> For the complete documentation index, see [llms.txt](https://hub.bsvblockchain.org/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://hub.bsvblockchain.org/wiki/cryptography-and-keys/cryptography/ecdsa-example.md).

# ECDSA Example

This page will walk you through a demonstration of the Elliptic Curve Digital Signature Algorithm using secp256k1.

1. ECDSA Signing Algorithm in Python

| Parameter | Value                                                                          | Descrption                                                                                                               |
| --------- | ------------------------------------------------------------------------------ | ------------------------------------------------------------------------------------------------------------------------ |
| p         | 115792089237316195423570985008687907853269984665640564039457584007908834671663 | The elliptic curve is defined over this value. P defines the size of the finite field.                                   |
| n         | 115792089237316195423570985008687907852837564279074904382605163141518161494337 | This value is the order of the group. It defines the number of possible elliptic curve points given the generator point. |
| Gx        | 55066263022277343669578718895168534326250603453777594175500187360389116729240  | This value is the x coordinate for the generator point.                                                                  |
| Gy        | 32670510020758816978083085130507043184471273380659243275938904335757337482424  | This value is the y coordinate for the generator point.                                                                  |

```bash
def ecdsa_sig(m, d):      # ecdsa_sig function takes a message and private key as an integer
k = random.randint(1, n - 1)     # Create the ephemeral key, k
m1 = hashlib.sha256()     # Create a hash object
m1.update(m)
hashed_message = m1.hexdigest()     # Hash the message
eph_point = Point_Multiplication(Gx, Gy, k, p)     # Calculate ephemeral point using k
eph_point_x = eph_point[0]
s_temp = (int(hashed_message, 16) + (d * eph_point_x))
s = (Mod_Inv(k, n) * (s_temp)) % n     # Create s value
r = eph_point_x     # Create r value
print("Signing Complete")
print("Eph Point x: " + str(eph_point[0]))
print("Eph point y: " + str(eph_point[1]))
print(" ")
print("R: " + str(r))
print("S: " + str(s))
"""
1. 0x30 indicates start of DER
2. One byte to encode length of data
3. 0x02 header byte indicating integer
4. One byte to encode length of r
5. The r value as big-endian integer
6. 0x02 header byte to indicate integer
7. One byte to include length of the following s value
8. The s value as big-endian integer
"""
# DER Format Code Begin
#------------------------------------------------------------
r_hex = "00"
r_hex = r_hex + str(hex(r)[2:])
s_hex = str(hex(s)[2:])
serial_1 = "30"
serial_2 = hex(int(((get_length(r_hex) / 2) + (get_length(s_hex) / 2) + 4)))[2:]
serial_3 = "02"
serial_4 = hex(int(get_length(hex(r)[2:]) / 2) + 1)[2:]
serial_5 = "00" + hex(r)[2:]
serial_6 = "02"
serial_7 = hex(int(get_length(hex(r)[2:]) / 2))[2:]
serial_8 = hex(s)[2:]
sig = serial_1 + str(serial_2) + serial_3 + str(serial_4)
sig = sig + str(serial_5) + serial_6 + str(serial_7) + str(serial_8)
sig = sig + str(binascii.hexlify(HASH_TYPE))[2:4]
sig = bytes.fromhex(sig)
return sig
```


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