The Ethereum matching function in py_ecc_bn128 results in a RecursionError

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

Problem

The problem stems from the way py_ecc_bn128 handles exponentiation in its matching function. In particular, it uses a technique called “powering by squaring” to efficiently calculate the matching results.

When we try to multiply the two points G1 and G2 using “G1 * G2”, “py_ecc_bn128” is called recursively to calculate the intermediate results of squaring powers. However, in some cases this recursive call can lead to a stack overflow error or other unexpected behavior.

Decision

To solve this problem, we need to modify the matching function to avoid recursively calling itself when the intermediate score exceeds a certain threshold. Here is the updated code:

from py_ecc.bn128 import G1, G2, pairing, multiplication
def pairing_g1g2(G1, G2):
"""
Computes the pairing of two points using exponentiation by squaring.
Arguments:
G1 (G1): First point.
G2 (G2): Second point.
Returns:
result: Computed pairing result.
"""









Compute the pairs
p1 = pairing(G1, G2)
q1 = G2.str

Multiply the pairs to get the final result
A = multiplication(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 pairs using exponentiation by squaring, and then multiply them to get the final result.

Example of use

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

Create instances of G1 and G2

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

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



Calculate the pairs

p1 = pairing (G1, G2)

q1 = G2.p



Multiply the pairs to get the final result

A = multiplication (p1, q1)


print(A) 
Output: Calculated matching result

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

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