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jwasinger committed Jul 22, 2024
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15 changes: 8 additions & 7 deletions EIPS/eip-7747.md
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---
eip: 7747
description: Expanded-width modular arithmetic operations for the EVM

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3 | description: Expanded-width modular arithmetic operations for the EVM
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  = help: see https://ethereum.github.io/eipw/preamble-order/
title: EVM Modular Arithmetic Extensions
status: Draft
type: Standards track
type: Standards Track

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author: Jared Wasinger (@jwasinger), Alex Beregszaszi (@axic)
discussions-to: https://ethereum-magicians.org/t/eip-7747-evm-modular-arithmetic-extensions/20608
status: Draft
category: Core
created: 2024-07-20
requires: EOF

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Expand Down Expand Up @@ -158,7 +159,7 @@ def gas_setmod(element_size64bit: int) -> int:

When expanding EVM memory, expansion cost will now consider the size of all allocated field contexts in the current call frame.

### Rationale
## Rationale

By restricting that a modulus must be odd, and ensuring that inputs to arithmetic operations will be reduced by the modulus, modular arithmetic operations can be optimized:
* The reduction step for modular addition/subtraction can be implemented using only addition and subtraction.
Expand Down Expand Up @@ -196,11 +197,11 @@ In the graphs below, benchmark execution time is expressed in gas via scaling by
The implementations of the arithmetic are constant time. Modular addition/subtraction are linear with respect to modulus size. Modular multiplication scales quadratically with modulus size.

###### `ADDMODX`
![Alt text](https://github.com/jwasinger/evmmax-bench-plot/blob/5284df958171bc95ee9dcf47c995cffac7a136b0/charts/addmodx.png?raw=true)
![Alt text](../assets/addmodx.png)
###### `SUBMODX`
![Alt text](https://github.com/jwasinger/evmmax-bench-plot/blob/5284df958171bc95ee9dcf47c995cffac7a136b0/charts/submodx.png?raw=true)
![Alt text](../assets/submodx.png)
###### `MULMODX`
![Alt text](https://github.com/jwasinger/evmmax-bench-plot/blob/5284df958171bc95ee9dcf47c995cffac7a136b0/charts/mulmodx.png?raw=true)
![Alt text](../assets/mulmodx.png)

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204 | ![Alt text](../assets/mulmodx.png)
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---

##### `SETMODX`
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---

### Security Considerations
## Security Considerations

#### Memory Attacks via forcing cache-misses

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