使用GNU nettle库Curve25519基点乘1结果不符的技术问询

Hey there! Let's break down exactly why your code isn't returning the 9 you expected—there are a few key Curve25519-specific details you're missing here:

1. Curve25519 scalar multiplication isn't regular integer multiplication #

First off, when you call curve25519_mul_g(result, one), you're not calculating 9 * 1 like a basic math problem. Curve25519 operates on the Montgomery elliptic curve (y^2 = x^3 + 486662x^2 + x), and scalar multiplication here means adding the base point G to itself k times (where k is your scalar). The output is the x-coordinate of that resulting curve point, which has no connection to simple integer multiplication.

2. Nettle automatically clamps your scalar (this is the big one) #

The Curve25519 specification requires secret scalars to be "clamped" to prevent small-subgroup attacks. Here's what clamping does to your input scalar:

• Sets the lowest 3 bits of the first byte to 0
• Sets the highest bit of the last byte to 1
• Sets the second-highest bit of the last byte to 0

Your one array is initialized to all zeros except one[31] = 1, which represents the scalar 1 in little-endian format. After clamping, this scalar gets modified to (2^{255} + 1) (we flip the highest bit of the last byte from 0 to 1). That's the actual value being used in the multiplication, not the 1 you intended—so the result you're seeing is correct for this clamped scalar, just not what you expected.

3. Byte order adds to the confusion #

Curve25519 uses little-endian byte order for both scalars and coordinate values. The hex string you're viewing is in big-endian format, which can throw you off. For example, the base point's x-coordinate 9 would be stored as a 32-byte array where the first byte is 0x09 and the rest are 0x00 (little-endian), not the reverse.

How to get the base point's x-coordinate directly #

If you just need the base point's x-value (9), you don't need to call curve25519_mul_g at all. You can construct it directly in little-endian format:

uint8_t base_x[32] = {0};
base_x[0] = 9; // Little-endian representation of x=9

If you want to experiment with valid scalar multiplication, remember that any scalar passed to curve25519_mul_g will be clamped. Using an unclamped scalar is not recommended for security, but if you need to test with exact values, you'd have to use a lower-level function that skips this step (though Nettle doesn't expose this by default for good reason).

内容的提问来源于stack exchange，提问作者Zeta