1. LAB 3: Digital Signature
NET 536 Network Security
Networks and Communication Department
LAB 3: Digital Signature

2. Digital Signatures: RSA ElGamal 6-Dec-19
Networks and Communication Department

3. Networks and Communication Department
Introduction
Digital signature is a data string which associates a message (in digital form) with some originating entity.
Digital signature verification is a method for verifying that a digital signature is authentic (was indeed created by the specific entity).
The main difference from a handwritten signature is that digital signature of a message is intimately connected with the message, and for different messages is different, whereas the handwritten signature is adjoined to the message and always looks the same.
6-Dec-19
Networks and Communication Department

4. Key Points
A digital signature is an authentication mechanism that enables the creator of a message to attach a code that act as a signature.
Typically, the signature is formed by taking the hash of the message and encrypting the message with the creator’s private key.
The signature guarantees the source and integrity of message.
6-Dec-19
Networks and Communication Department

5. Digital Signature Overview
Based on asymmetric crypto - Example: RSA
Properties of a Digital Signature:
Verification of the validity of a digital signature needs only the public key
Only the owner of the corresponding private key can produce a valid signature
There is also MAC (Message Authentication Code) – signing using a shared key (based on symmetric cryptography)
6-Dec-19
Networks and Communication Department

6. The Model of Digital Signature
6-Dec-19
Networks and Communication Department

7. RSA Digital Signature Construction:
Rivest, Shamir, and Adleman proposed in 1978.
Construction:
1. Choose two large prime numbers P and Q, then compute
N=P×Q.
2. Select an integer e such that gcd(e, (N))=1.
3. Compute d such that e×d mod (N)=1.
4. Public key = (N, e).
5. Private key = (N, d).
6-Dec-19
Networks and Communication Department

8. RSA Digital Signature
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Networks and Communication Department

9. RSA Digital Signature Example
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10. RSA Digital Signature Problems
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Networks and Communication Department

11. ElGamal Digital Signature
ElGamal proposed in 1985
ElGamal Public Key Cryptosystem
Security Basis:
Discrete Logarithm Problem
6-Dec-19
Networks and Communication Department

12. ElGamal Digital Signature
6-Dec-19
Networks and Communication Department

13. ElGamal Digital Signature
6-Dec-19
Networks and Communication Department

14. ElGamal Digital Signature
g is primitive root mod p if:
g ^ (p-1) mod p =1
Where 𝑔 𝑖 mod p ≠ 1 , 0 < i < p-1
Below is the proof where p=7, g=3
6-Dec-19
Networks and Communication Department

15. ElGamal Digital Signature Example
choose: p = 11, g = 2, d = 8
compute: y= 2^8 mod 11 = 3
Signing of m = 5,
choose d’ = 9 - O.K. because gcd(9, 10) = 1
compute s = 2^9 mod 11 = 6
solve equation: 5 = 8 · 6 + 9t (mod 10)
that is 7 = 9t (mod 10)  t=3
signature: (5, 6, 3)
6-Dec-19
Networks and Communication Department