This page is a placeholder. All examples on this page are currently AI-generated and are not correct. This documentation will be completed in the future with accurate, tested examples.
Overview
Opcode: 0x18
Introduced: Frontier (EVM genesis)
XOR performs bitwise exclusive OR on two 256-bit unsigned integers. Each bit in the result is 1 if the corresponding bits in the operands differ (one is 1, the other is 0). This operation is fundamental for toggling bits, comparing equality, and cryptographic operations.
Primary uses: toggling flags, comparing values for differences, symmetric encryption, checksum calculations.
Specification
Stack Input:
Stack Output:
Gas Cost: 3 (GasFastestStep)
Truth Table (per bit):
a | b | a ^ b
--|---|------
0 | 0 | 0
0 | 1 | 1
1 | 0 | 1
1 | 1 | 0
Behavior
XOR pops two values from the stack, performs bitwise XOR on each corresponding bit pair, and pushes the result. The operation is:
- Commutative: a ^ b = b ^ a
- Associative: (a ^ b) ^ c = a ^ (b ^ c)
- Identity element: a ^ 0 = a
- Self-inverse: a ^ a = 0
- Involution: (a ^ b) ^ b = a
Examples
Toggle Bit
import { xor } from '@tevm/voltaire/evm/bitwise';
import { createFrame } from '@tevm/voltaire/evm/Frame';
// Toggle bit 3
const value = 0b0000n;
const toggle = 0b1000n; // Bit 3
const frame = createFrame({ stack: [value, toggle] });
const err = xor(frame);
console.log(frame.stack[0].toString(2)); // '1000'
// Toggle again to clear
const frame2 = createFrame({ stack: [0b1000n, toggle] });
xor(frame2);
console.log(frame2.stack[0].toString(2)); // '0'
Compare for Differences
// Find differing bits between two values
const a = 0b11001100n;
const b = 0b10101010n;
const frame = createFrame({ stack: [a, b] });
xor(frame);
console.log(frame.stack[0].toString(2)); // '1100110' (bits that differ)
// Result is 0 if and only if a == b
Simple Encryption (XOR Cipher)
// Encrypt/decrypt with XOR (symmetric)
const plaintext = 0x48656C6C6F n; // "Hello"
const key = 0xDEADBEEFn;
const frame = createFrame({ stack: [plaintext, key] });
xor(frame);
const ciphertext = frame.stack[0];
// Decrypt: XOR again with same key
const frame2 = createFrame({ stack: [ciphertext, key] });
xor(frame2);
console.log(frame2.stack[0] === plaintext); // true (recovered)
Swap Variables (XOR Swap)
// Swap a and b without temporary variable
let a = 0x123n;
let b = 0x456n;
a = a ^ b; // a = 0x123 ^ 0x456
b = a ^ b; // b = (0x123 ^ 0x456) ^ 0x456 = 0x123
a = a ^ b; // a = (0x123 ^ 0x456) ^ 0x123 = 0x456
console.log({ a, b }); // { a: 0x456n, b: 0x123n }
XOR as NOT (with all ones)
// XOR with all ones is equivalent to NOT
const MAX = (1n << 256n) - 1n;
const value = 0x123456n;
const frame = createFrame({ stack: [value, MAX] });
xor(frame);
console.log(frame.stack[0] === ~value); // true (bitwise NOT)
Gas Cost
Cost: 3 gas (GasFastestStep)
XOR shares the lowest gas tier with:
- AND (0x16), OR (0x17), NOT (0x19)
- BYTE (0x1a)
- SHL (0x1b), SHR (0x1c), SAR (0x1d)
- ADD (0x01), SUB (0x03)
- Comparison operations
Edge Cases
Identity Element
// XOR with zero
const value = 0x123456n;
const frame = createFrame({ stack: [value, 0n] });
xor(frame);
console.log(frame.stack[0] === value); // true (identity)
Self-Inverse
// a ^ a = 0
const value = 0x123456n;
const frame = createFrame({ stack: [value, value] });
xor(frame);
console.log(frame.stack[0]); // 0n
Involution Property
// (a ^ b) ^ b = a
const a = 0x123456n;
const b = 0xABCDEFn;
const frame1 = createFrame({ stack: [a, b] });
xor(frame1);
const intermediate = frame1.stack[0];
const frame2 = createFrame({ stack: [intermediate, b] });
xor(frame2);
console.log(frame2.stack[0] === a); // true (recovered original)
XOR as NOT
// XOR with all ones = NOT
const MAX = (1n << 256n) - 1n;
const value = 0xAAAAAAAAn;
const frame = createFrame({ stack: [value, MAX] });
xor(frame);
// NOT flips all bits
console.log(frame.stack[0] === ~value & MAX); // true
Complementary Patterns
// Complementary patterns XOR to all ones
const pattern1 = 0xAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAn;
const pattern2 = 0x5555555555555555555555555555555555555555555555555555555555555555n;
const frame = createFrame({ stack: [pattern1, pattern2] });
xor(frame);
const MAX = (1n << 256n) - 1n;
console.log(frame.stack[0] === MAX); // true
Stack Underflow
// Insufficient stack items
const frame = createFrame({ stack: [0x123n] });
const err = xor(frame);
console.log(err); // { type: "StackUnderflow" }
Out of Gas
// Insufficient gas
const frame = createFrame({ stack: [0x123n, 0x456n], gasRemaining: 2n });
const err = xor(frame);
console.log(err); // { type: "OutOfGas" }
console.log(frame.gasRemaining); // 0n
Common Usage
Toggle Feature Flags
// Toggle specific flags on/off
uint256 constant FLAG_A = 1 << 0;
uint256 constant FLAG_B = 1 << 1;
function toggleFlags(uint256 current, uint256 mask) pure returns (uint256) {
return current ^ mask; // Flip bits in mask
}
// Usage
uint256 flags = 0b0101;
flags = toggleFlags(flags, FLAG_A); // 0b0100 (toggle bit 0)
flags = toggleFlags(flags, FLAG_A); // 0b0101 (toggle back)
Fast Equality Check
// Check if two values are equal
function areEqual(uint256 a, uint256 b) pure returns (bool) {
return (a ^ b) == 0; // 0 if equal, non-zero if different
}
Checksum Calculation
// Simple XOR checksum
function checksum(bytes memory data) pure returns (uint8) {
uint8 result = 0;
for (uint i = 0; i < data.length; i++) {
result ^= uint8(data[i]);
}
return result;
}
Symmetric Cipher (One-Time Pad)
// XOR encryption/decryption
function xorCipher(bytes32 data, bytes32 key) pure returns (bytes32) {
return data ^ key; // Same operation for encrypt and decrypt
}
// Usage
bytes32 plaintext = "secret message";
bytes32 key = keccak256("password");
bytes32 encrypted = xorCipher(plaintext, key);
bytes32 decrypted = xorCipher(encrypted, key); // Back to plaintext
In-Place Swap (Gas-Efficient)
// Swap two storage variables without temporary
function swap(uint256 slot1, uint256 slot2) internal {
assembly {
let a := sload(slot1)
let b := sload(slot2)
// XOR swap
a := xor(a, b)
b := xor(a, b)
a := xor(a, b)
sstore(slot1, a)
sstore(slot2, b)
}
}
Masking with Inversion
// Clear specific bits (XOR can toggle, AND clears)
function clearBits(uint256 value, uint256 mask) pure returns (uint256) {
// If bit in mask is 1 and bit in value is 1, clear it
return value & ~mask; // NOT + AND
// Alternative using XOR (only if bits are known to be set):
// return value ^ (value & mask);
}
Implementation
/**
* XOR opcode (0x18) - Bitwise XOR operation
*/
export function op_xor(frame: FrameType): EvmError | null {
// Consume gas (GasFastestStep = 3)
frame.gasRemaining -= 3n;
if (frame.gasRemaining < 0n) {
frame.gasRemaining = 0n;
return { type: "OutOfGas" };
}
// Pop operands
if (frame.stack.length < 2) return { type: "StackUnderflow" };
const a = frame.stack.pop();
const b = frame.stack.pop();
// Compute bitwise XOR
const result = a ^ b;
// Push result
if (frame.stack.length >= 1024) return { type: "StackOverflow" };
frame.stack.push(result);
// Increment PC
frame.pc += 1;
return null;
}
Testing
Test Coverage
import { describe, it, expect } from 'vitest';
import { op_xor } from './xor.js';
describe('XOR (0x18)', () => {
it('performs basic XOR', () => {
const frame = createFrame({ stack: [0b1100n, 0b1010n] });
expect(op_xor(frame)).toBeNull();
expect(frame.stack[0]).toBe(0b0110n);
});
it('toggles bits', () => {
const value = 0b0000n;
const toggle = 0b0101n;
const frame = createFrame({ stack: [value, toggle] });
expect(op_xor(frame)).toBeNull();
expect(frame.stack[0]).toBe(0b0101n);
});
it('handles identity (XOR with zero)', () => {
const value = 0x123456n;
const frame = createFrame({ stack: [value, 0n] });
expect(op_xor(frame)).toBeNull();
expect(frame.stack[0]).toBe(value);
});
it('is self-inverse (a ^ a = 0)', () => {
const value = 0x123456n;
const frame = createFrame({ stack: [value, value] });
expect(op_xor(frame)).toBeNull();
expect(frame.stack[0]).toBe(0n);
});
it('has involution property ((a ^ b) ^ b = a)', () => {
const a = 0x123456n;
const b = 0xABCDEFn;
const frame1 = createFrame({ stack: [a, b] });
op_xor(frame1);
const intermediate = frame1.stack[0];
const frame2 = createFrame({ stack: [intermediate, b] });
op_xor(frame2);
expect(frame2.stack[0]).toBe(a);
});
it('acts as NOT when XOR with MAX', () => {
const MAX = (1n << 256n) - 1n;
const value = 0xAAAAn;
const frame = createFrame({ stack: [value, MAX] });
op_xor(frame);
expect(frame.stack[0]).toBe(~value & MAX);
});
it('is commutative', () => {
const a = 0xAAAAn;
const b = 0x5555n;
const frame1 = createFrame({ stack: [a, b] });
const frame2 = createFrame({ stack: [b, a] });
op_xor(frame1);
op_xor(frame2);
expect(frame1.stack[0]).toBe(frame2.stack[0]);
});
it('returns StackUnderflow with insufficient stack', () => {
const frame = createFrame({ stack: [0x123n] });
expect(op_xor(frame)).toEqual({ type: 'StackUnderflow' });
});
it('returns OutOfGas when insufficient gas', () => {
const frame = createFrame({ stack: [0x123n, 0x456n], gasRemaining: 2n });
expect(op_xor(frame)).toEqual({ type: 'OutOfGas' });
});
});
Edge Cases Tested
- Basic XOR operations (truth table)
- Identity element (XOR with 0)
- Self-inverse property (a ^ a = 0)
- Involution property ((a ^ b) ^ b = a)
- XOR as NOT (with MAX_UINT256)
- Bit toggling
- Equality detection
- Commutative property
- Stack underflow
- Out of gas
Security
Weak Encryption
// INSECURE: XOR cipher with reused key is vulnerable
bytes32 key = keccak256("weak_password");
function encrypt(bytes32 data) pure returns (bytes32) {
return data ^ key; // NEVER reuse key for multiple messages!
}
// Attack: If attacker knows plaintext1, they can derive key
// key = ciphertext1 ^ plaintext1
// Then decrypt any other message: plaintext2 = ciphertext2 ^ key
Mitigation: Use unique keys (one-time pad) or proper encryption (AES):
// Better: Derive unique key per message
function encrypt(bytes32 data, uint256 nonce) pure returns (bytes32) {
bytes32 uniqueKey = keccak256(abi.encode(baseKey, nonce));
return data ^ uniqueKey;
}
XOR Swap Pitfalls
// DANGEROUS: XOR swap fails when variables overlap
function swap(uint256[] storage arr, uint256 i, uint256 j) internal {
if (i == j) return; // CRITICAL: Must check for same index!
arr[i] ^= arr[j];
arr[j] ^= arr[i];
arr[i] ^= arr[j];
}
// Without check: arr[5] ^= arr[5] results in arr[5] = 0!
Incorrect Equality Check
// Works but inefficient
function isEqual(uint256 a, uint256 b) pure returns (bool) {
return (a ^ b) == 0;
}
// Better: Direct comparison
function isEqual(uint256 a, uint256 b) pure returns (bool) {
return a == b; // More readable, same gas cost
}
Checksum Vulnerabilities
// WEAK: XOR checksum doesn't detect bit reordering
function checksum(bytes memory data) pure returns (uint8) {
uint8 result = 0;
for (uint i = 0; i < data.length; i++) {
result ^= uint8(data[i]);
}
return result;
}
// Problem: [0x12, 0x34] and [0x34, 0x12] have same checksum
// Use CRC or cryptographic hash for integrity checks
Benchmarks
XOR is one of the fastest EVM operations:
Execution time (relative):
- XOR: 1.0x (baseline, fastest tier)
- AND/OR: 1.0x (same tier)
- ADD: 1.0x (same tier)
- MUL: 1.2x
- DIV: 2.5x
Gas efficiency:
- 3 gas per 256-bit XOR operation
- ~333,333 XOR operations per million gas
- Native hardware instruction on all platforms
References