Digital signature
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Digital signatures provide authentication of digital documents through encryption with a private key. They offer advantages over physical signatures like non-repudiation and integrity verification by checking that the document contents have not changed. Digital signatures are created by running a hash function over a message to generate a message digest, then encrypting the digest with a private key. They can be used for a variety of applications including e-voting, online money transfers, and filing government forms electronically.
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Digital signature
- 2. Digital Signature1 Paper v/s Digital Signature2 Hash Function3 4 Area of application5 Overview Implementation
- 3. Digital Signature digital signature is a technique for establishing the origin of a particular message in order to settle later disputes about what message was sent. Hash value of a message when encrypted with the private key of a person is his digital signature on that e-Document.
- 4. LOGO Paper v/s Digital Signature Parameter Paper Electronic Authenticity May be forged Can not be copied Integrity Signature independent of the document Signature depends on the contents of the document Non- repudiation a. Handwriting expert needed b. Error prone a. Any computer user b. Error free V/s
- 5. Hash Function Hash function is a mathematical function that generally has the following three properties :- Condenses arbitrary long inputs into a fixed length output. Is one-way. It is hard to find two inputs with the same output.
- 7. Implementation Sender uses SHA (Secure Hash Algorithm) hash function to calculate a message digest (M). M=SHA(massage) Now generate digital signature using CRT-RSA algorithm with Modified Approach by BlÄomer, Otto and Seifert . Key generation :- 1. Select two distinct prime numbers p and q 2. Compute n = pq. 3. Compute euler’s phi totient, φ = (p-1)(q-1) 4. Select public key e < n such that gcd(e, phi)=1 5. Compute d = e^(-1) mod phi.
- 8. LOGO Implementation 6. Calculate t1 and t2 to compute mP = M^d mod pt1 and mQ = m^d mod qt2 such that a) gcd(t1,t2)=1. b) gcd(d,φ(t1))=gcd(d,φ(t2))=1. c) t1 and t2 are squarefree. d) ti#3 mod 4 for i@{1,2}. e) t2 doesn’t divide X= pt1*((pt1)^(-1) mod qt2), where pt1=p*t1 and qt2=q*t2. 7. Compute dP= d mod φ(pt1). 8. Compute dQ= d mod φ(qt2). 9. Compute et1 = dP^(-1) mod φ(t1). 10. Compute et2 = dQ^(-1) mod φ(t2). 11. Compute mP= M^(dP) mod pt1. 12. Compute mQ= M^(dQ) mod qt2.
- 9. LOGO9 7. Compute qt2Inv = qt2^(-1) mod pt1. 8. Compute h = (qt2Inv * (mP-mQ)) mod pt1. 9. Compute s= mQ+ h* qt2. 10. Compute c1=(M-(s^et1)+1) mod t2. 11. Compute c2=(M-(s^et2)+1) mod t1. 12. Return: Sig = (s^(c1*c2)) mod N ,if c1=c2=1; Error ,otherwise Implementation
- 10. LOGO10 Implementation Verification:- 1. Compute M’=Sig^e mod N. 2. Compare M and M’ ,where M is the hash of the received message. 3. If(M # M’) then accept.
- 11. LOGO Area of Application Issuing forms and licenses Filing tax returns online Online Government orders/treasury orders Registration Online file movement system Public information records E-voting Railway reservations & ticketing E-education Online money orders