> 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
```


---

# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.

## Querying This Documentation
If you need additional information that is not directly available in this page, you can query the documentation by asking a question.

Perform an HTTP GET request on the following URL with the `ask` and `goal` query parameters:

```
GET https://hub.bsvblockchain.org/wiki/cryptography-and-keys/cryptography/ecdsa-example.md?ask=<question>&goal=<user_goal>
```

`ask` is the immediate question: it should be specific, self-contained, and written in natural language.
`goal` is what the user is ultimately trying to achieve, the reason they need the answer. Sharing it helps GitBook give you a better, more relevant answer. A goal is most helpful when it describes the outcome the user wants rather than restating the question. For example, with `ask=how do I create an API token`, a goal like `automate deployments from our CI pipeline` lets GitBook tailor the answer to that use case.

The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.