EIP-6690: EVM Modular Arithmetic Extensions (EVMMAX)
Create modular addition, subtraction, and multiplication opcodes.
Abstract
This EIP proposes the addition of new optimized modular addition, subtraction and multiplication opcodes to the EVM. These support odd moduli up to 4096 bits in size.
Motivation
Benefits of the changes proposed in this EIP:
- enables elliptic curve arithmetic operations on various curves including BLS12-381 to be implemented as EVM contracts
- For operations on values up to 256bits in size, reduces gas cost per operation by 90-95% compared to the current
MULMODandADDMODopcodes. - for all cases where modexp precompile is useful, it could now be implemented as an EVM contract.
- enables substantial cost reductions for algebraic hash functions (e.g. MiMC/Poseidon), zkp verification in the EVM.
Specification
Overview
During contract execution, a contract calls a setup instruction SETUPX, sourcing a modulus from a specified memory offset/size and computing several parameters used to speed up modular multiplication (referred to as "Montgomery" parameters). A zeroed memory space (whose size is a stack parameter passed to SETUPX) is allocated separate from EVM memory.
The modulus, computed parameters and memory space are associated with the current call frame state and referred to as the active modulus state. If SETUPX is called again to switch to a different modulus, the memory space and Montgomery parameters of the previous active modulus state remain allocated (the memory spaces of active/previously-active modulus state are separate).
New store and load opcodes STOREX/LOADX are used to copy multiples values to/from EVM memory and the memory space of the active modulus state.
Arithmetic is performed with ADDMODX/SUBMODX/MULMODX opcodes which take and return no stack items, require a 3-byte immediate value appended to the opcode.
The immediate is interpreted as 3 1-byte values z, x, y which are indexes to the array of EVMMAX values that comprise the memory space of the active modulus state.
An arithmetic operation is performed on inputs at index x/y placing the result in index z.
Conventions
x === y % m:x % m == y % mpow(x, -1, m): The modular multiplicative inverse ofxwith respect to modulusm.- Opcode definition syntax is formatted as
mneumonic {immediate - type} {immediate2 - type} ...: stack_arg_1, stack_arg_2, ...where immediates are listed in the order that they proceed the opcode and stack arguments are ordered starting at the top of the stack. - In the provided pseudocode, it is assumed that opcode gas charging logic is executed prior to execution logic.
- Any exception thrown should immediately end the current execution frame and return to the caller.
Constants
| Name | Value | Description |
|---|---|---|
STOREX_BASE_GAS | 3 | base gas cost for STOREX opcode |
LOADX_BASE_GAS | 3 | base gas cost for LOADX opcode |
SETUPX_BASE_GAS | 3 | base gas cost for SETUPX opcode |
EVMMAX_MAX_MEM | 65,536 bytes | maximum amount of EVMMAX memory that can be used in a call frame |
MAX_MOD_SIZE | 4096 bits | tentative modulus size limit (can probably be removed because EVMMAX_MAX_MEM_SIZE effectively caps the modulus size) |
MULMODX_SUBQUADRATIC_START | 50 | modulus size in multiples of 8 bytes where we switch to subquadratic mulmont cost model |
SYSTEM_WORD_SIZE_BITS | varies depending on the system | word size in bits of a client's CPU |
Context Variables
| Name | Type | Meaning |
|---|---|---|
evmmax_state | EVMMAXState | a variable representing ephemeral state which exists for the duration of the current call and in the scope of the current call frame |
evm_memory | bytes | EVM memory for the current call context |
expand_evm_memory | func(size_words: int) | expands EVM memory by size_words * 32 bytes |
cost_evm_memory_expansion | func(new_size_evm_words: int) -> int | EVM memory expansion cost function, modified according to this EIP |
evm_stack | object | Allows access to the stack via pop() and peek(n) which return int stack elements |
contract_code | bytes | code of the currently-executing contract |
pc | int | EVM program counter |
Helpers
New Opcodes
| Mneumonic | Opcode | Immediate size (bytes) | Stack in | Stack out |
|---|---|---|---|---|
| SETUPX | 0x21 | 0 | 4 | 0 |
| ADDMODX | 0x22 | 3 | 0 | 0 |
| SUBMODX | 0x23 | 3 | 0 | 0 |
| MULMODX | 0x24 | 3 | 0 | 0 |
| LOADX | 0x25 | 0 | 3 | 0 |
| STOREX | 0x26 | 0 | 3 | 0 |
SETUPX
SETUPX : mod_id, mod_offset, mod_size, vals_used
Gas Charging
Execution
LOADX
LOADX: dst_offset, val_idx, num_vals
Description
Load EVMMAX values in the current active modulus state to EVM memory.
Gas Charging
Execution
STOREX
STOREX: dst_val, offset, num_vals
Description
Store values from EVM memory into EVMMAX memory space of the current active modulus state, validating that they are reduced by the modulus.
Gas Charging
Execution
ADDMODX
ADDMODX {z_offset - byte}, {x_offset - byte}, {y_offset - byte}:
Description
Compute the modular addition of two EVMMAX values, storing the result in an output.
Gas Charging
Execution
SUBMODX
SUBMODX {z_offset - byte}, {x_offset - byte}, {y_offset - byte}:
Description
Compute the modular subtraction of two EVMMAX values in the current active modulus state, storing the result in an output.
Gas Charging
Same as ADDMODX.
Execution
MULMODX
MULMODX {z_offset - byte}, {x_offset - byte}, {y_offset - byte}:
Description
Compute the Montgomery modular multiplication of two EVMMAX values in the current active modulus state, storing the result in an output.
Gas Charging
Execution
Changes to Contract Execution
EVM Memory Expansion Cost Function
Any EVM operation which expands memory x bytes will charge to expand memory to cur_evm_mem_size + x + evmmax_mem_size bytes where evmmax_mem_size is the size of all allocated EVMMAX values in the current call context (the sum of the values used by each mod_id that has been previously/currently set with SETUPX).
Jumpdest Analysis
Jumpdest analysis is modified to disallow jumps into immediate data for ADDMDOX/SUBMODX/MULMODX.
Rationale
Montgomery Modular Multiplication
EVMMAX values are stored internally in Montgomery form. Expressing values in Montgomery form enables the use of Montgomery reduction in modular multiplication which gives a substantial performance gain versus naive modular multiplication.
Modular addition and subtraction on Montgomery form values is computed the same as normal.
Memory Alignment for EVMMAX Values
LOADX/STOREX move 64bit-aligned big-endian values to/from the memory space of the active modulus state. SETUPX memory expansion pricing is tuned to assume that values will be stored in a as 64bit-aligned values in their EVMMAX memory space.
This choice is made to keep EVMMAX memory aligned to ensure performance.
Gas Costs
Gas models assume a rate of 1 gas per 25ns of execution time.
ADDMODX/SUBMODX/MULMODX
ADDMODX and SUBMODX can each be implemented using a single extended-precision addition, and single extended precision subtraction. This justifies a linear cost model.
MULMODX runtime scales quadratically with input size. After a certain threshold, the quadratic complexity of mulmont_quadratic dominates and it becomes more performant to use mulmont_subquadratic. Thus, there is a segmented cost model to reflect different asymptotic behavior between quadratic/subquadratic mulmont.
ADDMODX/SUBMODX/MULMODX pricing includes the cost of arithmetic and latency of accessing input values from CPU cache.
The price model assumes that the implementation will be generic for most bitwidths with the exception of 321-384bits which is priced aggressively.
LOADX/STOREX
These perform conversion to/from Montgomery and canonical forms for each value copied (a single mulmont per value converted). The overhead of memory loading/copying is covered by cost_mulmontx.
SETUPX
Backwards Compatibility
Jumpdest analysis changes in this EIP could potentially break existing contracts where a jump destination occurs in the 3 bytes proceeding a 0x22/0x23/0x24. This is unlikely to affect many existing contracts. Further analysis of deployed contract bytecode can determine with certainty, which (if any) contracts could be broken.
Security Considerations
Copyright
Copyright and related rights waived via CC0.