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VERIFYING MESSAGE
SIGNING
1. bob checks to see if 0<s1<q.
2. bob checks to see if 0<s2<q.
3. bob calculates a digest of m using the same hash algorithm used by alice.
4. bob calculates v= [( e1^h(m)s2^-1 e2^s1s2^-1) modp] modq.
5. if s1 is congurent to v, the message is accepted; otherwise, it is rejected.
1.alice chooses a random number r(1<=r<=q).
2. alice calculates the first signature s1=(e1^r modp)modq.
3. alice creates a digest of message h(m).
4. alice calculates the signature s2=(h(m)+ds1)r^-1 modq.
5. alice sends m,s1 and s2 to bob.
VERIFYING AND SIGNING
3. alices uses two multiplication groups <zp*,x> and <zq*,x>
4. Alice creates e1 to be the qth root of 1 modulo p(e1^p=1 mod p). to do so alice chooses a primitive element in zp,e0 and calculate e1=e0^(p-1)/q mod p.
5. alice chooces d as the private key and calcucaltes e2=e1^d.
6. alice's public key is(e1,e2,p,q);her private key is (d).
KEY GENERATION
before signing a message to any entity, alice needs to generate keys and annponce public ones to public.
1. alice chooses a prime p,between 512 and 1024 bits in length.
2. alice chooses a 160-bit prime q in such a way that it divides (p-1).
general idea behind dss scheme
What is the Standard?
DIGITAL SIGNATURE STANDARD
There are 3 algorithms suitable for digital signature generation under the dss standard.
they are: 1. Digital standard algo
2. rsa
3. elliptic curve digital
signature algo
- dss was adopted by national institute of standards and technology(nist) in 1994.
- dss uses a digital signature algorithm based on the elgamal schemes with some ideas from the schnorr scheme .
DIGITAL SIGNATURES
in this standard is a hash function to be used in the signature generation process.
it is used to obtain a condensed version of the data, which is called a message digest.
this messgae digest is then put into the digital signature algo to generate the digitally signed message.
- A digital signature is a mathematical scheme for demonstrating the authenticity of a digital message or documents.
- Digital signatures are commonly used for software distribution, financial transactions, and in other cases where it is important to detect forgery or tampering.
- when a message of any length < 2^64 bits is input, the sha produces a 160 bit output(message digest).
- signing the message digest rather than the message often improves the efficiency of the process because the message digest is usually much smaller in size than the message.