Crypto currency new way to invest in the crypto and increase your income. A cryptocurrency, crypto-currency, or crypto is a digital currency designed to work as a medium of exchange through a computer network that is not reliant. Cryptocurrency is a digital currency using cryptography to secure transactions. Learn about buying cryptocurrency and cryptocurrency scams to look out for.

1. BASIC CRYPTO PRIMITIVES - II
2

2. • Cryptographically Secured Hash Function
– CollisionFree
– Information Hiding
– Puzzle Friendly
• Hash Pointers and Data Structures
– Hashchain
– Hash Tree – Merkle Tree

3. • A digital code, which can be included with an electronically transmitted
document to verify
– The content of the document isauthenticated
– The identity of thesender
– Prevent non-repudiation – sender will not be able to deny about the
origin of the document

4. • Only the signing authority can sign a document, but everyone can verify
the signature
• Signature is associated with the particular document
– Signature of one document cannot be transferred to another document

5. • Also known as asymmetrical cryptography or asymmetric key
cryptography
• Key: A parameter that determines the functional output of a cryptography
algorithm

6. • Properties of a cryptographic key (you need to prevent it from being
guessed)
– Generate the key truly randomly so that the attacker can not guess it
– The key should be of sufficient length – increasing the length makes
the key difficult to guess
– The key should contain sufficient entropy, all the bits in the key should
be equally random

7. • Two keys are used
– Private key: Only Alice has her privatekey
– Public key: “Public” to everyone – everyone knows Alice’s publickey
Encrypt the
message with
Bob’s public key
𝑩
𝑩
𝑴
𝑴
′ = 𝑬
𝑬
(
𝑴
𝑴
,𝑲
𝑲
𝒑
𝒑
𝒑
𝒑
𝒑
𝒑
)
Encrypt the
message with his
private key
𝑴
𝑴= 𝑬
𝑬
(
𝑴
𝑴
′
,𝑲
𝑲
𝑩
𝑩 )
𝒑
𝒑
𝒑
𝒑
𝒑
𝒑
M’

8. • Four phases
– Key generation
– Key distribution
– Encryption
– Decryption

9. • Sign the message using the Private key
– Only Alice can know her private key
• Verify the signature using the Public key
– Everyone has Alice’s public key and they can verify thesignature
Sign the message
with her private
key
𝑨
𝑨
𝑴
𝑴
′ = 𝑬
𝑬
(
𝑴
𝑴
,𝑲
𝑲
𝒑
𝒑
𝒑
𝒑
𝒑
𝒑
)
Verify the
signature using
Alice’s public key
𝒑
𝒑
𝒑
𝒑
𝒑
𝒑
𝑴
𝑴= 𝑬
𝑬
(
𝑴
𝑴
′
,𝑲
𝑲
𝑨
𝑨 )
M, M’

10. • Use the message digest to sign, instead of the original message
Sign the message
with her private key
𝑺
𝑺= 𝑬
𝑬
(
𝑯
𝑯
(
𝑴
𝑴
)
,𝑲
𝑲
𝑨
𝑨 )
𝒑
𝒑
𝒑
𝒑
𝒑
𝒑 𝑨
𝑨
Verify the signature
using Alice’s public key
𝑯
𝑯
(
𝑴
𝑴
)= 𝑬
𝑬
(
𝑺
𝑺
,𝑲
𝑲
𝒑
𝒑
𝒑
𝒑
𝒑
𝒑
)
M, S

11. • Used to validate the origin of a transaction
– Prevent non-repudiation
• Alice can not deny her own transactions
• No one else can claim Alice’s transaction as his/her own transaction
• Bitcoin uses Elliptic Curve Digital Signature Algorithm (ECDSA)
– Based on elliptic curvecryptography
– Supports good randomness in keygeneration

12. • Alice generates 10 coins
• Sign the transaction A:10 using Alice’s private key and put that in the
blockchain
A:10, Sig(A)

13.  A:10, Sig(A)
 • Alice transfers 5 coins to Bob
 • Sign the transaction A-B:5 using Alice’s private key and put that in
the blockchain
H(0) H(1)
A->B:5, Sig(A)

14. • Maintain the economy
– Generate new coins withtime
– Delete old coins withtime
• A central authority like bank can create and destroy coins based on
economic policies
• Crucial Question: How can we distribute coin management (creation and
destroy)

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