Digital signature

Presented byMohsin (09-CSS-46)

ShriPrakash(08-CSS-66)

DIGITAL SIGNATURE

Digital Signature1

Paper v/s Digital Signature2

Hash Function3

4

Area of application5

Overview

Implementation

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.

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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

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.

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Proposed Scheme

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.

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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.

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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-(sêt1)+1) mod t2.

11. Compute c2=(M-(sêt2)+1) mod t1.

12. Return:

Sig = (s^(c1*c2)) mod N ,if c1=c2=1;

Error ,otherwise

Implementation

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Implementation

Verification:-

1. Compute M’=Sigê mod N.

2. Compare M and M’ ,where M is the hash of the received message.

3. If(M # M’) then accept.

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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

Engineering

Digital signature