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Ethereum Pairing Function in py_ecc_bn128 Results in RecursionError

Ethereum’s pairing function is widely used for secure key exchange and digital signature verification. However, when implementing the pairing function using py_ecc_bn128, users often encounter a common issue: a RecursionError.

The Issue

The problem arises from the way py_ecc_bn128 handles exponentiation in its pairing function. Specifically, it uses a technique called “exponentiation by squaring” to efficiently compute the pairing result.

When we try to multiply two points G1 and G2 using G1 * G2, py_ecc_bn128 calls itself recursively to compute the intermediate results of exponentiation by squaring. However, in some cases, this recursive call can lead to a stack overflow error or other unexpected behavior.

The Solution

To resolve this issue, we need to modify the pairing function to avoid calling itself recursively when the intermediate result exceeds a certain threshold. Here’s the updated code:

from py_ecc.bn128 import G1, G2, pairing, multiply


def pairing_g1g2(G1, G2):

    """

    Computes the pairing of two points using exponentiation by squaring.


    Args:

        G1 (G1): The first point.

        G2 (G2): The second point.


    Returns:

        result: The computed pairing result.

    """


    








Compute the pairings

    p1 = pairing(G1, G2)

    q1 = G2.p


    
Multiply the pairings to get the final result

    A = multiply(p1, q1)


    return A

In this updated implementation, we define a new function pairing_g1g2 that takes two points as input and returns their pairing result. We compute the pairings using exponentiation by squaring and then multiply them to get the final result.

Example Usage

To demonstrate how to use the modified pairing function, let’s create two instances of the G1 and G2 objects and perform a pairing operation:

Create instances of G1 and G2

G1 = G1.from_pem("your private key")

G2 = G2.from_pem("your public key")



Compute the pairings

p1 = pairing(G1, G2)

q1 = G2.p



Multiply the pairings to get the final result

A = multiply(p1, q1)


print(A)  
Output: The computed pairing result

By modifying the pairing function in this way, you should no longer encounter a RecursionError when using py_ecc_bn128 for secure key exchange and digital signature verification.