ModExp Gas Cost Increase

Abstract

This EIP is modifying the ModExp precompile pricing algorithm introduced in EIP-2565.

Motivation

Currently the ModExp precompile is underpriced in certain scenarios relative to its resource consumption. By adjusting the pricing formula, this EIP aims to address these discrepancies, making ModExp sufficiently efficient to enable potential increases in the block gas limit.

Specification

Upon activation of this EIP, the gas cost of calling the precompile at address 0x0000000000000000000000000000000000000005 will be calculated as follows:

def calculate_multiplication_complexity(base_length, modulus_length):
    max_length = max(base_length, modulus_length)
    words = math.ceil(max_length / 8)
    multiplication_complexity = 16
    if max_length > 32: multiplication_complexity = 2 * words**2
    return multiplication_complexity

def calculate_iteration_count(exponent_length, exponent):
    iteration_count = 0
    if exponent_length <= 32 and exponent == 0: iteration_count = 0
    elif exponent_length <= 32: iteration_count = exponent.bit_length() - 1
    elif exponent_length > 32: iteration_count = (16 * (exponent_length - 32)) + ((exponent & (2**256 - 1)).bit_length() - 1)
    return max(iteration_count, 1)

def calculate_gas_cost(base_length, modulus_length, exponent_length, exponent):
    multiplication_complexity = calculate_multiplication_complexity(base_length, modulus_length)
    iteration_count = calculate_iteration_count(exponent_length, exponent)
    return max(500, math.floor(multiplication_complexity * iteration_count))

The specific changes from the algorithm defined in EIP-2565:

1. Increased minimal and general price

The gas cost calculation is modified from:

    return max(200, math.floor(multiplication_complexity * iteration_count / 3))

to:

    return max(500, math.floor(multiplication_complexity * iteration_count))

This change increases the minimum gas cost from 200 to 500 and triples the general cost by removing the division by 3.

2. Increase cost for exponents larger than 32 bytes

The gas cost calculation is modified from:

    elif exponent_length > 32: iteration_count = (8 * (exponent_length - 32)) + ((exponent & (2**256 - 1)).bit_length() - 1)

to:

    elif exponent_length > 32: iteration_count = (16 * (exponent_length - 32)) + ((exponent & (2**256 - 1)).bit_length() - 1)

The multiplier for exponents larger than 32 bytes is increased from 8 to 16, doubling its impact.

3. Assume the minimal base / modulus length to be 32 and increase the cost when it is larger than 32 bytes

The gas cost calculation is modified from:

def calculate_multiplication_complexity(base_length, modulus_length):
    max_length = max(base_length, modulus_length)
    words = math.ceil(max_length / 8)
    return words**2

to:

def calculate_multiplication_complexity(base_length, modulus_length):
    max_length = max(base_length, modulus_length)
    words = math.ceil(max_length / 8)
    multiplication_complexity = 16
    if max_length > 32: multiplication_complexity = 2 * words**2
    return multiplication_complexity

This change introduces a minimal multiplication complexity of 16 and doubles the complexity if the base or modulus length exceeds 32 bytes.

Rationale

Benchmarking the ModExp precompile revealed several scenarios where its gas cost was significantly underestimated. Pricing adjustments are designed to rectify underpriced edge cases by modifying the existing ModExp pricing formula parameters. Specifically, the minimum cost for ModExp will rise from 200 to 500 (a 150% increase), the general cost will triple (a 200% increase), a minimum base/modulus length of 32 bytes will be assumed and the cost will scale more aggressively when the base, modulus, or exponent exceed 32 bytes. These modifications aim to ensure that the ModExp precompile's performance, even in its most resource-intensive edge cases across all execution layer clients, no longer impedes potential increases to the block gas limit.

Backwards Compatibility

This EIP introduces a backwards-incompatible change. However, similar gas repricings have occurred multiple times in the Ethereum ecosystem, and their effects are well understood.

Test Cases

The most common usages (approximately 99.69% of historical Modexp calls as of January 4th, 2025) will experience either a 150% increase (from 200 to 500 gas) or a 200% increase (tripling from approximately 1360 gas). No changes are made to the underlying interface or arithmetic algorithms, allowing existing test vectors to be reused. The table below presents the updated gas costs for these test vectors:

Test Case	EIP-2565 Pricing	EIP-7883 Pricing	Increase
modexp_nagydani_1_square	200	500	150%
modexp_nagydani_1_qube	200	500	150%
modexp_nagydani_1_pow0x10001	341	2048	501%
modexp_nagydani_2_square	200	512	156%
modexp_nagydani_2_qube	200	512	156%
modexp_nagydani_2_pow0x10001	1365	8192	501%
modexp_nagydani_3_square	341	2048	501%
modexp_nagydani_3_qube	341	2048	501%
modexp_nagydani_3_pow0x10001	5461	32768	500%
modexp_nagydani_4_square	1365	8192	501%
modexp_nagydani_4_qube	1365	8192	501%
modexp_nagydani_4_pow0x10001	21845	131072	500%
modexp_nagydani_5_square	5461	32768	500%
modexp_nagydani_5_qube	5461	32768	500%
modexp_nagydani_5_pow0x10001	87381	525288	500%
modexp_marius_1_even	2057	45296	2102%
modexp_guido_1_even	2298	51136	2125%
modexp_guido_2_even	2300	51152	2124%
modexp_guido_3_even	5400	32400	500%
modexp_guido_4_even	1026	94448	9105%
modexp_marcin_1_base_heavy	200	1152	476%
modexp_marcin_1_exp_heavy	215	16624	7632%
modexp_marcin_1_balanced	200	1200	500%
modexp_marcin_2_base_heavy	867	5202	500%
modexp_marcin_2_exp_heavy	852	16368	1821%
modexp_marcin_2_balanced	996	5978	500%
modexp_marcin_3_base_heavy	677	2032	200%
modexp_marcin_3_exp_heavy	765	4080	433%
modexp_marcin_3_balanced	1360	4080	200%

Security Considerations

This EIP does not introduce any new functionality or make existing operations cheaper, therefore there are no direct security concerns related to new attack vectors or reduced costs. The primary security consideration for this EIP is the potential for ModExp scenarios to be overpriced, though this is deemed a lesser risk compared to the current underpricing issues.

Copyright

Copyright and related rights waived via CC0.