FORM 2
THE PATENTS ACT, 1970
(39 of 1970)
&
THE PATENT RULES, 2003
COMPLETE SPECIFICATION
(See Section 10 and Rule 13)
Title of invention:
A METHOD AND ENGINES FOR GENERATION OF ELLIPTIC CURVE (EC)
SCALAR MULTIPLICATION AND SECURE COMMUNICATION PROTOCOLS
Applicant:
Tata Consultancy Services Limited A company Incorporated in India under The Companies Act, 1956
Having address:
Nirmal Building, 9th Floor,
Nariman Point, Mumbai 400021,
Maharashtra, India
The following specification particularly describes the invention and the manner in which it is to be performed.

FIELD OF THE INVENTION
The present application relates to Digital Signal Processing and Information Security applications. More particularly, the application relates to a method and engines for generation of Elliptic Curve (EC) scalar multiplication.
BACKGROUND OF THE INVENTION
Elliptic Curve Cryptography (ECC) has applied for lot of Information Security applications because of smaller key-length and increased theoretical robustness. In ECC, scalar multiplication (or point multiplication) is the operation of calculating an integer multiple of an element in additive group of elliptic curve. In other words, it is a computation of kP for any integer k and a point P on the elliptic curve. To compute Elliptic Curve (EC) scalar multiplications, one can easily adapt historical exponentiation methods to scalar multiplication, replacing multiplication by addition and squaring by doubling. Nowadays, Double Base Number System (DBNS) and Multi Base Number System (MBNS) methods have been used to reduce the computational complexity of EC scalar multiplications. However, the computations resources and time for computing EC scalar multiplication are very high thereby increasing the computational cost.
Thus, in the light of the above mentioned background of the art, it is evident that, there is a need for a method, system, device or engine which utilizes less computation resources and time for computing EC scalar multiplication reducing computational cost.
OBJECT OF THE INVENTION
The principal object is to provide a method and engine which utilizes less computation resources and time for computing EC scalar multiplication thereby saving computational cost.

SUMMARY OF THE INVENTION
Before the present systems and methods, enablement are described, it is to be understood that this application is not limited to the particular systems, and methodologies described, as there can be multiple possible embodiments which are not expressly illustrated in the present disclosures. It is also to be understood that the terminology used in the description is for the purpose of describing the particular versions or embodiments only, and is not intended to limit the scope of the present application.
The present application provides a method and engine which utilizes less computation resources and time for computing EC scalar multiplication.
In one aspect, a method for computing Elliptic Curve (EC) scalar multiplication value comprising the machine implemented steps of: receiving at least one input scalar value (n), the scalar value n is either one of the value of Double Base Number System (DBNS) sum, DBNS sum with repetitive summands, Multiple Base Number System (MBNS) sum or MBNS sum with repetitive summands; receiving at least one EC point (P), the P is P e E(F) and the E(F) is an elliptic curve over a prime/binary field F; and computing at least one output EC scalar multiplication value (z) using an input scalar 'value (n) and the EC point (P), wherein the z is nP e E(F).
In another aspect, the input scalar value (n) can be output from greedy form of n, the greedy form comprises of representing at least one character set with respect to bases 2, 3 or 5.
In one aspect, the input scalar value (n) is computed by the following steps: receiving at least one positive integer (x); generating at least one scalar value (n) using the received positive integer (x), the scalar value n is either one of the value of Double Base Number System (DBNS) sum, DBNS sum with repetitive summands, Multiple Base Number System (MBNS) sum or MBNS sum with repetitive summands.

In one aspect of the invention, an Elliptic Curve Digital Signature Algorithm (ECDSA) engine for generating at least one EC scalar multiplication value comprises of: a module adapted to: receive at least one positive integer (x); and generate at least one scalar value (n) using the received positive integer (x), the scalar value n is either one of the value of Double Base Number System (DBNS) sum, DBNS sum with repetitive summands, Multiple Base Number System (MBNS) sum or MBNS sum with repetitive summands. Elliptic Curve (EC) scalar multiplication generation module adapted to: receive at least one input scalar value (n); receive at least one EC point (P), the P is P e E(F) and the E(F) is an elliptic curve over a prime/binary field F; and compute at least one output EC scalar multiplication value (z) using the input scalar value (n) and the EC point (P), wherein the z is nP e E(F).
In another aspect of the invention, the input scalar value (n) can be output from greedy form of n, the greedy form comprises of representing at least one character set with respect to bases 2, 3 or 5.
In one aspect of the invention, an Elliptic Curve Encryption (ECE) engine for generating at least one EC scalar multiplication value comprises of: a module adapted to: receive at least one positive integer (x); and generate at least one scalar value (n) using the received positive integer (x), the scalar value n is either one of the value of Double Base Number System (DBNS) sum, DBNS sum with repetitive summands, Multiple Base Number System (MBNS) sum or MBNS sum with repetitive summands. Elliptic Curve (EC) scalar multiplication generation module adapted to: receive at least one input scalar value (n); receive at least one EC point (P), the P is P e E(F) and the E(F) is an elliptic curve over a prime/binary field F; and compute at least one output EC scalar multiplication value (z) using the input scalar value (n) and the EC point (P), wherein the z is nP e E(F).

In another aspect, the input scalar value (n) can be output from greedy form of n, the greedy form comprises of representing at least one character set with respect to bases 2, 3 or 5.
BRIEF DESCRIPTION OF THE DRAWINGS
The foregoing summary, as well as the following detailed description of preferred embodiments, is better understood when read in conjunction with the appended drawings. There is shown in the drawings example embodiments, however, the application is not limited to the specific system and method disclosed in the drawings.
Figure 1 is a flowchart illustrating conversion of positive integer into MBNS with decreasing order of exponents according to one exemplary embodiment of the invention.
Figure 2 is a flowchart illustrating conversion of positive integer into MBNS with decreasing order of exponents according to another exemplary embodiment of the invention.
Figure 3 is a flowchart illustrating conversion of positive integer into DBNS with decreasing order of exponents according to one exemplary embodiment of the invention.
Figure 4 is a flowchart illustrating ECDSA engine used for EC Digital signature generation and verification according to one exemplary embodiment of the invention.
Figure 5 is a flowchart illustrating ECE engine used for EC Encryption and EC Decryption according to one exemplary embodiment of the invention.
Figure 6 is a flowchart illustrating ECDSA/ECE engine that is utilized the multiprocessors according to one exemplary embodiment of the invention.

Figure 7 is a flowchart illustrating inner product computation unit for generation of DBNS according to one exemplary embodiment of the invention.
Figure 8 is a flowchart illustrating inner product computation unit for generation of MBNS according to one exemplary embodiment of the invention.
Figure 9 is a flowchart illustrating Mobile learning application using Greedy ASCII form.
Figure 10 is a flowchart illustrating Mobile learning platform using DBNS/MBNS methods.
DETAILED DESCRIPTION OF THE INVENTION
Some embodiments, illustrating its features, will now be discussed in detail. The words "comprising," "having," "containing," and "including," and other forms thereof, are intended to be equivalent in meaning and be open ended in that an item or items following any one of these words is not meant to be an exhaustive listing of such item or items, or meant to be limited to only the listed item or items. It must also be noted that as used herein and in the appended claims, the singular forms "a," "an," and "the" include plural references unless the context clearly dictates otherwise. Although any methods, and systems similar or equivalent to those described herein can be used in the practice or testing of embodiments, the preferred methods, and systems are now described. The disclosed embodiments are merely exemplary.
The application provides a method and engine which utilize the less computation resources and time for computing EC scalar multiplication thereby saving the computational cost. In one embodiment, a method for computing Elliptic Curve (EC) scalar multiplication value comprising the various machine implemented steps.
In the first step of the proposed method, at least one input scalar value (n) is received.

In one exemplary embodiment, the input scalar value (n) can be output from greedy form of n, the greedy form comprises of representing at least one character set with respect to bases 2, 3 or 5. In an embodiment, the scalar value (n) is either one of the values of Double Base Number System (DBNS) sum, DBNS sum with repetitative summands. Multiple Base Number System (MBNS) sum or MBNS sum with repetitative summands. In one exemplary embodiment, the scalar value (n) is Double Base Number System (DBNS) sum. In another exemplary embodiment, the scalar value (n) DBNS sum with repetitative summands.
In the next step, at least one EC point (P) is received, the P is P e E(F) and the E(F) is an elliptic curve over a prime/binary field F.
In the final step of the proposed method, at least one output EC scalar multiplication value (z) is computed using the input scalar value (n) and the EC point (P), wherein the z is nP e E(F). The above proposed method improves the performance of an Elliptic Curve Digital Signature Algorithm (ECDSA) and an Elliptic Curve Encryption (ECE).
According one exemplary embodiment, Algorithm 1: A pseudo code for computing EC scalar multiplication using DBNS sum is explained below:
Input: An integer n = £flnite2x3y = £ss 2bi3(i, (i = 1,2,... ,m) with si e {-1,1}, and such
that bi > b2 > . ..> bm > 0, and ti > t2 > ... > tm > 0; and a point P e E(F).
Output: the point nP e E(F), where E(F) is an elliptic curve over a prime/binary field F.
1. z←sjP
2. For i = \,2,...,m-\ do
3. u ← bj - bj+i
4. V ← tj - tj+j
5. ifu = 0then
z←3(3v"'z) + si+iP

else z ←3vz
6. u = 0 (mod 2) z ← 4z + Sj+jP else
z←2z + Sj+|P
According another exemplary embodiment, Algorithm 2: A pseudo code for EC scalar multiplication using DBNS sum with repetitative summands is explained below:
Input: An integer n = %%rmite 2X 3y = £si2b'3u, (i = 1,2, ... ,m) with si e {-1,1}, and such
that bi > b2> ...> bm > 0, and tj > t2 > ... > lm > 0; and a point P e E(F).
Output: the point nP e E(F), where E(F) is an elliptic curve over a prime/binary field F.
1. z←s,P
2. For i = l,2,...,m-l do 3_ u←bj-bi+i

4. V ← tj - tj+i
5. Rsum=0
6. Case 1: u = v = 0
6.1 If bj = bj+i = 0 and tj = ti+i = 0
6.2 z← z + Sj+i? 6.3If(bisti) = (bi+,sti+,)^0
6.4 Compute Rsum = ^finite s 2b,+l 311+l + Rsum

7. Case 2: u = 0
7.1 z ←3(3v-lz) + si+iP
8. Case3:u#0
8.1z←3vz
8.2 z - 4 aD(L"1)/2a z
9. Case 4: u = 0 (mod 2) 9.1 z←4z + si+,P
10. Case 5: u#O (mod 2) 10.1 z<-2z + si+iP
11. Rsum undergoes Case 2 to 5
12. Output z
In one exemplary embodiment, the input scalar value (n) is computed by the following
steps:
In the first step, at least one positive integer (x) is received. In the final step, upon receiving
the positive integer (x) . at least one scalar value (n) is generated using the received
positive integer (x), wherein the scalar value n is either one of the value of Double Base
Number System (DBNS) sum, DBNS sum with repetitative summands. Multiple Base
Number System (MBNS) sum or MBNS sum with repetitative summands.
The above said computation of the MBNS sum and MBNS sum with repetitative summands are explained in the Figure 1 and 2 respectively and the said DBNS sum is explained in the Figure 3.
According to one exemplary embodiment, algorithm 3: A pseudo code of the proposed algorithm for MBNS (as shown in Figure I)

Conversion of a positive integer to MBNS with decreasing order of exponents is explained below:
Input: A positive integer n
Output: the sequence of exponents (bm, cm! dm) (such that b| > b2> .. .bm > 0,
d >C2> cm> 0 anddi > d2 > dm> 0) leading to one MBNS representation of n.
1. Find z = 2b'3c,5di. the largest 3-integer less than or equal to n
2. k←n
3. k ←[k-z|
4. bm8X←-min(b[,(niog2kD+l))
← min(ci,(DIog3kD+l)) u. umax ←min(d,,(niog5kn+I))
7. s←1
8. Whilek>0do

7.1 Define z = 2b3c5d, the best approximation* of k with 0k. Find
out the best triplet (b',c\d') such that = 2b 3C' 5d' is the closest to k Here 'closest' means (z-
k) or (k-z) is minimal.
Examples:
1 66-22315! + 213,5°
2 84 = 243°5l+20305l-203°50
According to another exemplary embodiment, algorithm 4: A pseudo code of the proposed algorithm for MBNS (as shown in Figure 2)
Conversion of a positive integer to MBNS with decreasing order of exponents is explained below:
Input: A positive integer n
Output: the sequence of exponents (bm, cm, dm) (such that b| > D2 > .. bm > 0,
Ci >c2> cm> 0 and d| >d2> dm> 0) leading to one MBNS representation of n.
1. Log_base_5_process
1.1 Findt=Dlog5nD
1.2 Find z = 2bl3tl5dl, the largest 3-integer less than or equal to n (where b]; Ci, di € {0,1,2,...,!})
1.3k*-n 1.4k*-|k-z]
2. While k > 0 do Log_base_5_process
2.1 Write (bi cJ; dt)
3. Compute n = Σ.2h3c5d
Examples:
1. 84= 203152 + 2°3°5,+ 2°3°51 - 2°3°5° 2 35= 2,315l+ 2°3°5l

According to another exemplary embodiment, algorithm 5: A pseudo code of the proposed algorithm for DBNS (as shown in Figure 3)
Conversion of a positive integer to DBNS with decreasing order of exponents is explained below:
Input: A positive integer n
Output: the sequence of exponents (bm, cm) (such that bj > b2> .. .bm > 0 and
C1 > c2 > cm > 0) leading to one DBNS representation of n.
1. bits_computingjprocess
1.1 Find t = #(n2) where t gives number of bits for n
1.2 w= Dt/2D
1.2 Find z = 2bl3cl, the largest 2-integer less than or equal to n (where b1, c1 € {0,l,2,...,w}) 1.3k*-n
1.4k←[k-z]
2. Whilek> 0 do bits_computing_process
2.1 Write (bi,cj)
3. Compute n = Σ2b3c
Examples:
l- 38 = 2V+213°
2' 127 = 2233+ 2l32 + 2°3t)
3- 34 = 2'32+ 2l32-2'3°
Explanation
1. A given number n = 3 8
2. t = #(38) = #(1001102) = 6
3. w = 3
4. z ~ 36 = 22 32 (the largest 2-integer less than or equal to n)
5. k = 38-36 = 2

6. Bit computation for k
7. k= 21 3°
8 n=2232+ 2'3°
In one embodiment, for given an integer n, the n is expressed in the form of DBNS/ MBNS, a deterministic polynomial time problem. This result is proved using transcendental number theory and exponential Diophantine equations. To compute the best approximation of n in DBNS/MBNS (decreasing order), it is not yet proven in the complexity class of P. For instance, n=1000 has 1295579 DBNS in which it will be a difficult task to find the best one in decreasing order without repetition of terms. The proposed computational complexity of DBNS / MBNS can be solved in at most 0(log n / log log n) for a given positive integer n.
Figure 4 is a flowchart illustrating ECDSA engine used for EC Digital signature generation and verification according to one exemplary embodiment of the invention. In one exemplary embodiment, an Elliptic Curve Digital Signature Algorithm (ECDSA) engine for generating at least one EC scalar multiplication value comprises of: a module adapted to: receive at least one positive integer (x); and generate at least one scalar value (n) using the received positive integer (x), the scalar value n is either one of the value of Double Base Number System (DBNS) sum, DBNS sum with repetitative summands, Multiple Base Number System (MBNS) sum or MBNS sum with repetitative summands. Elliptic Curve (EC) scalar multiplication generation module adapted to: receive at least one input scalar value (n); receive at least one EC point (P). the P is P e E(F) and the E(F) is an elliptic curve over a prime/binary field F; and compute at least one output EC scalar multiplication value (z) using the input scalar value (n) and the EC point (P), wherein the z is nP e E(F).
In another embodiment, the input scalar value (n) can be output from greedy form of n, the greedy form comprises of representing at least one character set with respect to bases 2, 3 or 5.

According to another embodiment, a digital signature generation module is configured with ECDSA engine to: receive at least one generated EC scalar multiplication value (z): and generate at least one digital signature using the received output EC scalar multiplication value (z).
According to another embodiment, a digital signature verification module is configured with ECDSA engine and the digital signature generation module adapted to; receive at least one digital signature from the digital signature generation module; retrieve the EC scalar multiplication value (z); generate a new EC scalar multiplication value (y) based on the retrieved EC scalar multiplication value (z) using the ECDSA engine; and verify the EC scalar multiplication value (z) by comparing the EC scalar multiplication value (y) with the retrieved EC scalar multiplication value (z).
Figure 5 is a flowchart illustrating ECE engine used for EC Encryption and EC Decryption according to one exemplary embodiment of the invention. In one exemplary embodiment. an Elliptic Curve Encryption (ECE) engine for generating at least one EC scalar multiplication value comprises of: a module adapted to: receive at least one positive integer (x); and generate at least one scalar value (n) using the received positive integer (x), the scalar value n is either one of the value of Double Base Number System (DBNS) sum, DBNS sum with repetitative summands. Multiple Base Number System (MBNS) sum or MBNS sum with repetitative summands. Elliptic Curve (EC) scalar multiplication generation module adapted to: receive at least one input scalar value (n); receive at least one EC point (P), the P is P € E(F) and the E(F) is an elliptic curve over a prime/binary field F; and compute at least one output EC scalar multiplication value (z) using the input scalar value (n) and the EC point (P), wherein the z is nP e E(F).
In another embodiment, the input scalar value (n) can be output from greedy form of n, the greedy form comprises of representing at least one character set with respect to bases 2, 3 or 5.

According to another embodiment. Elliptic Curve (EC) Encrypted signal generation module is configured with ECE engine adapted to: receive at least one generated EC scalar multiplication value (z); and generate at least one EC Encrypted signal using the received output EC scalar multiplication value (z).
According to another embodiment, an EC Decryption module is configured with EC Encrypted signal generation module and ECE engine to; receive at least one EC Encrypted signal from the EC Encrypted signal generation module; retrieve the EC scalar multiplication value (z); generate a new EC scalar multiplication value (y) based on the retrieved EC scalar multiplication value (z) using the ECE engine; and verify the EC scalar multiplication value (z) by comparing the EC scalar multiplication value (y) with the retrieved EC scalar multiplication value (z).
Figure 6 is a flowchart illustrating ECDSA/ECE engine that is utilized the multiprocessors according to one exemplary embodiment of the invention.
Figure 7 is a flowchart illustrating inner product computation unit for generation of DBNS
according to one exemplary embodiment of the invention. Mathematical Notation: To
summarize. DBNS representation provides {si, a„ bj} and {s,, a„ b,-, c,} for each integer x,
where s,- stands +1 or - 1 and aj, b; and c, are the exponents of 2, 3 and 5. For DBNS, a
given integer x written as x = Σfinite S; T 3b
In according to one embodiment, arithmetic operations for DBNS are explained below:
DBNS representations for integers x and y: {sx, aX) b*} and {sy, ay> by}
Multiplication: x.y = {sx + sy, ax + ay, bx + by}
Division: x / y = {sx - sy, ax - ay, bx - by}
For multiplication and division operations in hardware implementation, two independent
binary adders and simple logic for the sign correction (+ or -) is used.
Addition and substration can be done through precomputed DBNS values using Lookup
table is mentioned below (Table 1).

Figure 8 is a flowchart illustrating inner product computation unit for generation of MBNS according to one exemplary embodiment of the invention. Mathematical Notation: To summarize, DBNS representation provides {s„ ai, b,} and {si, a,-, b,-. c,} for each integer x, where 5; stands +1 or - 1 and a,, b; and a are the exponents of 2, 3 and 5. For MBNS. a given integer x is written as x = ^finite s, 2a3b 5c
In according to one embodiment, arithmetic operations for MBNS are explained below: MBNS representations for integers x and y: {sx, aX; bx, cx} and {sy, ayi by, cy} Multiplication: x.y = {sx+ sy, ax + av, bx + by; cx + cy} Division: x / y = {sx - sy, ax - ay > bx_ by, cx - cy}
For multiplication and division operations in hardware implementation, we have to do three independent binary adders and simple logic for the sign correction (+ or -). Addition and subtraction can be done through pre-computed MBNS values using Lookup table is mentioned below (Table 1).
Analytical Results
Lemma 1: Let n = Σfinite 2" 3y 5Z. Then the set t = {ip,jq,kr} of exponents of n is compact
over nonnegative reals.
Proof: Suppose the cardinality of t = {ipjq,kr} for a given n is uncountably many indices,
then the set t has infinite terms. This leads to express n as an infinite sum - a contradiction.
Theorem 2: Every positive integer n can be represented as the sum (or difference) of at
most O (log n/ log log n) {2, 3, 5}-integers.
Proof: As per algorithm 4, for a given integer n, every exponent is bounded by
Dlogs nD . By Lemma 1, the number of exponents of the given n is finite. There exists an
absolute constant C> 0 such that there is always a number of the form
2X 3y 5Z between n - (n / (log n) ) and n. Therefore each n has summands that should not
exceed O(1og n/ log log n). Hence the theorem.

Theorem 3: Every positive integer n can be expressed as a sum of two {2,3.5 }-integers, i.e.. n= 2*3y5z + k 2a3b5c where k > 0.
Proof: Given n has factors 2, 3 and 5 only. It is straight forward to check the hypothesis. Suppose n has a factor not in the set {2.3,5}. then find a large C > 0 (by Theorem 2) such that 2s 3y 5Z = On - (n / (log n)c)D. It follows that s = (n - 2* 3r 5Z) is minimal and expressed as k (2a 3b 5C) where k > 0. Hence the theorem.
Corrollary 4: Every positive integer n can be expressed as a sum of two {2,3 {-integers, i.e., n= 2*3y +k 2a3b where k>0.
Generally, computers use ASCII (American Standard Code Information Interchange) codes to represent text for transferring data from one computer to another. The standard ASCII character set uses 7 bits for each character. This character set is also represented by a greedy form using DBNS / MBNS algorithms. It is a novel way of expressing the character set w.r.to bases 2, 3 and 5. Therefore, we call this character set as Greedy ASCII.
As per algorithm 5 (DBNS), we express numbers w.r.to bases 2 and 3.
For example,
n=223l-203°={21}-{00}
15 = 2231+2°31-{02}{01}
63=2232+2'32 + 2°32={22}{12}{02}
As per algorithm 4 (MBNS), we express numbers w.r.to bases 2,1 and 5
For example,
] 7 = 2°3'5' + 2°3°50 + 2 03050= {011} {000} {000}
29 = 2°3°52 + 2°3°51 -203°5°= {002} {001 >-{000}
123 = 223°52 + 2°3°52 -2°3°5°- 2°3°5° = {202}{002}-{000}-{000}

Dec Hex Oct
DBNS (Algorithm
MBNS (Algorithm 4) Char
i Description
i

0
10 000 0 0 null
1 1 001 {00} {000} start of
heading
2 2 '002 {00}{00} {000} {000} start of text
3 !3 003
i {00}{00}{00} {000}{000}{000} j
lend of text
4 4 004 {01}{00} {000}{000}{000}{000} end of
' transmission
5 5 005 {01}{00}{00} {001} [enquiry
6 6 006 {11} {110} acknowledge
7
i
8 I7
1
IS 007 010 {11}{00} {110}{000} bell

{11}{10} {110}{100} | backspace
9 9 on {ii}{0i} {110}{010} horizontal tab
10 A |012 ~~|{11}{01}{00} {101} j new line
11 B 013 {21}-{00} {101}{000} vertical tab
12 C 014 [{21} i {101}{100} 'new page
13 D 015 '{21}{00}
I {101}{100}{000} carriage
! return
14
E 016 {21}{10} {101}{001}-{000}
shift out
15
16
F 017 {21}{01} {011} shift in

10 020 {21}{20} {011}{000} data link
17 escape

11 021 {2i}{n}-{oo} {011}{000}{000} | device
control 1
18
i 12 |022 {12} {011}{010} device

i

{32}{00} control 2
19 t 13 023
1(011}(001}-{000} device
. control 3
20 14024 {12}{10} {011H001} device




control 4

21 Il5 025 {12}{01}
1 {011} {001} {000} 1 negative
acknowledge
22 J
16 J026 |{12}{01}{00}"
1 , .__ . . ; _._ j
{011}{001}{000}{000} synchronous

(idle
23 :17 027 {12J{11-{00} {011}{001}{000}{000}{! jendoftrans.
1

000} block
24
i 18 30 {12}{11} {011}{001}{001}-{000} cancel
25 19 031
1 {12}{11}{00} {002} end of

IA| medium
26
032 {12}{02}-{00} {002}{000} substitute
'21
1B 033 {12}{02} {002}{000}{000} escape
28
1C 034 {12H02}{00} {002}{000}{000}{000} fileseparator ■
129
1D 035 {12}{02}{00}{00} {002}{001}-{000} group
30 separator

1E |036
{12}{02}{01} | {111} record )

1F 037
20 040 separator
31 32
{12}{02}{01}{00} !
{111}{000} unit separator

{12}{12}-{01}- {111}{100} space
{00}

33 21 041
{12}(12}-{0l} {111}{010} 33
34 22 1042 1 {12}{12}-{I0} {HI}{001}-{000} 34

[35 23 043 {12}{12}-{00} I{111}{001} # 35
36 24 044 {22} {220} $ 36
37 25 045 {22}{00} {220}{000} % 37
38 26 046 {22}{10} {220}{100} & 38
39 27 047 l{22}{01} {220}{010} 39
40 28 [050 {22}{20} {220}{200} ( 40
41 29 1051 {22}{ll}-{00} {220}{001}-{000} ) 41
42 2A 052 {22}{11} {220}{110} * 42
43 2B 053 {22} {11 }{00} {220}{110}{000} + 43
44 2C !054
i {22}{02}-{O0} {220}{020}-{000}
44
45 2D 055 {22}{02} {021}
45
46 :2E 056 {22}{02}{00} {021}{000} 46
|47 2F 057 {22}{21}{00}
{021}{000}{000} / 47
48 130 060 {22}{21}
{021}{010} 0 48
49 31
50 32 061 {22}{21}{00} {02l}{001}-{000} 1

062 {22}{21}{10} {102} 2 50
51 133 063 {22}{12}-{01} {102}{000} 3 51
52 34 064 {22"}{"l2}-{10} {102}{100} 4 52
53 35 065 {22}{12}-{00} {102}{100}{000}
5 53
54 36 066 {22}{12} {102}{001}-{000} 6
7 54
55 37 067 {22}{12}{00} {102}{001}
55
56 38 070 {22}{12}{10} {102}{001}{000} 8 56
57 39 071 j{22}{12}{01} {102}{001}{000}{000}
9 57
58 3A
072 {22}{12}{01}{00} {102}{101}-{100} 1 i 58

59
3B 073 {22}{12}{ll}-{00} {102}{101}-{000} > 59
60 3C
61 |3D 074
075 {22}{12}{11} {211} < 60
61

{22}{12}{11}{00} {211}{000} =

62 l3E :076 {22}{12}{02}- |{211}{100} > 62
{00}
63 3F 077 {22}{12}{02} {211}{010} 63
64 40 100 l{13}{02}{00} {211}{200}
64
65 4l 101 {13}{02}{00}{00} {211}{001} A 65
66 .42 102 {13}{02>{01> {211}{110}
B 66
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Applications of ASCII are as mentioned below:
1. Transmission of telecommunication data
2. Creating text editors and word processors
3. Encoding and Decoding operations
4. Increase the performance of Operating Systems
5. ASCII art programs w.r.to bases 2, 3 and 5 for image processing
The methodology and techniques described with respect to the exemplary embodiments can be performed using a machine or other computing device within which a set of instructions, when executed, may cause the machine to perform any one or more of the methodologies discussed above. In some embodiments, the machine operates as a standalone device. In some embodiments, the machine may be connected (e.g., using a network) to other machines. In a networked deployment, the machine may operate in the capacity of a server or a client user machine in a server-client user network environment, or as a peer machine in a peer-to-peer (or distributed) network environment. The machine may comprise a server computer, a client user computer, a personal computer (PC), a tablet PC, a laptop computer, a desktop computer, a control system, a network router, switch or bridge, or any machine capable of executing a set of instructions (sequential or otherwise) that specify actions to be taken by that machine, Further, while a single machine is illustrated, the term "machine" shall also be taken to include any collection of machines that individually or jointly execute a set (or multiple sets) of instructions to perform any one or more of the methodologies discussed herein.

The machine may include a processor (e.g., a central processing unit (CPU), a graphics processing unit (GPU, or both), a main memory and a static memory, which communicate with each other via a bus. The machine may further include a video display unit (e.g., liquid crystals display (LCD), a flat panel, a solid state display, or a cathode ray tube (CRT)). The machine may include an input device (e.g., a keyboard) or touch-sensitive screen, a cursor control device (e.g., a mouse), a disk drive unit, a signal generation device (e.g., a speaker or remote control) and a network interface device.
The disk drive unit may include a machine-readable medium on which is stored one or more sets of instructions (e.g., software) embodying any one or more of the methodologies or functions described herein, including those methods illustrated above. The instructions may also reside, completely or at least partially, within the main memory, the static memory, and/or within the processor during execution thereof by the machine. The main memory and the processor also may constitute machine-readable media.
Dedicated hardware implementations including, but not limited to, application specific integrated circuits, programmable logic arrays and other hardware devices can likewise be constructed to implement the methods described herein. Applications that may include the apparatus and systems of various embodiments broadly include a variety of electronic and computer systems. Some embodiments implement functions in two or more specific interconnected hardware modules or devices with related control and data signals communicated between and through the modules, or as portions of an application-specific integrated circuit. Thus, the example system is applicable to software, firmware, and hardware implementations.
In accordance with various embodiments of the present disclosure, the methods described herein are intended for operation as software programs running on a computer processor. Furthermore, software implementations can include, but not limited to, distributed processing or component/object distributed processing, parallel processing, or virtual machine processing can also be constructed to implement the methods described herein.

The present disclosure contemplates a machine readable medium containing instructions, or that which receives and executes instructions from a propagated signal so that a device connected to a network environment can send or receive voice, video or data, and to communicate over the network using the instructions. The instructions may further be transmitted or received over a network via the network interface device.
While the machine-readable medium can be a single medium, the term "machine-readable medium'1 should be taken to include a single medium or multiple media (e.g., a centralized or distributed database, and/or associated caches and servers) that store the one or more sets of instructions. The term "machine-readable medium" shall also be taken to include any medium that is capable of storing, encoding or carrying a set of instructions for execution by the machine and that cause the machine to perform any one or more of the methodologies of the present disclosure.
The term "machine-readable medium" shall accordingly be taken to include, but not be limited to: tangible media; solid-state memories such as a memory card or other package that houses one or more read-only (non-volatile) memories, random access memories, or other re-writable (volatile) memories; magneto-optical or optical medium such as a disk or tape; non-transitory mediums or other self-contained information archive or set of archives is considered a distribution medium equivalent to a tangible storage medium. Accordingly, the disclosure is considered to include any one or more of a machine-readable medium or a distribution medium, as listed herein and including art-recognized equivalents and successor media, in which the software implementations herein are stored.
The illustrations of arrangements described herein are intended to provide a general understanding of the structure of various embodiments, and they are not intended to serve as a complete description of all the elements and features of apparatus and systems that might make use of the structures described herein. Many other arrangements will be apparent to those of skill in the art upon reviewing the above description. Other arrangements may be utilized and derived there from, such that structural and logical

substitutions and changes may be made without departing from the scope of this disclosure. Figures are also merely representational and may not be drawn to scale. Certain proportions thereof may be exaggerated, while others may be minimized. Accordingly, the specification and drawings are to be regarded in an illustrative rather than a restrictive sense.
The preceding description has been presented with reference to various embodiments. Persons skilled in the art and technology to which this application pertains will appreciate that alterations and changes in the described structures and methods of operation can be practiced without meaningfully departing from the principle and scope.
ADVANTAGES OF THE INVENTION:
1. The above propose method improves the performance on Digital Signature schemes and Elliptic Curve Encryption methods;
2. The above propose method improves the performance of filter bank design in mobile handsets, hearing aid instruments and other tiny devices;
3. With the reduction in the size of the number representation, the above propose method promises low-cost (area X power) implementation of the arithmetic operations required in linear and non-linear filtering and compression,
4. The above propose method is used for encoding and decoding formats on Data Compression. They are helpful to reduce the size of data subsets, as the result, the entire data has been compressed into a smaller size.
5. A Hybrid DBNS / MBNS processor is 8 times smaller than binary based processor. So, the above propose method is useful in Hybrid processors for saving power consumption at least 50 % compared to binary processors.
6. The intera ction process of the present invention helps to save travel cost and to
increase paperless transaction.

Advantages of Trusted Mobile Education Software using DBNS/MBNS are as follows:
1. The proposed Mobile Education software tool provides a trusted network connection among users.
2. The tool builds confidentiality, authentication, authorization and accounting (CAAA) among users.
3. Users satisfy non-repudiation setup.
4. No password-based negotiation between customers and an administrator.
5. The tool has a robust, tamper-proof and lightweight authentication mechanism.
6. The tool helps to transmit data packets through secure communication protocols based on Double Base Number Systems / Multi Base Number Systems (DBNS /MBNS).
7. The tool sends and receives voice, data and video transmission without any delay.
8. The tool supports Point-and-shoot learning with camera phones and 3D codes.
BEST MODE / EXAMPLE OF WORKING OF THE INVENTION
Figure 10 is a flowchart illustrating Mobile learning platform using DBNS/MBNS methods.
For trusted interactions among disparate users using digital communication devices, a underlying network path and corresponding communication protocols are devised that are based on Double base number system or Multi base number system. During the interaction, the devices are enabled to send messages of shorter length, with reduced data errors and high throughput (heavy data transfer). For confidentiality, authentication, authorization and accounting purposes, a Network Security protocols is adapted to offer privacy and security among users during the trusted interactions. Such trusted interaction may be employed for defense, corporate and retail sectors to promote secured communication and business activities without any hindrance.

CLAIMS:
1. A method for computing Elliptic Curve (EC) scalar multiplication value comprising machine implemented steps of:
a) receiving at least one input scalar value (n);
b) representing each received scalar value( n) in at least one greedy form using at least one of deterministic polynomial time form from a Double Base Number System (DBNS) sum, a DBNS sum with repetitive summands, a Multiple Base Number System (MBNS) sum or a MBNS sum with repetitive summands, each deterministic polynomial time form comprising a decreasing order of exponent;
c) receiving a sequence of exponents, each exponent greater than or equal to zero, for at least one deterministic polynomial time form and computing the a sum thereof each polynomial in the said sequence;
d) computing at least one EC point (P) for an elliptic curve E(F) over a prime/binary field F using the sum of at least one deterministic polynomial time form; and
e) computing at least one output EC scalar multiplication value (z) using the input scalar value (n) and the EC point (P), wherein the z is nP e E(F).

2. The method of claim 1, wherein at least one of the deterministic polynomial time form is represented in the decreasing order of exponent to generate the greedy form of the scalar value (n) facilitating computation of the EC scalar multiplication.
3. The method of claim 1, wherein the input scalar value (n) is an output from greedy form of n, the greedy form comprises of representing at least one character set with respect to bases 2, 3 or 5.
4. The method of claim 1, wherein the input scalar value (n) is computed by the following steps:
a) receiving at least one positive integer (x); and

b) generating at least one scalar value (n) using the received positive integer (x), the scalar value n is either one of the value of Double Base Number System (DBNS) sum, DBNS sum with repetitive summands, Multiple Base Number System (MBNS) sum or MBNS sum with repetitive summands.
5. The method of claim 1. wherein a character set of ASCII codes are represented in the greedy form exploiting the said at least one deterministic polynomial time form from the Double Base Number System (DBNS) sum, DBNS sum with repetitive summands. Multiple Base Number System (MBNS) sum or MBNS sum with repetitive summands.
6. An Elliptic Curve Digital Signature Algorithm (ECDSA) engine for generating at least one EC scalar multiplication value comprises of:
a) a module adapted to:
i. receive at least one positive integer (x); and
ii. generate at least one scalar value (n) using the received positive integer (x), the scalar value (n) represented in at least one of the deterministic polynomial time form including Double Base Number System (DBNS) sum, DBNS sum with repetitive summands. Multiple Base Number System (MBNS) sum or MBNS sum with repetitive summands.
b) an Elliptic Curve (EC) scalar multiplication generation module adapted to:
i. receive at least one input scalar value (n);
ii. receive at least one EC point (P), the P is P e E(F) and the E(F) is an elliptic
curve over a prime/binary field F; and iii. compute at least one output EC scalar multiplication value (z) using the input
scalar value (n) and the EC point (P), wherein the z is nP e E(F).
7. An ECDSA engine according to claim 6, wherein the input scalar value (n) can be output from greedy form of n, the greedy form comprises of representing at least one character set with respect to bases 2, 3 or 5.

8. An ECDSA engine according to claim 6, further comprises of digital signature
generation module adapted to:
i. receive at least one generated EC scalar multiplication value (z); and ii. generate at least one digital signature using the received output EC scalar multiplication value (z).
9. An ECDSA engine according to claim 8, further comprises of digital signature
verification module adapted to;
i. receive at least one digital signature from the digital signature generation
module; ii. retrieve the EC scalar multiplication value (z); iii. generate a new EC scalar multiplication value (y) based on the retrieved EC
scalar multiplication value (z) using the ECDSA engine; and iv. verify the EC scalar multiplication value (z) by comparing the EC scalar
multiplication value (y) with the retrieved EC scalar multiplication value (z).
10. An Elliptic Curve Encryption (ECE) engine for generating at least one EC scalar
multiplication value comprises of:
a) a module adapted to:
i. receive at least one positive integer (x); and
ii. generate at least one scalar value (n) using the received positive integer (x), the scalar value (n) represented in at least one of deterministic polynomial time form including Double Base Number System (DBNS) sum, DBNS sum with repetitive summands, Multiple Base Number System (MBNS) sum or MBNS sum with repetitive summands.
b) Elliptic Curve (EC) scalar multiplication generation module adapted to:
i. receive at least one input scalar value (n);
ii. receive at least one EC point (P), the P is P e E(F) and the E(F) is an elliptic curve over a prime/binary field F; and

iii. compute at least one output EC scalar multiplication value (z) using the input scalar value (n) and the EC point (P), wherein the z is nP e E(F).
11. An ECE engine according to claim 10, wherein the input scalar value (n) can be output from greedy form of n, the greedy form comprises of representing at least one character set with respect to bases 2, 3 or 5.
12. An ECE engine according to claim 10, further comprises of EC Encrypted signal generation module adapted to:
i. receive at least one generated EC scalar multiplication value (z); and ii. generate at least one EC Encrypted signal using the received output EC scalar multiplication value (z).
13. An ECE engine according to claim 12, further comprises of EC Decrypted signal
module adapted to;
i. receive at least one EC Encrypted signal from the EC Encrypted signal generation
module; ii. retrieve the EC scalar multiplication value (z); iii. generate a new EC scalar multiplication value (y) based on the retrieved EC scalar
multiplication value (z) using the ECE engine; and iv, verify the EC scalar multiplication value (z) by comparing the EC scalar
multiplication value (y) with the retrieved EC scalar multiplication value (z).