swfchan: 21fe8 3f8f000 by maxnaik.swf (info)

Text

Introduction

Classic Cryptography

Public-key cryptography

Introduction to Cryptography

Created by R.sudhir kumar (10e11a1250)

Introduction

People have always been fascinated with the idea of
hiding information from others. For thousands of years,
history has given us numerous examples of people
trying to keep information secret from adversaries.
Cryptography is the study of the art and science of
designing and using methods to conceal messages.
These methods range from simple toy examples (e.g.
secret decoder rings) to highly theoretical algorithms
that rely heavily on mathematics.

Intro 1 of 7

In a basic communication scenario, using cryptography
is relatively simple.

Imagine two people wanting to communicate secretly.
Alice wants to send a message to Bob that nobody else
can read.

Intro 2 of 7

Bob

Alice

meet me
at noon

Alice must somehow transform her message, called
plaintext, so that an adversary can't read it.

Intro 3 of 7

Encrypt

Alice uses an encryption algorithm to transform her
plaintext message into ciphertext. Ciphertext is a
"scrambled" form of her original message that hopefully
prevents an adversary from eavesdropping.

meet me at noon

Intro 4 of 7

meet me at noon

key

In order to encrypt a message, the encryption routine
takes as input both the plaintext of the original
message, plus a key that tells the algorithm how to
"scramble" the plaintext into ciphertext.

phhw ph dw qrrq

Intro 5 of 7

There is just one problem. The message has been
encrypted to prevent adversaries from eavesdropping,
but now Bob can't read the message. What we need is
a way to retrieve the original plaintext message from
the ciphertext.

phhw ph dw qrrq

meet me at noon

Intro 6 of 7

Both Alice and Bob use the same algorithm to encrypt
and decrypt. They both use a key, that must be kept
secret, to transform their communications. If anyone
else discovers the key, their communications would be
compromised.

Decrypt

meet me at noon

phhw ph dw qrrq

Introduction

meet me at noon

Intro 7 of 7

Classic Cryptography

To illustrate how a basic cryptographic system works, you
will be introduced to some simple classic cryptographic
algorithms. The first is called a shift cipher, sometimes
called a Caesar cipher because it is said that Caesar used
this technique to communicate secretly with his generals
in the field.

- Shift Ciphers

Classic Cryptography

Classic 1 of 7

Letter +
Key

Shift ciphers are simple. To encrypt a message, each
letter is shifted a certain number of characters in the
alphabet. The number of characters to shift is based on
the value of the key. For example, if the plaintext
message is "a" and the key for this message is 3, then the
encryption algorithm will generate "a"+3 = "d".

- Shift Ciphers

Classic Cryptography

Classic 2 of 7

Shift ciphers work with larger messages by performing
the encryption function on one letter at a time. Each letter
in the ciphertext is the result of the original letter plus the
value of the key.

apple

dssoh

- Shift Ciphers

Classic Cryptography

Classic 3 of 7

Letter -
Key

How does Bob retrieve the original message from the
encrypted message he receives? First, Alice and Bob
have to agree ahead of time on the key they will use. For
shift ciphers, both the sender and receiver must use the
same key. Then, Bob simply takes the text he receives
and subtracts the value of the key from each letter.

dssoh

apple

- Shift Ciphers

Classic Cryptography

Classic 4 of 7

There are a few issues involved with shift ciphers. First,
what happens when plaintext letters appear near the end
of the alphabet and "fall off" the end when their value is
added to the key? The solution is to "wrap around" to the
beginning of the alphabet whenever this occurs. For
example, the letter "x" would become a "b" with a key of 4.

xray

bvec

Classic 5 of 7

Another issue with this type of cipher is how do Alice and
Bob agree on a key ahead of time? There is an entire set
of problems in the field of cryptography devoted to this
subject -- how keys are exchanged. For the purposes of
this simple cipher, just assume that Alice and Bob have
some mechanism in place to agree on a common key.

Classic 6 of 7

Encrypt
Button

Encrypt

Test your understanding of the shift cipher by entering a
short plaintext message in the white text box above Alice's
name. Enter a key in the key field. To see the encryption
take place, click on the encrypt button. Can you
determine what the cipher text will be for a given plaintext
and key? Try several different messages and keys.

Classic 7 of 7

- Shift Ciphers

Classic Cryptography

Public-Key Cryptography

Public-key cryptography is different in several significant
ways from classic encryption schemes:
- Instead of a single key, there is a key pair.
- One of the keys is kept secret (private key).
- The other key is made available to anyone (public key).

Public-Key Cryptography

Public 1 of 14

KR
Bob

KU
Bob

KR
Alice

KU
Alice

Each user first generates a pair of keys to be used for the
encryption and decryption of messages. KU indicates a
public key, KR indicates a private key.

Public 2 of 14

All users publish their public keys to a central server so that
anyone can access them. This is an essential step because
people will need an intended recipient's public key in order to
send them an encrypted message.

Public Server

Public 3 of 14

Suppose Alice wants to send an encrypted message to Bob.
To do so, she obtains his public key, which is available to
anyone, and uses that key to encrypt her message.

Public 4 of 14

Hi, Bob!

#dG;9)m

When Bob receives a message, he decrypts it with his
private key. No one else can decrypt the message except
Bob because only he knows the private key!

Public 5 of 14

Hi, Bob!

Public Server

Public-Key Cryptography

Public 6 of 14

RSA is one of the most popular public-key algorithms.
Named after the three researchers (Rivest, Shamir, and
Adleman) who published the algorithm in the late 1970's, it
has become widely used in many modern cryptographic
systems. The fundamental security of the algorithm is based
on the difficulty of factoring very large numbers into their
prime factors.

Public-Key Cryptography

Public 7 of 14

The first step of the RSA algorithm is to create the public and
private keys for a user:
Step 1: Generate 2 very large (random) primes, p and q
The numbers need to be very large to make factoring
difficult, and they need to be random so an adversary can't
guess what they might be.
Step 2: Calculate n = p * q
This is simply the product of the two numbers.

Public-Key Cryptography

Public 8 of 14

Step 1: Generate 2 very large (random) primes, p and q
Step 2: Calculate n = p * q
Step 3: Calculate phi(n) = (p-1)(q-1)
This value is needed for the next two steps.
Step 4: Select integer e, such that gcd(phi(n), e)=1
That is, we need to find a value for e that is relatively prime
to phi(n). There are algorithms that can do this very quickly.

Public-Key Cryptography

Public 9 of 14

Step 1: Generate 2 very large (random) primes, p and q
Step 2: Calculate n = p * q
Step 3: Calculate phi(n) = (p-1)(q-1)
Step 4: Select integer e, such that gcd(phi(n), e)=1
Step 5: Calculate d, where d*e=1 mod phi(n)
We need a value of d, such that when it is multiplied by e
from the previous step, the product is equal to 1 when we
take the remainder when divided by phi(n).

Public-Key Cryptography

Public 10 of 14

Step 1: Generate 2 very large (random) primes, p and q
Step 2: Calculate n = p * q
Step 3: Calculate phi(n) = (p-1)(q-1)
Step 4: Select integer e, such that gcd(phi(n), e)=1
Step 5: Calculate d, where d*e=1 mod phi(n)
The public key, KU, is {e, n}. Make these values available to
everyone.
The private key, KR, is {d, n}. Keep d secret!

Public-Key Cryptography

Public 11 of 14

Although real RSA implementations use very large numbers,
for the purposes of this tutorial, we will us relatively small
numbers so that the calculations are easier.
Enter p and q such that they are prime and less than 100.

Calculate n

phi(n)=

n=p*q

(p-1) *(q-1)

Verify e

Now find e such that the gcd(phi(n), e) = 1.

gcd(phi(n), e) =

n=p*q

(p-1) *(q-1)

Calculate d (using Euclid's algorithm),
where d·e=1 mod phi(n)

Public-Key Cryptography

Public 12 of 14

Decrypt
Button

Decrypt

To encrypt plaintext M, do the following (M must be less
than n) :
Ciphertext: C=M
e
mod n
To decrypt ciphertext C at the receiving end:
Plaintext: M=C
d
mod n
Try some values for M above and press the encrypt and
decrypt buttons to see the encryption values for the
keys generated on the previous page.

Public-Key Cryptography

Public 13 of 14

To summarize RSA:
Step 1: Generate 2 very large (random) primes, p and q
Step 2: Calculate n = p * q
Step 3: Calculate phi(n) = (p-1)(q-1)
Step 4: Select integer e, such that gcd(phi(n), e)=1
Step 5: Calculate d, where d*e=1 mod phi(n)
Step 6: The public key, KU, is {e, n}.
Step 7: The private key, KR, is {d, n}. Keep d secret!
Ciphertext: C=M
e
mod n
Plaintext: M=C
d
mod n

Public-Key Cryptography

Public 14 of 14

Additional References:
Applied Cryptography, 2nd Ed., Bruce Schneier, John Wiley, 1996.
Cryptography: Theory and Practice, 2nd Ed., Douglas Stinson,
Chapman & Hall, 2002.
Introduction to Cryptography with Coding Theory, Wade Trappe and
Lawrence Washington, Prentice Hall, 2002
Handbook of Applied Cryptography, Menezes, van Oorschot, and
Vanstone, CRC Press, 1997.
Cryptography and Network Security, William Stallings, Prentice Hall,
2003.

Public-Key Cryptography

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Symbol 63 Button	Uses:1 28 3 38 39 6 40	Used by:Timeline
Symbol 64 EditableText	Uses:20	Used by:Timeline
Symbol 65 EditableText	Uses:20	Used by:Timeline
Symbol 66 EditableText	Uses:20	Used by:Timeline
Symbol 67 Button	Uses:1 28 3 4 5 6	Used by:Timeline
Symbol 68 Button	Uses:1 28 3 38 39 6 40	Used by:Timeline
Symbol 69 EditableText	Uses:20	Used by:Timeline
Symbol 70 EditableText	Uses:20	Used by:Timeline
Symbol 71 EditableText	Uses:20	Used by:Timeline
Symbol 72 EditableText	Uses:20	Used by:Timeline
Symbol 73 Button	Uses:1 28 3 38 39 6 40	Used by:Timeline
Symbol 74 EditableText	Uses:10	Used by:Timeline
Symbol 75 EditableText	Uses:20	Used by:Timeline
Symbol 76 EditableText	Uses:20	Used by:Timeline
Symbol 77 EditableText	Uses:10	Used by:Timeline
Symbol 78 EditableText	Uses:20	Used by:Timeline
Symbol 79 Button	Uses:1 28 3 4 5 6	Used by:Timeline
Symbol 80 EditableText	Uses:20	Used by:Timeline
Symbol 81 EditableText	Uses:10	Used by:Timeline
Symbol 82 Text	Uses:20 25	Used by:Timeline
Symbol 83 EditableText	Uses:20	Used by:Timeline
Symbol 84 EditableText	Uses:10	Used by:Timeline
Symbol 85 EditableText	Uses:10	Used by:Timeline
Symbol 86 EditableText	Uses:10	Used by:Timeline
Symbol 87 Button	Uses:1 28 3 4 5 6	Used by:Timeline
Symbol 88 EditableText	Uses:20	Used by:Timeline
Symbol 89 Graphic	Used by:Timeline
Symbol 90 EditableText	Uses:10	Used by:Timeline
Symbol 91 Text	Uses:25 20	Used by:Timeline
Symbol 92 EditableText	Uses:20	Used by:Timeline
Symbol 93 EditableText	Uses:20	Used by:Timeline
Symbol 94 EditableText	Uses:20	Used by:Timeline
Symbol 95 EditableText	Uses:20	Used by:Timeline
Symbol 96 EditableText	Uses:20	Used by:Timeline
Symbol 97 EditableText	Uses:20	Used by:Timeline
Symbol 98 EditableText	Uses:10	Used by:Timeline
Symbol 99 EditableText	Uses:10	Used by:Timeline
Symbol 100 Button	Uses:1 28 3 4 5 6	Used by:Timeline
Symbol 101 Button	Uses:1 28 3 38 39 6 40	Used by:Timeline
Symbol 102 EditableText	Uses:20	Used by:Timeline
Symbol 103 Text	Uses:25 20	Used by:Timeline
Symbol 104 EditableText	Uses:20	Used by:Timeline
Symbol 105 EditableText	Uses:20	Used by:Timeline
Symbol 106 EditableText	Uses:20	Used by:Timeline
Symbol 107 EditableText	Uses:10	Used by:Timeline
Symbol 108 EditableText	Uses:10	Used by:Timeline
Symbol 109 Button	Uses:1 28 3 4 5 6	Used by:Timeline
Symbol 110 Button	Uses:1 28 3 38 39 6 40	Used by:Timeline
Symbol 111 EditableText	Uses:20	Used by:Timeline
Symbol 112 EditableText	Uses:10	Used by:Timeline
Symbol 113 Text	Uses:20 10	Used by:Timeline
Symbol 114 EditableText	Uses:20	Used by:Timeline
Symbol 115 EditableText	Uses:20	Used by:Timeline
Symbol 116 EditableText	Uses:20	Used by:Timeline
Symbol 117 EditableText	Uses:10	Used by:Timeline
Symbol 118 EditableText	Uses:10	Used by:Timeline
Symbol 119 Button	Uses:1 28 3 4 5 6	Used by:Timeline
Symbol 120 Button	Uses:1 28 3 38 39 6 40	Used by:Timeline
Symbol 121 EditableText	Uses:20	Used by:Timeline
Symbol 122 EditableText	Uses:20	Used by:Timeline
Symbol 123 EditableText	Uses:20	Used by:Timeline
Symbol 124 EditableText	Uses:20	Used by:Timeline
Symbol 125 EditableText	Uses:20	Used by:Timeline
Symbol 126 Button	Uses:1 28 3 4 5 6	Used by:Timeline
Symbol 127 Button	Uses:1 28 3 38 39 6 40	Used by:Timeline
Symbol 128 EditableText	Uses:20	Used by:Timeline
Symbol 129 EditableText	Uses:20	Used by:Timeline
Symbol 130 Graphic	Used by:131
Symbol 131 MovieClip	Uses:130	Used by:Timeline
Symbol 132 Button	Uses:1 28 3 4 5 6	Used by:Timeline
Symbol 133 Button	Uses:1 28 3 38 39 6 40	Used by:Timeline
Symbol 134 EditableText	Uses:20	Used by:Timeline
Symbol 135 EditableText	Uses:20	Used by:Timeline
Symbol 136 EditableText	Uses:20	Used by:Timeline
Symbol 137 EditableText	Uses:10	Used by:141 260 266
Symbol 138 EditableText	Uses:10	Used by:141 260 266
Symbol 139 EditableText	Uses:10	Used by:141 260 266
Symbol 140 EditableText	Uses:10	Used by:141 260 266
Symbol 141 Button	Uses:42 137 138 139 140	Used by:Timeline
Symbol 142 EditableText	Uses:10	Used by:Timeline
Symbol 143 Font	Used by:144 199 204 209 214 219 221 223 225 230 232 234 235 237 238 240 241 248 249 253 254 269 272 273 274 281 286
Symbol 144 Text	Uses:20 143 10	Used by:Timeline
Symbol 145 Button	Uses:1 28 3 4 5 6	Used by:Timeline
Symbol 146 Button	Uses:1 28 3 38 39 6 40	Used by:Timeline
Symbol 147 EditableText	Uses:20	Used by:Timeline
Symbol 148 EditableText	Uses:20	Used by:Timeline
Symbol 149 EditableText	Uses:20	Used by:Timeline
Symbol 150 EditableText	Uses:20	Used by:Timeline
Symbol 151 EditableText	Uses:20	Used by:Timeline
Symbol 152 EditableText	Uses:20	Used by:Timeline
Symbol 153 EditableText	Uses:20	Used by:Timeline
Symbol 154 EditableText	Uses:20	Used by:Timeline
Symbol 155 EditableText	Uses:10	Used by:Timeline
Symbol 156 EditableText	Uses:10	Used by:Timeline
Symbol 157 EditableText	Uses:10	Used by:Timeline
Symbol 158 EditableText	Uses:10	Used by:Timeline
Symbol 159 Text	Uses:20 25	Used by:Timeline
Symbol 160 EditableText	Uses:10	Used by:Timeline
Symbol 161 EditableText	Uses:10	Used by:Timeline
Symbol 162 Button	Uses:1 28 3 4 5 6	Used by:Timeline
Symbol 163 EditableText	Uses:20	Used by:Timeline
Symbol 164 Text	Uses:20	Used by:Timeline
Symbol 165 Text	Uses:20	Used by:Timeline
Symbol 166 Text	Uses:20	Used by:Timeline
Symbol 167 Text	Uses:20	Used by:Timeline
Symbol 168 Text	Uses:20 25	Used by:Timeline
Symbol 169 Button	Uses:1 28 3 4 5 6	Used by:Timeline
Symbol 170 Button	Uses:1 28 3 38 39 6 40	Used by:Timeline
Symbol 171 EditableText	Uses:20	Used by:Timeline
Symbol 172 EditableText	Uses:20	Used by:Timeline
Symbol 173 EditableText	Uses:20	Used by:Timeline
Symbol 174 Graphic	Used by:Timeline
Symbol 175 Button	Uses:1 28 3 4 5 6	Used by:Timeline
Symbol 176 Button	Uses:1 28 3 38 39 6 40	Used by:Timeline
Symbol 177 EditableText	Uses:20	Used by:Timeline
Symbol 178 EditableText	Uses:20	Used by:Timeline
Symbol 179 Button	Uses:1 28 3 4 5 6	Used by:Timeline
Symbol 180 Button	Uses:1 28 3 38 39 6 40	Used by:Timeline
Symbol 181 EditableText	Uses:20	Used by:Timeline
Symbol 182 EditableText	Uses:10	Used by:Timeline
Symbol 183 EditableText	Uses:10	Used by:Timeline
Symbol 184 EditableText	Uses:20	Used by:Timeline
Symbol 185 Button	Uses:1 28 3 4 5 6	Used by:Timeline
Symbol 186 Button	Uses:1 28 3 38 39 6 40	Used by:Timeline
Symbol 187 EditableText	Uses:20	Used by:Timeline
Symbol 188 EditableText	Uses:10	Used by:Timeline
Symbol 189 EditableText	Uses:20	Used by:Timeline
Symbol 190 EditableText	Uses:10	Used by:Timeline
Symbol 191 Button	Uses:1 28 3 4 5 6	Used by:Timeline
Symbol 192 Button	Uses:1 28 3 38 39 6 40	Used by:Timeline
Symbol 193 EditableText	Uses:20	Used by:Timeline
Symbol 194 EditableText	Uses:20	Used by:Timeline
Symbol 195 EditableText	Uses:10	Used by:Timeline
Symbol 196 Button	Uses:1 28 3 4 5 6	Used by:Timeline
Symbol 197 Button	Uses:1 28 3 38 39 6 40	Used by:Timeline
Symbol 198 EditableText	Uses:20	Used by:Timeline
Symbol 199 Text	Uses:20 143	Used by:Timeline
Symbol 200 EditableText	Uses:10	Used by:Timeline
Symbol 201 Button	Uses:1 28 3 4 5 6	Used by:Timeline
Symbol 202 Button	Uses:1 28 3 38 39 6 40	Used by:Timeline
Symbol 203 EditableText	Uses:20	Used by:Timeline
Symbol 204 Text	Uses:20 143 25	Used by:Timeline
Symbol 205 EditableText	Uses:10	Used by:Timeline
Symbol 206 Button	Uses:1 28 3 4 5 6	Used by:Timeline
Symbol 207 Button	Uses:1 28 3 38 39 6 40	Used by:Timeline
Symbol 208 EditableText	Uses:20	Used by:Timeline
Symbol 209 Text	Uses:20 143	Used by:Timeline
Symbol 210 EditableText	Uses:10	Used by:Timeline
Symbol 211 Button	Uses:1 28 3 4 5 6	Used by:Timeline
Symbol 212 Button	Uses:1 28 3 38 39 6 40	Used by:Timeline
Symbol 213 EditableText	Uses:20	Used by:Timeline
Symbol 214 Text	Uses:20 143	Used by:Timeline
Symbol 215 EditableText	Uses:10	Used by:Timeline
Symbol 216 Button	Uses:1 28 3 4 5 6	Used by:Timeline
Symbol 217 Button	Uses:1 28 3 38 39 6 40	Used by:Timeline
Symbol 218 EditableText	Uses:20	Used by:Timeline
Symbol 219 Text	Uses:20 143	Used by:Timeline
Symbol 220 EditableText	Uses:20	Used by:Timeline
Symbol 221 Text	Uses:143 20	Used by:Timeline
Symbol 222 EditableText	Uses:20	Used by:Timeline
Symbol 223 Text	Uses:143 20	Used by:Timeline
Symbol 224 Graphic	Used by:229 239 245 251
Symbol 225 Text	Uses:20 143	Used by:229 245
Symbol 226 Graphic	Used by:229 239 245 251
Symbol 227 Graphic	Used by:229 239 245 251
Symbol 228 Graphic	Used by:229 239 245 251
Symbol 229 Button	Uses:224 225 226 227 228	Used by:Timeline
Symbol 230 Text	Uses:143 20	Used by:Timeline
Symbol 231 EditableText	Uses:20	Used by:Timeline
Symbol 232 Text	Uses:20 143	Used by:Timeline
Symbol 233 EditableText	Uses:20	Used by:Timeline
Symbol 234 EditableText	Uses:143	Used by:Timeline
Symbol 235 EditableText	Uses:143	Used by:Timeline
Symbol 236 EditableText	Uses:20	Used by:Timeline
Symbol 237 Text	Uses:143 20	Used by:Timeline
Symbol 238 Text	Uses:20 143	Used by:239 251
Symbol 239 Button	Uses:224 238 226 227 228	Used by:Timeline
Symbol 240 Text	Uses:20 143	Used by:Timeline
Symbol 241 Text	Uses:20 143	Used by:Timeline
Symbol 242 EditableText	Uses:20	Used by:Timeline
Symbol 243 EditableText	Uses:20	Used by:Timeline
Symbol 244 EditableText	Uses:20	Used by:Timeline
Symbol 245 Button	Uses:224 225 226 227 228	Used by:Timeline
Symbol 246 EditableText	Uses:20	Used by:Timeline
Symbol 247 EditableText	Uses:20	Used by:Timeline
Symbol 248 EditableText	Uses:143	Used by:Timeline
Symbol 249 EditableText	Uses:143	Used by:Timeline
Symbol 250 EditableText	Uses:20	Used by:Timeline
Symbol 251 Button	Uses:224 238 226 227 228	Used by:Timeline
Symbol 252 EditableText	Uses:20	Used by:Timeline
Symbol 253 Text	Uses:20 143	Used by:Timeline
Symbol 254 Text	Uses:143 20	Used by:Timeline
Symbol 255 EditableText	Uses:20	Used by:Timeline
Symbol 256 EditableText	Uses:10	Used by:Timeline
Symbol 257 Button	Uses:1 28 3 4 5 6	Used by:Timeline
Symbol 258 Button	Uses:1 28 3 38 39 6 40	Used by:Timeline
Symbol 259 EditableText	Uses:20	Used by:Timeline
Symbol 260 Button	Uses:42 137 138 139 140	Used by:Timeline
Symbol 261 EditableText	Uses:10	Used by:265 267
Symbol 262 EditableText	Uses:10	Used by:265 267
Symbol 263 EditableText	Uses:10	Used by:265 267
Symbol 264 EditableText	Uses:10	Used by:265 267
Symbol 265 Button	Uses:42 261 262 263 264	Used by:Timeline
Symbol 266 Button	Uses:42 137 138 139 140	Used by:Timeline
Symbol 267 Button	Uses:42 261 262 263 264	Used by:Timeline
Symbol 268 EditableText	Uses:20	Used by:Timeline
Symbol 269 Text	Uses:143 20	Used by:Timeline
Symbol 270 EditableText	Uses:20	Used by:Timeline
Symbol 271 EditableText	Uses:20	Used by:Timeline
Symbol 272 Text	Uses:143 20	Used by:Timeline
Symbol 273 Text	Uses:20 143 10 25	Used by:Timeline
Symbol 274 Text	Uses:143 20	Used by:Timeline
Symbol 275 EditableText	Uses:10	Used by:Timeline
Symbol 276 EditableText	Uses:10	Used by:Timeline
Symbol 277 EditableText	Uses:10	Used by:Timeline
Symbol 278 Button	Uses:1 28 3 4 5 6	Used by:Timeline
Symbol 279 Button	Uses:1 28 3 38 39 6 40	Used by:Timeline
Symbol 280 EditableText	Uses:20	Used by:Timeline
Symbol 281 Text	Uses:20 143 10 25	Used by:Timeline
Symbol 282 EditableText	Uses:10	Used by:Timeline
Symbol 283 Button	Uses:1 28 3 4 5 6	Used by:Timeline
Symbol 284 Button	Uses:1 28 3 38 39 6 40	Used by:Timeline
Symbol 285 EditableText	Uses:20	Used by:Timeline
Symbol 286 Text	Uses:20 143	Used by:Timeline
Symbol 287 EditableText	Uses:10	Used by:Timeline
Symbol 288 Button	Uses:1 28 3 4 5 6	Used by:Timeline
Symbol 289 Button	Uses:1 28 3 38 39 6 40	Used by:Timeline

Labels

"intro - 1"	Frame 31
"intro - 2"	Frame 62
"intro - 3"	Frame 77
"intro - 4"	Frame 127
"intro - 5"	Frame 177
"intro - 6"	Frame 197
"intro - 7"	Frame 217
"cc - 1"	Frame 246
"cc - 2"	Frame 278
"cc - 3"	Frame 295
"cc - 4"	Frame 316
"cc - 5"	Frame 336
"cc - 6"	Frame 356
"cc - 7"	Frame 376
"cc - 8"	Frame 396
"cc - 9"	Frame 401
"cc - 10"	Frame 406
"cc - 11"	Frame 415
"cc - 12"	Frame 425
"cc - 13"	Frame 435
"cc -14"	Frame 446
"pc - 1"	Frame 456
"pc - 2"	Frame 488
"pc - 3"	Frame 505
"pc - 4"	Frame 526
"pc - 5"	Frame 546
"pc - 6"	Frame 566
"pc - 7"	Frame 586
"pc - 8"	Frame 606
"pc - 9"	Frame 625
"pc - 10"	Frame 646
"pc - 11"	Frame 666
"pc - 12"	Frame 686
"pc - 13"	Frame 706
"pc - 14"	Frame 725
"pc -15"	Frame 746
"pc - 16"	Frame 766
"pc - 17"	Frame 786

Dynamic Text Variables

change	Symbol 135 EditableText	""
text	Symbol 136 EditableText	""
keyval	Symbol 142 EditableText	""
c1	Symbol 148 EditableText	""
c1	Symbol 149 EditableText	""
c3	Symbol 150 EditableText	""
c1	Symbol 151 EditableText	""
c3	Symbol 152 EditableText	""
c1	Symbol 153 EditableText	""
text	Symbol 154 EditableText	""
p	Symbol 220 EditableText	""
q	Symbol 222 EditableText	""
n	Symbol 231 EditableText	""
phi	Symbol 233 EditableText	""
e	Symbol 236 EditableText	""
gcd	Symbol 242 EditableText	""
p	Symbol 243 EditableText	""
q	Symbol 244 EditableText	""
n	Symbol 246 EditableText	""
phi	Symbol 247 EditableText	""
e	Symbol 250 EditableText	""
gcd	Symbol 252 EditableText	""
dd	Symbol 255 EditableText	""
M	Symbol 268 EditableText	""
cipher	Symbol 270 EditableText	""
decipher	Symbol 271 EditableText	""
pub	Symbol 275 EditableText	""
priv	Symbol 276 EditableText	""