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**DSA** stands for “Digital Signature Algorithm” - and is specifically designed to produce digital signatures, not perform encryption.

**DSA** stands for “Digital Signature Algorithm” - and is specifically designed to produce digital signatures, not perform encryption.

- The requirement for public/private keys in this system is for a slightly different purpose - whereas in RSA, a key is needed so anyone can encrypt, in DSA a key is needed so anyone can verify. In RSA, the private key allows decryption; in DSA, the private key allows signature creation.
- DSA
**Private**Key is used for generating**Signature**file - DSA
**public**Key is used for**Verifying**the Signature. - DSA is a variant on the ElGamal and Schnorr algorithms creates a 320 bit signature, but with 512-1024 bit security security again rests on difficulty of computing discrete logarithms has been quite widely accepted

**OpenSSL Commands for generating DSA Param, Singing File & verify File**

```
openssl dsaparam 2048 < /dev/random > dsa_param.pem
openssl gendsa dsa_param.pem -out dsa_priv.pem
openssl dsa -in dsa_priv.pem -pubout -out dsa_pub.pem
# DSA system now made up of: dsa_param.pem, dsa_pub.pem, dsa_priv.pem
echo "foobar" > foo.txt
openssl sha1 < foo.txt > foo.txt.sha1
openssl dgst -dss1 -sign dsa_priv.pem foo.txt.sha1 > foo.txt.sig
openssl dgst -dss1 -verify dsa_pub.pem -signature foo.txt.sig foo.txt.sha1
```

- firstly shared global public key values
**(p,q,g)**are chosen: - choose a large prime p = 2 power L where L= 512 to 1024 bits and is a multiple of 64
- choose q, a 160 bit prime factor of p-1
- choose g = h power (p-1)/q for any h1 then each user chooses a private key and computes their public key:
- choose x compute y = g power x(mod p)

DSA key generation is related to, but somewhat more complex than El Gamal. Mostly because of the use of the secondary 160-bit modulus q used to help speed up calculations and reduce the size of the resulting signature.

**To sign a message M**

- generate random signature key k, k compute

```
r = (g power k(mod p))(mod q)
s = k-1.SHA(M)+ x.r (mod q)
```

- send signature (r,s) with message

**to verify a signature, compute:**

- w = s-1(mod q)
- u1= (SHA(M).w)(mod q)
- u2= r.w(mod q)
- v = (g power u1.y power u2(mod p))(mod q)

if v=r then the signature is verified

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