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

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

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

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

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

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

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

RSA Digital Signature 6-Dec-19 Networks and Communication Department

RSA Digital Signature Example 6-Dec-19 Networks and Communication Department

RSA Digital Signature Problems 6-Dec-19 Networks and Communication Department

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

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

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

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

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