakra : Upa-Cakra is a matrix of size 9x9 and is derived by partitioning of a Cakra Matrix into 9 Nine sub-matrices in an ordered manner as shown in previous slide. These partitioned sub-matrices of a Cakra are decoded in various permutations in different Adhyāyas as part of encryption scheme termed as Navamānk-Bandha. Bandha : Bandha is manner in which contents from a Cakra is revealed. Bandha basically describes the method to traverse the Cakra (27x27 matrix) and substitute respective numbers into Mūla Varṇas to uncover the Ślokas or verses hidden therein the Cakra. Acārya Kumudendu has enumerated many Bandhas, which are deployed in encryption of Siribhūvalaya. Śreṇī Bandha with its two variants viz. Cakra-Bandha and Navmānk-Bandha is applied in the first Khaṇḍa i.e. ṁagala Prābhr̥ta. 14
Basic Elements of Siribhūvalaya - 2 Śreṇī Bandha: Śreṇī Bandha is primarily applied to decode all the Cakras to extract base Kannada verses from all the Adhyāyas of ṁagala Prābhr̥ta Khaṇḍa in Siribhūvalaya. Śreṇī Bandha has two variants termed as - ‘Cakra-Bandha’ and ‘Navamānk-Bandha’. When Śreṇī Bandha is applied over whole Cakra i.e. on 27x27 matrix, it is called Cakra- Bandha; and when Śreṇī Bandha is applied to sub-matrix of Cakra of 9x9 elements, it is called Navamānk-Bandha. Note: It is noteworthy that Śreṇī Bandha traversal pattern results in Magic Squares of size 27x27 (sum 9855) or 9x9 (sum 369). A Magic Square is a square matrix of Integers wherein sum of integers in any of the rows is equal to sum of integers in any of the columns or sum of integers in any of the diagonals. 15
Basic Elements of Siribhūvalaya - 3 Krama-Cakra : This is the key for Transposition Cipher and is represented as square matrix of order 27. Each of the elements in this matrix contains a distinct integer number in the range 1 to 729 i.e. no two elements are of identical value. Each element of Krama-Cakra represents position of corresponding element (at same row and column) in Cakra in the transformed number vector with 729 elements. Each Adhyaya has distinct Krama-Cakra for decoding Cakras of that Adhyāya. First Cakra of each Adhyāya contains a 3x3 matrix on the left-hand corner which is representative of the Krama-Cakra applicable to that particular Adhyāya. Following slides show Krama-Cakra for Cakra-Bandha for (27x27) matrix and Navmānk-Bandha (9x9) matrix as applicable to First Adhyaya of ṁagala Prābhr̥ta. Kumudendu Code Table (KCT): This is the key for Substitution Cipher. it is used for substituting Numerals in Cakras into corresponding Phonetic Alphabet Characters (Mūla Varṇa) in specific script. Since KCT is script dependent there exist KCTs each of the scripts e.g. Devanāgarī, Kannada or Brāhmī etc. KCT has 64 elements . KCT is the key for Substitution cipher as deployed in ‘Siribhūvalaya’. 16
Transposition Key : Krama-Cakra for Cakra-Bandha l l 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 17
Transposition Key: Krama-Cakra for Navamānk- Bandha 18
Cakra Bandha Example with 5x5 Matrix 1 2 3 4 5 1 4 53 28 45 4 2 1 45 47 59 54 3 7 16 1 56 55 4 28 43 8 1 52 5 10 51 1 7 7 1 2 3 4 5 1 17 24 1 8 15 2 23 5 7 14 16 3 4 6 13 20 22 4 10 12 19 21 3 5 11 18 25 2 9 Example Anka-Cakra (5x5) Example Kram-Cakra (5x5) 28 7 52 7 45 16 47 45 7 28 10 43 1 59 4 54 4 51 8 56 1 55 1 53 1 Result of Applying Bandha 19
Applying Substitution using Kumudendu Code Table Result after applying Substitution Cipher into result from De-Transposition from previous slide : 20
Step -5 Example of Multi-Lingual content from First Adhyaya 21
Step – 5 : Content in Prakrit & Samskrit from First Chakra Checksum 22
Step -5 : Example of Multi-lingual contents from first Anubandh of Shrutavatar 23
Step – 5 : Content in Prakrit, Geervan, Telugu, Tamil & Apabhramsh from first anubandha of Shrutavatar 24
Why is Acarya Kumudendu Inimitable? • Master Mathematician who shone with brilliance in creating not only intricate framework of Cakras and Bandhas, but also expressed mathematical interpretations on variety topics. • Eminent Scholar of religious foundations, scriptures, practices and ancient sciences of diverse domains. • Highly Competent Linguist with proficiency in multiple languages prevalent in India at his time. • Extremely genius poet who chose two-dimensional array of numerals for his creative expressions. • Great Composer who intertwined verses in multiple languages into a solitary piece of magnificent work. • Exceedingly Talented Graphics artist who could implant poetry into multitude of shapes and figures. • Strong Proponent of Puşpāyurveda (िुष्पायुवेद ) 25
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ತುಂಬ ಧನ್ಯ ವಾದಗಳು धन्यवाद 27

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"Introduction to Siribhūvalaya" - Talk at Jain Academy of Scholars

  • 1. Siribhūvalaya : An Introduction Virtual Talk at Jain Academy of Scholars 27th February 2024 by Er. Anil Kumar Jain FIETE, FIE(I), SMCSI, LM-ISCA email: jain.anilk@gmail.com Siri Bhūvalaya Śōdha evam Praśikșaṇa Kēndra Kundakunda Jñānapīṭha Shri Digambar Jain Udasin Ashram Trust 584, M. G. Road, Indore - 452001
  • 2. Siribhūvalaya : Key Historic Transitions ProCreation Period : 9th Century (about 1200 years ago) Setting : Ancient Karnataka, Near Bengaluru Focal Characters : Acārya Kumudendu - Outstanding inimitable Genius who scripted this inimitable epic. Mahāmata Mallikabbe - Ardent Benefactor who distributed copies of Siribhūvalaya – one of these survived to be rediscovered in twentieth century. Long Intermission: Wonderful Masterpiece laid into oblivion for next 1000 years due to complexity in deciphering it. Resurrection : In early 20th Century By Paņdit Yellappā Śāstrī (The arduous Redeemer who strived resurrection efforts till his death )2
  • 3. One Cakra from Original Manuscript in Aṅka-Lipi 3
  • 4. Transliteration by Paņdit Yellappā Śāstrī (Preserved at National Archives of India, N. Delhi) 4
  • 5. First Chakra of Siribhūvalaya 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 1 59 23 1 16 1 28 28 1 1 56 59 4 56 1 1 47 16 34 1 7 16 1 1 7 56 1 60 2 53 54 47 28 1 47 45 28 7 4 59 41 4 45 1 30 47 47 45 42 53 28 51 1 52 1 1 3 1 22 1 30 2 1 2 55 30 1 7 45 47 52 1 4 1 47 1 1 1 1 53 1 52 59 52 4 59 30 2 55 55 13 16 2 53 60 1 4 16 47 48 45 16 56 56 43 45 1 56 1 4 1 13 5 47 45 1 1 22 30 51 1 2 56 38 30 4 1 1 56 1 1 16 1 57 7 56 56 1 22 1 6 54 52 52 45 1 7 55 48 1 58 52 35 28 55 1 38 45 30 55 4 47 7 45 38 45 38 1 7 1 1 1 28 13 56 55 51 54 1 1 1 1 42 2 4 4 1 43 16 47 7 1 13 4 51 4 8 28 53 47 22 8 1 53 59 38 7 43 40 1 52 59 54 30 1 45 16 1 28 23 50 7 43 43 9 1 2 45 51 30 1 52 58 48 59 47 54 4 4 1 47 45 47 56 28 1 45 1 13 7 7 7 10 55 1 53 47 56 1 1 7 1 1 2 60 48 56 1 1 16 1 1 54 1 52 17 30 54 45 45 11 59 56 52 1 45 1 55 28 52 28 1 2 1 52 54 4 43 60 48 28 1 16 23 8 53 7 1 12 2 1 53 52 43 23 2 4 16 52 44 54 1 2 42 7 1 7 47 30 28 48 47 1 54 52 16 13 45 54 23 4 28 45 45 30 1 59 1 56 28 2 54 53 38 2 2 1 28 55 40 60 4 50 28 14 2 13 47 1 1 4 17 45 1 56 1 52 56 51 1 47 55 55 45 7 2 54 1 56 7 1 1 15 23 4 53 54 59 48 13 56 1 47 23 1 2 55 16 1 1 47 40 54 16 52 1 47 60 43 60 16 45 16 43 1 7 47 1 7 1 4 54 54 1 43 28 28 7 1 2 7 52 30 1 4 47 4 13 17 42 1 54 13 1 28 1 45 42 5 48 56 1 1 1 52 54 7 1 1 2 56 56 2 43 1 1 18 56 43 22 45 56 43 2 2 56 1 8 48 59 59 7 16 53 55 53 48 1 1 46 2 30 53 1 19 47 45 1 2 54 56 56 2 55 51 4 16 7 13 30 16 1 1 4 52 52 4 54 47 2 38 1 20 1 54 60 56 54 1 60 1 1 16 40 38 17 1 47 56 33 55 1 1 59 48 1 53 7 1 1 21 1 52 16 1 60 1 30 53 30 7 47 13 13 22 8 13 45 59 54 1 2 42 54 47 53 52 53 22 16 30 1 4 52 47 56 1 28 16 1 22 59 51 1 1 7 28 53 60 7 1 16 16 1 1 58 23 4 53 56 1 52 2 13 52 38 30 45 7 1 30 56 16 1 1 1 30 48 56 54 54 55 28 45 24 1 47 47 1 28 22 1 47 1 1 45 46 1 1 47 53 55 52 1 1 7 43 2 1 1 1 43 25 1 4 53 1 45 43 16 55 52 4 47 55 45 22 51 56 1 38 13 30 2 28 56 13 56 28 55 26 4 16 46 1 1 16 1 1 1 1 1 47 59 4 8 38 58 1 1 48 1 7 22 1 1 1 60 27 52 4 30 56 53 52 54 1 30 52 1 16 54 7 58 1 30 54 1 56 51 53 56 57 56 4 60 5 IMPORTANT : Aṅka-Lipi (Numeral Script) allowed efficient implementation of Transposition and Substitution Ciphers (Cryptographic Mechanisms) by Acārya Kumudendu.
  • 6. Partitioning of 27x27 Matrix of Cakra into Nine 9x9 Sub-Matrices Sub-Matrix 3 Sub-Matrix 2 Sub-Matrix 1 Sub-Matrix 4 Sub-Matrix 9 Sub-Matrix 5 Sub-Matrix 6 Sub-Matrix 8 Sub-Matrix 7 6
  • 7. Substitution Cipher Key (KCT) for different scripts क ु मुदेन्दु कोड सारणी में देवनागरी, कन्नड़ एवं ब्राह्मी लिलि क े ध्वन्याक्षर 7
  • 8. Conversion of a Word into Numbers (Encoding) शब्द वर्ण ववच्छे द अङ्क-विवि भूविय भ् ऊ व् अ ि् अ य् अ 51-8-56-1-55-1-53-1 ज्ञानिीठ ज् ञ् आ न् अ ि् ई ठ् अ 35-37-2-47-1-48-5-39-1 लक्षलिश्री क ् ष् इ ि् इ श् र् ई 28-58-4-43-4-57-54-5 8 This is an example of Alphabetic Writing System which represent the phonological structure of the language. Vowels and Consonants have equal status and are presented in a sequence. This type of writing system is in contrast with Abugida (Alphasyllabary), in which a single symbol denotes the combination of one consonant and one vowel. Example - Most of the European Scripts - which are descendents of Latin and Greek writing systems.
  • 9. Conversion of Numbers into Word (Decoding) अङ्क-विवि वर्ण प्रस्थािन शब्द 59. 4. 54. 4. 51. 8। 56. 1. 55. 1. 53. 1 स् इ र् इ भ् ऊ व् अ ि् अ य् अ विरि भूविय 1. 58. 38. 1. 52. 1. 60. 2. 48. 54. 2. 43. 4. 60. 2. 54. 53. 1 अ ष् ट् अ म् अ ह् आ ि् र् आ ि् इ ह् आ र् य् अ अष्ट महाप्रविहायण 9 An Abugida (Alphasyllabary) is a writing system in which Consonant- Vowel sequences are written as units; each unit is based on a Consonant, and Vowel notation is secondary, like a diacritical mark. Example - Scripts used in Indian Subcontinent. Another Important Characteristics of Aṅka-Lipi Aṅka-Lipi (Numeral Script) allows transliteration in any of the Script of choice, without any need to know any other script.
  • 10. 10 अ ष् ट् अ म् अ ह् आ ि् र् आ ि् इ ह् आ र् य् अ व् अ य् भ् अ व् अ द् इ न् द् अ अ ष् ट् अ ग् उ ण् अ न् ग् अ ळ ओो ळ ओो म् द् अ म् स् र् ष् ट् इ ग् ए म् अ न् ग् अ ळ अ ि् अ र् य् आ य् अ द् इ न् इ ि् अ अ ष् ट् अ म् अ ज् इ न् अ ग् ए र् अ ग् उ व् ए न् उ ||1|| 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 𑀅 ||𑀅|| ಅ ಷ್ ಟ್ ಅ ಮ್ ಅ ಹ್ ಆ ಪ್ ರ್ ಆ ತ್ ಇ ಹ್ ಆ ರ್ ಯ್ ಅ ವ್ ಅ ಯ್ ಭ್ ಅ ವ್ ಅ ದ್ ಇ ನ್ ದ್ ಅ ಅ ಷ್ ಟ್ ಅ ಗ್ ಉ ಣ್ ಅ ನ್ ಗ್ ಅ ಳ್ ಓ ಳ್ ಓ ಮ್ ದ್ ಅ ಮ್ ಸ್ ರ್ ಷ್ ಟ್ ಇ ಗ್ ಎ ಮ್ ಅ ನ್ ಗ್ ಅ ಳ್ ಅ ಪ್ ಅ ರ್ ಯ್ ಆ ಯ್ ಅ ದ್ ಇ ನ್ ಇ ತ್ ಅ ಅ ಷ್ ಟ್ ಅ ಮ್ ಅ ಜ್ ಇ ನ್ ಅ ಗ್ ಎ ರ್ ಅ ಗ್ ಉ ವ್ ಎ ನ್ ಉ ||೧|| a ṣ ṭ a m a h ā p r ā t i h ā r y a v a y bh a v a d i n d a a ṣ ṭ a g u ṇ a n g a ḷ ō ḷ ō m d a m s r ṣ ṭ i g ē m a n g a ḷ a p a r y ā y a d i n i t a a ṣ ṭ a m a j i n a g ē r a g u v ē n u ||1|| Easy Transliteration of Aṅka-Lipi into various scripts
  • 11. Conjoining Mūla Varṇās into words, phrases results in Padas and Ślōkas 11
  • 12. स्तम्भ-काव्य युक्ति िे प्रकट अन्ति-िावहत्य सक्रमवर्त्ती - प्राक ृ ि अट्टववहकम्म ववयिा वर्वट्टय कज्जा िर्ट्टिंिािा । वदट्ट ियित्थ िािा विक्तिआ विक्तिम् मम वदिन्तु ।।1।। अक्रमवर्त्ती - संस्क ृ ि ओकािम् विन्दु िंयुिं वनत्यम् ध्यायक्तन्त योविनः। कामदं मोक्षदम् चैव ओंकािाय नमो नमः ।।1।। 12
  • 13. Khaṇḍa / Volumes of Siribhūvalaya Entire content of Siribhūvalaya is segmented into nine divisions called Khaṇḍa and each of Khaṇḍas is further divided into Adhyāyas. Each Adhyāya is constituted with a number of related Cakras. These Khaṇḍas (Volumes) have been named by Acārya Kumudendu as: 13
  • 14. Basic Elements of Siribhūvalaya - 1 Cakra : One Cakra is an encrypted arrangement of integer numbers (in range 1 to 64) in a matrix of 27 rows and 27 columns. Transcript of the first Cakra from the first Adhyāya of Siribhūvalaya is shown in a previous slide. This Cakra will be referred as an example for explanation of cryptographic mechanisms in Siribhūvalaya. Upa-Cakra : Upa-Cakra is a matrix of size 9x9 and is derived by partitioning of a Cakra Matrix into 9 Nine sub-matrices in an ordered manner as shown in previous slide. These partitioned sub-matrices of a Cakra are decoded in various permutations in different Adhyāyas as part of encryption scheme termed as Navamānk-Bandha. Bandha : Bandha is manner in which contents from a Cakra is revealed. Bandha basically describes the method to traverse the Cakra (27x27 matrix) and substitute respective numbers into Mūla Varṇas to uncover the Ślokas or verses hidden therein the Cakra. Acārya Kumudendu has enumerated many Bandhas, which are deployed in encryption of Siribhūvalaya. Śreṇī Bandha with its two variants viz. Cakra-Bandha and Navmānk-Bandha is applied in the first Khaṇḍa i.e. ṁagala Prābhr̥ta. 14
  • 15. Basic Elements of Siribhūvalaya - 2 Śreṇī Bandha: Śreṇī Bandha is primarily applied to decode all the Cakras to extract base Kannada verses from all the Adhyāyas of ṁagala Prābhr̥ta Khaṇḍa in Siribhūvalaya. Śreṇī Bandha has two variants termed as - ‘Cakra-Bandha’ and ‘Navamānk-Bandha’. When Śreṇī Bandha is applied over whole Cakra i.e. on 27x27 matrix, it is called Cakra- Bandha; and when Śreṇī Bandha is applied to sub-matrix of Cakra of 9x9 elements, it is called Navamānk-Bandha. Note: It is noteworthy that Śreṇī Bandha traversal pattern results in Magic Squares of size 27x27 (sum 9855) or 9x9 (sum 369). A Magic Square is a square matrix of Integers wherein sum of integers in any of the rows is equal to sum of integers in any of the columns or sum of integers in any of the diagonals. 15
  • 16. Basic Elements of Siribhūvalaya - 3 Krama-Cakra : This is the key for Transposition Cipher and is represented as square matrix of order 27. Each of the elements in this matrix contains a distinct integer number in the range 1 to 729 i.e. no two elements are of identical value. Each element of Krama-Cakra represents position of corresponding element (at same row and column) in Cakra in the transformed number vector with 729 elements. Each Adhyaya has distinct Krama-Cakra for decoding Cakras of that Adhyāya. First Cakra of each Adhyāya contains a 3x3 matrix on the left-hand corner which is representative of the Krama-Cakra applicable to that particular Adhyāya. Following slides show Krama-Cakra for Cakra-Bandha for (27x27) matrix and Navmānk-Bandha (9x9) matrix as applicable to First Adhyaya of ṁagala Prābhr̥ta. Kumudendu Code Table (KCT): This is the key for Substitution Cipher. it is used for substituting Numerals in Cakras into corresponding Phonetic Alphabet Characters (Mūla Varṇa) in specific script. Since KCT is script dependent there exist KCTs each of the scripts e.g. Devanāgarī, Kannada or Brāhmī etc. KCT has 64 elements . KCT is the key for Substitution cipher as deployed in ‘Siribhūvalaya’. 16
  • 17. Transposition Key : Krama-Cakra for Cakra-Bandha l l 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 17
  • 18. Transposition Key: Krama-Cakra for Navamānk- Bandha 18
  • 19. Cakra Bandha Example with 5x5 Matrix 1 2 3 4 5 1 4 53 28 45 4 2 1 45 47 59 54 3 7 16 1 56 55 4 28 43 8 1 52 5 10 51 1 7 7 1 2 3 4 5 1 17 24 1 8 15 2 23 5 7 14 16 3 4 6 13 20 22 4 10 12 19 21 3 5 11 18 25 2 9 Example Anka-Cakra (5x5) Example Kram-Cakra (5x5) 28 7 52 7 45 16 47 45 7 28 10 43 1 59 4 54 4 51 8 56 1 55 1 53 1 Result of Applying Bandha 19
  • 20. Applying Substitution using Kumudendu Code Table Result after applying Substitution Cipher into result from De-Transposition from previous slide : 20
  • 21. Step -5 Example of Multi-Lingual content from First Adhyaya 21
  • 22. Step – 5 : Content in Prakrit & Samskrit from First Chakra Checksum 22
  • 23. Step -5 : Example of Multi-lingual contents from first Anubandh of Shrutavatar 23
  • 24. Step – 5 : Content in Prakrit, Geervan, Telugu, Tamil & Apabhramsh from first anubandha of Shrutavatar 24
  • 25. Why is Acarya Kumudendu Inimitable? • Master Mathematician who shone with brilliance in creating not only intricate framework of Cakras and Bandhas, but also expressed mathematical interpretations on variety topics. • Eminent Scholar of religious foundations, scriptures, practices and ancient sciences of diverse domains. • Highly Competent Linguist with proficiency in multiple languages prevalent in India at his time. • Extremely genius poet who chose two-dimensional array of numerals for his creative expressions. • Great Composer who intertwined verses in multiple languages into a solitary piece of magnificent work. • Exceedingly Talented Graphics artist who could implant poetry into multitude of shapes and figures. • Strong Proponent of Puşpāyurveda (िुष्पायुवेद ) 25
  • 26. 26

Editor's Notes

  • #2: There are many distinctive features of this unique creation, but in this presentation focus is on the Cryptographic constituents which are strikingly similar to ones used in modern applications of Cryptography in Information Security. One can noticeably observe creative deployment of Substitution and Transposition Ciphers in Cakras of this epic. Built upon notions of Matrices these are mathematical applications of combinatorics and permutations. A generalized version of this mechanism in modern terminology has been proposed as KES (Kumudendu Encryption System) which can measure up to a versatile and robust block cipher as compared to existing ones. Besides encryption mechanisms Muni Kumudendu implemented a scheme to check Integrity of the verses in each of Adhyāyas in a smart manner. Muni Kumudendu has very creatively used Steganography for interweaving not only multi-lingual verses in base Kannada text but also deployed this technique to enclose scriptures from other sources.
  • #3: Siribhūvalaya was scripted by Acharya Kumudendu during 8th century AD In the state of in Karnataka. It remained largely obscure to large number of scholars and prominent Jain ācāryas because of its indecipherable content. This was primarily because Achaarya Kumudendu worked out an exclusive writing system for this unique creation which was based on universal script of numbers and independent of any language specific scripts. Herein one Cakra or a page contained only integer numbers arranged in a square matrix of dimension 27. Integer, in each of the cells of the matrix in the range of 1 to 64, represented one of the 64 Mūla Varṇas or phonetic alphabets as enumerated in texts of earlier Ācāryas in lineage to which Acharya Kumudendu belonged to.
  • #4: This is the image of one sheet of manuscript wherein we can identify one matrix of size 27x27 and another matrix of size 3x3 near top left corner. Elements in both of these matrix contains integer numerals in Kannada script. On minute observation one can identify partitioning of 27x27 matrix into nine sub-matrices of size 9x9 each. 3x3 matrix at the top left corner provides vital clue in construction of key for the Transposition Cipher.