Where we explain the basics of cryptography that is used to create crypto-currency and other new age financial instruments. This one part of a three part slide deck. For the full deck and the context please visit http://bit.ly/pm-bbc

1. Bitcoin,
Blockchain &
CryptoContracts
Part 1
cryptographic fundamentals
Prithwis Mukerjee, PhD, Praxis Business School, Calcutta, India

2. What is Cryptography ?
Cryptography is a mathematical technique by which information in the form
of text files or any digital string of numbers and characters are changed into
another string so that the contents are not readily understandable by others.
It was originally used for keeping secrets but now it has many uses.

3. Cryptographic Functions
A cryptographic
function is an
operator that
converts an input
string of numbers
and characters into
an output string as
per rules defined by
the function and a
key value
k=2, x+k
k=2, xk
k=2, Crypt()
anagram(2)
9 11
3 9
prithwis rtkvjyku
prithwis wish trip

4. One Way Functions
In a one-way
cryptographic
function it is quite
difficult to reverse
the process. Difficult
to derive the input by
looking at the output
125 8sum of digits
40706 8sum of digits
prithwis mukerjee BODPM4264EPAN(:-)
prithwis mukerjee SHA-256
1b18b866382f05d8698ebcb8eae7c881
1b3a988e7112503c1ecc9aacd9cc63e8
collision

5. SHA-256 Hash Function
Generates 256 bit
output irrespective of
the size (or length) of
input.
Collision resistant -
two inputs will “never”
generate the same
output.
Hash(“prithwis”)
1b18b866382f05d8698ebcb8eae7c8811b3a988e7112503c1ecc9aacd9cc63e8
Hash(“prithwish”)
4486d9ef726a5a4a559f24cce58480968a4527004cfb7ceb8cf6fccbef2886bc
Hash(“Our price bid is Rs 2,00,000”)
62b72cda490d54e56ac0978d263906ef892b6449c1175ebf0af839c7f99e772f
Hash(pm.jpg) <- a full image file
af9493c777bcb88e57fb3e08cf05807d117f945fdffc932f3deddcc82835b385

6. Tamper-proof messages
If we send the
message along
with its hash, then
recipient can
detect if the
message has been
altered later on
Communication Transmitted
“Pay Rs 2,00,000 to Prithwis Mukerjee”
Hash = 4949504ab01a4a8d4ebec5f38bd13a7ea2819a60d1004690a09b6aa518a02922
Communication Received
“Pay Rs 20,00,000 to Prithwis Mukerjee”
Hash = 4949504ab01a4a8d4ebec5f38bd13a7ea2819a60d1004690a09b6aa518a02922
Recipient Verifies Hash of message
“Pay Rs 20,00,000 to Prithwis Mukerjee”
Hash = 5331cf192a895d1b7cb8d0d5b1e78090aa8f33e1a781103ed4d9eab8282704a7
You can also send the hash of [message+hash of message] to make sure
that the hash value has not been tampered with either!
Mismatch
detected

7. Encryption
Hashing is irreversible.
Encryption is reversible
It is a two step process of
converting clear-text
(human understandable)
into cypher-text by
sender and reconverting
it back to clear-text by
receiver using
passphrases
Original Message in Clear Text secretKey
ENCRYPT function
Unreadable Message in Cypher Text
Unreadable Message in Cypher Text
DECRYPT function
Retrieved Message in Clear Text
secretKey

8. Encryption for Privacy during Transmission
Here we see that Arup is
sending a secret message
to Bina and both of them
do not want anybody else
to read the message
Arup will meet Bina at 2PM at Victoria p@ssw0rd
ENCRYPT
xyza erty 78s& a3 0w@ uTc99srt
xyza erty 78s& a3 0w@ uTc99srt
DECRYPT
Arup will meet Bina at 2PM at Victoria
p@ssw0rd
secure, private
transmission
insecure
transmission
can be
intercepted
and used to
break
privacy

9. Asymmetric Encryption & Decryption
Two Keys
Encryption with
one key,
decryption with
other.
Called Public key,
Private Key
Clear Text MessageK2 K1
ENCRYPT
Cypher Text 1 Cypher Text 2K2
DECRYP
T
K1 K1
ENCRYPT
K2
DECRYP
T
DECRYP
T
DECRYP
T
Clear Text Message

10. Asymmetric Encryption : Privacy
Arup, Bina have a
pair of keys, one
Private Key and
one Public Key
KPrA, KPrB are
“private” keys
and KPuA, KPuB
are “public” keys
of Arup and Bina
Arup will meet Bina at 2PM at VictoriaKPuAKPrA
Arup will meet Bina at 2PM at Victoria
KPuB
KPuB
ENCRYPT
xyza erty 78s& a3 0w@ uTc99srt
xyza erty 78s& a3 0w@ uTc99srt KPrB
DECRYPT
secure, private
transmission
insecure
transmission
can be
intercepted
but cannot
be used to
break
privacy

11. Asymmetric Encryption : Authentication
Arup appends his
encrypted public key
as signature to
message
Bina confirms that
signature was
created by person
whose public key is
same as that of Arup
Hence authentic
Arup loves BinaKPrAKPuA
ENCRYPT
DECRYPT
public
transmission
sigA Arup loves Bina
sigA Arup loves BinaKPuA
Arup loves BinaKPuAKPuA

12. Contracts without Trust!
Bina transfers and asset, House25, to Chandru
Bina claims that Arup transferred this asset to Bina and so she has
clear title to transfer asset to Chandru
Chandru does not trust Bina
Bina produces transfer contract that Arup gave to Bina
How can we use cryptofunctions to ensure that Bina does have the
asset that she is transferring to Chandru

13. Arup transfers asset to Bina
Arup creates contract C1
transferring H25 to B
Arup adds his signature
to C1
sigA
Arup completes the contract
by adding a hash HC1
KPuA KPrA
KPuA H25 KPuB
KPuA H25 KPuB
sigA KPuA H25 KPuBHC1
Since all
individuals are
anonymous, the
contract will
represent them
by their public
keys

14. Bina tries to transfer asset to Chandru
Bina creates similar
contract C2
sigB KPuB H25 KPuCHC2
Chandru does not trust
Bina. Does she really
own H25?
sigB KPuB H25 KPuCHC2
Bina prefixes C1 to C2
but still not trusted! sigB KPuB H25 KPuCHC2
sigA KPuA H25 KPuBHC1
Since all
individuals are
anonymous, the
contract will
represent them
by their public
keys

15. Chandru verifies cryptographically
Since all
individuals are
anonymous, the
contract will
represent them
by their public
keys
Has Bina tampered with C1?
Perhaps Arup has sold House
22? Did he sell to Bina? Check
Hash
sigB KPuB H25 KPuCHC2
sigA KPuA H25 KPuBHC1
sigB KPuB H25 KPuCHC2
sigA KPuA H25 KPuBHC1
Hash matches! We know
house was sold to Bina. Is
Bina the Bina referred to in
C1? Check Bina signature
sigB KPuB H25 KPuCHC2
sigB KPuB
KPuB
sigA KPuA H25 KPuBKPuA
Chandru accepts
1. Bina got H25 from Arup
2. Bina can sell to Chandru
sigB KPuB H25 KPuCHC2
YES!
matches
bitcoin txn
validation is
similar, not
same

16. When Chandru transfer to Dipa
Since all
individuals are
anonymous, the
contract will
represent them
by their public
keys
Chandru will create unverified
contract C3 that transfers H25
to Dipak
sigB KPuB H25 KPuCHC2
sigC KPuC H25 KPuDHC3
Process
Continues

17. What about?
What if Bina had already sold the house
to Esha? -- Double Spend?
Who will do all this verification? Why will
they do all this?
The first contract? How do we know
that Arup owns the asset? How far in
the past do we go? -- the “Genesis” ?
All these issues
are addressed by
Bitcoin. See next
presentation
Prithwis Mukerjee, PhD, Praxis Business School, Calcutta, India