Final ss2-digital-signature-group5

1. Digital Signature
Group 5
Chu Huu Thanh 4C13
Phan The Minh 4C13
Tran Thi Thu 4C13
Nguyen Thi Thuy Ngan 4C13

2. Definition:
 A digital signature for an electronic message is equivalent to a
personal signature on a written document.
 It is created by using a form of cryptography.
 A unique electronic binding of the identity of the signer to the
origin of the message is provided by the digital signature on a
message.
 It make the proof of the message origin and a method to verify the
integrity of the message.

3. Model of Digital Signature
- Signer feeds data to the hash function and generates hash of data.
- Signature is appended to the data and then both are sent to the verifier.
- The verification algorithm gives some value as output.
- This hash value and output of verification algorithm are compared. Based on the comparison
result, verifier decides whether the digital signature is valid.
- digital signature is created by ‘private’ key of signer.

5. RSA is a public-key cryptosystem, it was invented in 1977 by Ronald L. Rivest .Public-
key cryptography, also known as asymmetric cryptography. It uses that key pair for
encryption and decryption.
•Public key:key to encrypt
•Private key:key to decrypt
•Plaintext: original format
•Ciphertext: data encrypted
•Encryption:is the process of converting the original data into data encryption
•Decryption: is the reverse process of coding , data transformation is encoded into the
original format .
II.RS
A

6. Processsing: The data will be encrypted with the recipient’s public key in order to
just only he/she can read it by hash function, which creates X.Then the recipient
use his/her private key which only he/she know to decrypt X to see the content of
sender’s message.

7. Advantages
 Security and convenience
 Key distribution much
easier
 Disadvantages
 Low speed
 Easy fake
 No repudiation.
ADVANTAGES AND DISADVANTAGES OF
RSA ALGORITHM

8. RSA variants:
The objectives behind these variants are either to improve RSA decryption
time, to accelerate RSA encryption time or to rebalance RSA encryption and
decryption time:
 Rebalanced RSA-CRT variant
 Rebalance RSA-CRT scheme A
 Rebalance RSA-CRT scheme B
 Mprime RSA variant
 Rprime RSA
 RAM-RSA
 RBM-RSA

9. The Elliptic Curve

10. The Elliptic Curve
An elliptic curve E is the graph of points of the plane curve defined by the
Weierstrass-equation: y^2 = x^3 + ax + b (mod p),(i, j)

11. A Geometric Approach
 Adding two points on
an ellipse
 Adding two points reflected
across the x-axis

12. A Geometric Approach
Doubling the point P
Doubling P when y-coordinate is
zero

13. The Elliptic Curve in a picture

14. Why Signing with ECC?
 Key pair generation:
Randomly select d [1, n-1].∈
Compute Q=dP, P, Q is a point on the curve
(Public key is Q, private key is d)
The naive algorithm to draw the d from Q is the
computation of a sequence of points P, 2P, 3P, 4P, until
Q=dP.
If we know d and P, finding Q is an easy work. But if we
know Q and GP, finding the PK is hard because it
requires us to solve the discrete logarithm problem.

15. III.
 The Elliptic Curve Digital Signature Algorithm (ECDSA) is the elliptic
curve analogue of the Digital Signature Algorithm (DSA). A digital
signature scheme should be existentially non-forgeable under chosen
message attack. The ECDSA have a smaller key size, which makes
faster computation time and reduction in processing power, storage
space and bandwidth. This makes the ECDSA ideal for constrained
devices such as pagers and smart cards.

16. ECDSA in Bitcoin

17.  Algorithm

18. In ECDSA, the signature generation and verification is similar to DSA,
but the key generation is based on ECC algorithm. A digital signature
scheme typically includes three algorithms:
 A key generation algorithm that selects a private key uniformly
at random from a set of possible private keys. The algorithm outputs
the private key and a corresponding public key.
 A signing algorithm that, given a message and a private key,
produces a signature.
 A signature verifying algorithm that, given a message, public
key and a signature, either accepts or rejects the message’s claim to
authenticity.

22. Implementation

23. Result - ECC

24. Result - RSA

25. DEMO
By Mr. Silver