ext/node_crypto/dh.rs - main - githubmirror/deno

ext/node_crypto/dh.rs
332 строки15 KB
Nathan Whitaker
fix(ext/node_crypto): use named group exponent sizes (#36347)
05 авг 2026, 00:04
05 авг 2026, 00:04610bdd6
// Copyright 2018-2026 the Deno authors. MIT license.

use num_bigint_dig::BigUint;
use num_bigint_dig::RandBigInt;
use num_traits::FromPrimitive;

use super::primes::Prime;

#[derive(Clone, PartialEq)]
pub struct PublicKey(BigUint);

impl PublicKey {
  pub fn from_bytes(bytes: &[u8]) -> Self {
    let public_key = BigUint::from_bytes_be(bytes);
    Self(public_key)
  }

  pub fn into_vec(self) -> Vec<u8> {
    self.0.to_bytes_be()
  }
}

#[derive(Clone, PartialEq)]
pub struct PrivateKey(BigUint);

impl PrivateKey {
  pub fn new(exponent_bits: usize) -> Self {
    let mut rng = rand::thread_rng();
    let exponent = rng.gen_biguint(exponent_bits);
    Self(exponent)
  }

  pub fn from_bytes(bytes: &[u8]) -> Self {
    let exponent = BigUint::from_bytes_be(bytes);
    Self(exponent)
  }

  /// Diffie-Hellman modular exponentiation.
  /// s = g^x mod p
  pub fn compute_public_key(
    &self,
    generator: &BigUint,
    modulus: &BigUint,
  ) -> PublicKey {
    let public_key = generator.modpow(&self.0, modulus);
    PublicKey(public_key)
  }

  pub fn into_vec(self) -> Vec<u8> {
    self.0.to_bytes_be()
  }
}

/// Classic DH
pub struct DiffieHellman {
  pub private_key: PrivateKey,
  pub public_key: PublicKey,
}

impl DiffieHellman {
  pub fn group<G>() -> Self
  where
    G: DiffieHellmanGroup,
  {
    let private_key = PrivateKey::new(G::EXPONENT_BITS);

    let generator = BigUint::from_usize(G::GENERATOR).unwrap();
    // MODULUS arrays are stored as big-endian u32 words (matching RFCs).
    // Convert to big-endian bytes for correct BigUint construction.
    let modulus_bytes: Vec<u8> =
      G::MODULUS.iter().flat_map(|x| x.to_be_bytes()).collect();
    let modulus = BigUint::from_bytes_be(&modulus_bytes);

    let public_key = private_key.compute_public_key(&generator, &modulus);

    Self {
      private_key,
      public_key,
    }
  }

  pub fn new(prime: Prime, generator: usize) -> Self {
    let private_key = PrivateKey::new(prime.bits());

    let generator = BigUint::from_usize(generator).unwrap();
    let public_key = private_key.compute_public_key(&generator, &prime);

    Self {
      private_key,
      public_key,
    }
  }
}

/// Well-known modp groups
//
/// More Modular Exponential (MODP) Diffie-Hellman groups for Internet Key Exchange (IKE)
/// https://www.rfc-editor.org/rfc/rfc3526
///
/// Insecure groups `modp1` and `modp2` from https://www.rfc-editor.org/rfc/rfc2409.txt
/// are deprecated in Node.js. We don't support them.
pub trait DiffieHellmanGroup {
  const GENERATOR: usize;
  const MODULUS: &'static [u32];
  /// Private exponent size in bits, matching OpenSSL's named-group defaults.
  const EXPONENT_BITS: usize;
}

/// 1536-bit MODP Group
/// https://www.rfc-editor.org/rfc/rfc3526#section-2
pub struct Modp1536;
impl DiffieHellmanGroup for Modp1536 {
  const GENERATOR: usize = 2;
  const EXPONENT_BITS: usize = 200;

  const MODULUS: &'static [u32] = &[
    0xFFFFFFFF, 0xFFFFFFFF, 0xC90FDAA2, 0x2168C234, 0xC4C6628B, 0x80DC1CD1,
    0x29024E08, 0x8A67CC74, 0x020BBEA6, 0x3B139B22, 0x514A0879, 0x8E3404DD,
    0xEF9519B3, 0xCD3A431B, 0x302B0A6D, 0xF25F1437, 0x4FE1356D, 0x6D51C245,
    0xE485B576, 0x625E7EC6, 0xF44C42E9, 0xA637ED6B, 0x0BFF5CB6, 0xF406B7ED,
    0xEE386BFB, 0x5A899FA5, 0xAE9F2411, 0x7C4B1FE6, 0x49286651, 0xECE45B3D,
    0xC2007CB8, 0xA163BF05, 0x98DA4836, 0x1C55D39A, 0x69163FA8, 0xFD24CF5F,
    0x83655D23, 0xDCA3AD96, 0x1C62F356, 0x208552BB, 0x9ED52907, 0x7096966D,
    0x670C354E, 0x4ABC9804, 0xF1746C08, 0xCA237327, 0xFFFFFFFF, 0xFFFFFFFF,
  ];
}

/// 2048-bit MODP Group
/// https://www.rfc-editor.org/rfc/rfc3526#section-3
pub struct Modp2048;
impl DiffieHellmanGroup for Modp2048 {
  const GENERATOR: usize = 2;
  const EXPONENT_BITS: usize = 225;

  const MODULUS: &'static [u32] = &[
    0xFFFFFFFF, 0xFFFFFFFF, 0xC90FDAA2, 0x2168C234, 0xC4C6628B, 0x80DC1CD1,
    0x29024E08, 0x8A67CC74, 0x020BBEA6, 0x3B139B22, 0x514A0879, 0x8E3404DD,
    0xEF9519B3, 0xCD3A431B, 0x302B0A6D, 0xF25F1437, 0x4FE1356D, 0x6D51C245,
    0xE485B576, 0x625E7EC6, 0xF44C42E9, 0xA637ED6B, 0x0BFF5CB6, 0xF406B7ED,
    0xEE386BFB, 0x5A899FA5, 0xAE9F2411, 0x7C4B1FE6, 0x49286651, 0xECE45B3D,
    0xC2007CB8, 0xA163BF05, 0x98DA4836, 0x1C55D39A, 0x69163FA8, 0xFD24CF5F,
    0x83655D23, 0xDCA3AD96, 0x1C62F356, 0x208552BB, 0x9ED52907, 0x7096966D,
    0x670C354E, 0x4ABC9804, 0xF1746C08, 0xCA18217C, 0x32905E46, 0x2E36CE3B,
    0xE39E772C, 0x180E8603, 0x9B2783A2, 0xEC07A28F, 0xB5C55DF0, 0x6F4C52C9,
    0xDE2BCBF6, 0x95581718, 0x3995497C, 0xEA956AE5, 0x15D22618, 0x98FA0510,
    0x15728E5A, 0x8AACAA68, 0xFFFFFFFF, 0xFFFFFFFF,
  ];
}

/// 3072-bit MODP Group
/// https://www.rfc-editor.org/rfc/rfc3526#section-4
pub struct Modp3072;
impl DiffieHellmanGroup for Modp3072 {
  const GENERATOR: usize = 2;
  const EXPONENT_BITS: usize = 275;

  const MODULUS: &'static [u32] = &[
    0xFFFFFFFF, 0xFFFFFFFF, 0xC90FDAA2, 0x2168C234, 0xC4C6628B, 0x80DC1CD1,
    0x29024E08, 0x8A67CC74, 0x020BBEA6, 0x3B139B22, 0x514A0879, 0x8E3404DD,
    0xEF9519B3, 0xCD3A431B, 0x302B0A6D, 0xF25F1437, 0x4FE1356D, 0x6D51C245,
    0xE485B576, 0x625E7EC6, 0xF44C42E9, 0xA637ED6B, 0x0BFF5CB6, 0xF406B7ED,
    0xEE386BFB, 0x5A899FA5, 0xAE9F2411, 0x7C4B1FE6, 0x49286651, 0xECE45B3D,
    0xC2007CB8, 0xA163BF05, 0x98DA4836, 0x1C55D39A, 0x69163FA8, 0xFD24CF5F,
    0x83655D23, 0xDCA3AD96, 0x1C62F356, 0x208552BB, 0x9ED52907, 0x7096966D,
    0x670C354E, 0x4ABC9804, 0xF1746C08, 0xCA18217C, 0x32905E46, 0x2E36CE3B,
    0xE39E772C, 0x180E8603, 0x9B2783A2, 0xEC07A28F, 0xB5C55DF0, 0x6F4C52C9,
    0xDE2BCBF6, 0x95581718, 0x3995497C, 0xEA956AE5, 0x15D22618, 0x98FA0510,
    0x15728E5A, 0x8AAAC42D, 0xAD33170D, 0x04507A33, 0xA85521AB, 0xDF1CBA64,
    0xECFB8504, 0x58DBEF0A, 0x8AEA7157, 0x5D060C7D, 0xB3970F85, 0xA6E1E4C7,
    0xABF5AE8C, 0xDB0933D7, 0x1E8C94E0, 0x4A25619D, 0xCEE3D226, 0x1AD2EE6B,
    0xF12FFA06, 0xD98A0864, 0xD8760273, 0x3EC86A64, 0x521F2B18, 0x177B200C,
    0xBBE11757, 0x7A615D6C, 0x770988C0, 0xBAD946E2, 0x08E24FA0, 0x74E5AB31,
    0x43DB5BFC, 0xE0FD108E, 0x4B82D120, 0xA93AD2CA, 0xFFFFFFFF, 0xFFFFFFFF,
  ];
}

/// 4096-bit MODP Group
/// https://www.rfc-editor.org/rfc/rfc3526#section-5
pub struct Modp4096;
impl DiffieHellmanGroup for Modp4096 {
  const GENERATOR: usize = 2;
  const EXPONENT_BITS: usize = 325;

  const MODULUS: &'static [u32] = &[
    0xFFFFFFFF, 0xFFFFFFFF, 0xC90FDAA2, 0x2168C234, 0xC4C6628B, 0x80DC1CD1,
    0x29024E08, 0x8A67CC74, 0x020BBEA6, 0x3B139B22, 0x514A0879, 0x8E3404DD,
    0xEF9519B3, 0xCD3A431B, 0x302B0A6D, 0xF25F1437, 0x4FE1356D, 0x6D51C245,
    0xE485B576, 0x625E7EC6, 0xF44C42E9, 0xA637ED6B, 0x0BFF5CB6, 0xF406B7ED,
    0xEE386BFB, 0x5A899FA5, 0xAE9F2411, 0x7C4B1FE6, 0x49286651, 0xECE45B3D,
    0xC2007CB8, 0xA163BF05, 0x98DA4836, 0x1C55D39A, 0x69163FA8, 0xFD24CF5F,
    0x83655D23, 0xDCA3AD96, 0x1C62F356, 0x208552BB, 0x9ED52907, 0x7096966D,
    0x670C354E, 0x4ABC9804, 0xF1746C08, 0xCA18217C, 0x32905E46, 0x2E36CE3B,
    0xE39E772C, 0x180E8603, 0x9B2783A2, 0xEC07A28F, 0xB5C55DF0, 0x6F4C52C9,
    0xDE2BCBF6, 0x95581718, 0x3995497C, 0xEA956AE5, 0x15D22618, 0x98FA0510,
    0x15728E5A, 0x8AAAC42D, 0xAD33170D, 0x04507A33, 0xA85521AB, 0xDF1CBA64,
    0xECFB8504, 0x58DBEF0A, 0x8AEA7157, 0x5D060C7D, 0xB3970F85, 0xA6E1E4C7,
    0xABF5AE8C, 0xDB0933D7, 0x1E8C94E0, 0x4A25619D, 0xCEE3D226, 0x1AD2EE6B,
    0xF12FFA06, 0xD98A0864, 0xD8760273, 0x3EC86A64, 0x521F2B18, 0x177B200C,
    0xBBE11757, 0x7A615D6C, 0x770988C0, 0xBAD946E2, 0x08E24FA0, 0x74E5AB31,
    0x43DB5BFC, 0xE0FD108E, 0x4B82D120, 0xA9210801, 0x1A723C12, 0xA787E6D7,
    0x88719A10, 0xBDBA5B26, 0x99C32718, 0x6AF4E23C, 0x1A946834, 0xB6150BDA,
    0x2583E9CA, 0x2AD44CE8, 0xDBBBC2DB, 0x04DE8EF9, 0x2E8EFC14, 0x1FBECAA6,
    0x287C5947, 0x4E6BC05D, 0x99B2964F, 0xA090C3A2, 0x233BA186, 0x515BE7ED,
    0x1F612970, 0xCEE2D7AF, 0xB81BDD76, 0x2170481C, 0xD0069127, 0xD5B05AA9,
    0x93B4EA98, 0x8D8FDDC1, 0x86FFB7DC, 0x90A6C08F, 0x4DF435C9, 0x34063199,
    0xFFFFFFFF, 0xFFFFFFFF,
  ];
}

/// 6144-bit MODP Group
/// https://www.rfc-editor.org/rfc/rfc3526#section-6
pub struct Modp6144;
impl DiffieHellmanGroup for Modp6144 {
  const GENERATOR: usize = 2;
  const EXPONENT_BITS: usize = 375;

  const MODULUS: &'static [u32] = &[
    0xFFFFFFFF, 0xFFFFFFFF, 0xC90FDAA2, 0x2168C234, 0xC4C6628B, 0x80DC1CD1,
    0x29024E08, 0x8A67CC74, 0x020BBEA6, 0x3B139B22, 0x514A0879, 0x8E3404DD,
    0xEF9519B3, 0xCD3A431B, 0x302B0A6D, 0xF25F1437, 0x4FE1356D, 0x6D51C245,
    0xE485B576, 0x625E7EC6, 0xF44C42E9, 0xA637ED6B, 0x0BFF5CB6, 0xF406B7ED,
    0xEE386BFB, 0x5A899FA5, 0xAE9F2411, 0x7C4B1FE6, 0x49286651, 0xECE45B3D,
    0xC2007CB8, 0xA163BF05, 0x98DA4836, 0x1C55D39A, 0x69163FA8, 0xFD24CF5F,
    0x83655D23, 0xDCA3AD96, 0x1C62F356, 0x208552BB, 0x9ED52907, 0x7096966D,
    0x670C354E, 0x4ABC9804, 0xF1746C08, 0xCA18217C, 0x32905E46, 0x2E36CE3B,
    0xE39E772C, 0x180E8603, 0x9B2783A2, 0xEC07A28F, 0xB5C55DF0, 0x6F4C52C9,
    0xDE2BCBF6, 0x95581718, 0x3995497C, 0xEA956AE5, 0x15D22618, 0x98FA0510,
    0x15728E5A, 0x8AAAC42D, 0xAD33170D, 0x04507A33, 0xA85521AB, 0xDF1CBA64,
    0xECFB8504, 0x58DBEF0A, 0x8AEA7157, 0x5D060C7D, 0xB3970F85, 0xA6E1E4C7,
    0xABF5AE8C, 0xDB0933D7, 0x1E8C94E0, 0x4A25619D, 0xCEE3D226, 0x1AD2EE6B,
    0xF12FFA06, 0xD98A0864, 0xD8760273, 0x3EC86A64, 0x521F2B18, 0x177B200C,
    0xBBE11757, 0x7A615D6C, 0x770988C0, 0xBAD946E2, 0x08E24FA0, 0x74E5AB31,
    0x43DB5BFC, 0xE0FD108E, 0x4B82D120, 0xA9210801, 0x1A723C12, 0xA787E6D7,
    0x88719A10, 0xBDBA5B26, 0x99C32718, 0x6AF4E23C, 0x1A946834, 0xB6150BDA,
    0x2583E9CA, 0x2AD44CE8, 0xDBBBC2DB, 0x04DE8EF9, 0x2E8EFC14, 0x1FBECAA6,
    0x287C5947, 0x4E6BC05D, 0x99B2964F, 0xA090C3A2, 0x233BA186, 0x515BE7ED,
    0x1F612970, 0xCEE2D7AF, 0xB81BDD76, 0x2170481C, 0xD0069127, 0xD5B05AA9,
    0x93B4EA98, 0x8D8FDDC1, 0x86FFB7DC, 0x90A6C08F, 0x4DF435C9, 0x34028492,
    0x36C3FAB4, 0xD27C7026, 0xC1D4DCB2, 0x602646DE, 0xC9751E76, 0x3DBA37BD,
    0xF8FF9406, 0xAD9E530E, 0xE5DB382F, 0x413001AE, 0xB06A53ED, 0x9027D831,
    0x179727B0, 0x865A8918, 0xDA3EDBEB, 0xCF9B14ED, 0x44CE6CBA, 0xCED4BB1B,
    0xDB7F1447, 0xE6CC254B, 0x33205151, 0x2BD7AF42, 0x6FB8F401, 0x378CD2BF,
    0x5983CA01, 0xC64B92EC, 0xF032EA15, 0xD1721D03, 0xF482D7CE, 0x6E74FEF6,
    0xD55E702F, 0x46980C82, 0xB5A84031, 0x900B1C9E, 0x59E7C97F, 0xBEC7E8F3,
    0x23A97A7E, 0x36CC88BE, 0x0F1D45B7, 0xFF585AC5, 0x4BD407B2, 0x2B4154AA,
    0xCC8F6D7E, 0xBF48E1D8, 0x14CC5ED2, 0x0F8037E0, 0xA79715EE, 0xF29BE328,
    0x06A1D58B, 0xB7C5DA76, 0xF550AA3D, 0x8A1FBFF0, 0xEB19CCB1, 0xA313D55C,
    0xDA56C9EC, 0x2EF29632, 0x387FE8D7, 0x6E3C0468, 0x043E8F66, 0x3F4860EE,
    0x12BF2D5B, 0x0B7474D6, 0xE694F91E, 0x6DCC4024, 0xFFFFFFFF, 0xFFFFFFFF,
  ];
}

/// 8192-bit MODP Group
/// https://www.rfc-editor.org/rfc/rfc3526#section-7
pub struct Modp8192;
impl DiffieHellmanGroup for Modp8192 {
  const GENERATOR: usize = 2;
  const EXPONENT_BITS: usize = 400;

  const MODULUS: &'static [u32] = &[
    0xFFFFFFFF, 0xFFFFFFFF, 0xC90FDAA2, 0x2168C234, 0xC4C6628B, 0x80DC1CD1,
    0x29024E08, 0x8A67CC74, 0x020BBEA6, 0x3B139B22, 0x514A0879, 0x8E3404DD,
    0xEF9519B3, 0xCD3A431B, 0x302B0A6D, 0xF25F1437, 0x4FE1356D, 0x6D51C245,
    0xE485B576, 0x625E7EC6, 0xF44C42E9, 0xA637ED6B, 0x0BFF5CB6, 0xF406B7ED,
    0xEE386BFB, 0x5A899FA5, 0xAE9F2411, 0x7C4B1FE6, 0x49286651, 0xECE45B3D,
    0xC2007CB8, 0xA163BF05, 0x98DA4836, 0x1C55D39A, 0x69163FA8, 0xFD24CF5F,
    0x83655D23, 0xDCA3AD96, 0x1C62F356, 0x208552BB, 0x9ED52907, 0x7096966D,
    0x670C354E, 0x4ABC9804, 0xF1746C08, 0xCA18217C, 0x32905E46, 0x2E36CE3B,
    0xE39E772C, 0x180E8603, 0x9B2783A2, 0xEC07A28F, 0xB5C55DF0, 0x6F4C52C9,
    0xDE2BCBF6, 0x95581718, 0x3995497C, 0xEA956AE5, 0x15D22618, 0x98FA0510,
    0x15728E5A, 0x8AAAC42D, 0xAD33170D, 0x04507A33, 0xA85521AB, 0xDF1CBA64,
    0xECFB8504, 0x58DBEF0A, 0x8AEA7157, 0x5D060C7D, 0xB3970F85, 0xA6E1E4C7,
    0xABF5AE8C, 0xDB0933D7, 0x1E8C94E0, 0x4A25619D, 0xCEE3D226, 0x1AD2EE6B,
    0xF12FFA06, 0xD98A0864, 0xD8760273, 0x3EC86A64, 0x521F2B18, 0x177B200C,
    0xBBE11757, 0x7A615D6C, 0x770988C0, 0xBAD946E2, 0x08E24FA0, 0x74E5AB31,
    0x43DB5BFC, 0xE0FD108E, 0x4B82D120, 0xA9210801, 0x1A723C12, 0xA787E6D7,
    0x88719A10, 0xBDBA5B26, 0x99C32718, 0x6AF4E23C, 0x1A946834, 0xB6150BDA,
    0x2583E9CA, 0x2AD44CE8, 0xDBBBC2DB, 0x04DE8EF9, 0x2E8EFC14, 0x1FBECAA6,
    0x287C5947, 0x4E6BC05D, 0x99B2964F, 0xA090C3A2, 0x233BA186, 0x515BE7ED,
    0x1F612970, 0xCEE2D7AF, 0xB81BDD76, 0x2170481C, 0xD0069127, 0xD5B05AA9,
    0x93B4EA98, 0x8D8FDDC1, 0x86FFB7DC, 0x90A6C08F, 0x4DF435C9, 0x34028492,
    0x36C3FAB4, 0xD27C7026, 0xC1D4DCB2, 0x602646DE, 0xC9751E76, 0x3DBA37BD,
    0xF8FF9406, 0xAD9E530E, 0xE5DB382F, 0x413001AE, 0xB06A53ED, 0x9027D831,
    0x179727B0, 0x865A8918, 0xDA3EDBEB, 0xCF9B14ED, 0x44CE6CBA, 0xCED4BB1B,
    0xDB7F1447, 0xE6CC254B, 0x33205151, 0x2BD7AF42, 0x6FB8F401, 0x378CD2BF,
    0x5983CA01, 0xC64B92EC, 0xF032EA15, 0xD1721D03, 0xF482D7CE, 0x6E74FEF6,
    0xD55E702F, 0x46980C82, 0xB5A84031, 0x900B1C9E, 0x59E7C97F, 0xBEC7E8F3,
    0x23A97A7E, 0x36CC88BE, 0x0F1D45B7, 0xFF585AC5, 0x4BD407B2, 0x2B4154AA,
    0xCC8F6D7E, 0xBF48E1D8, 0x14CC5ED2, 0x0F8037E0, 0xA79715EE, 0xF29BE328,
    0x06A1D58B, 0xB7C5DA76, 0xF550AA3D, 0x8A1FBFF0, 0xEB19CCB1, 0xA313D55C,
    0xDA56C9EC, 0x2EF29632, 0x387FE8D7, 0x6E3C0468, 0x043E8F66, 0x3F4860EE,
    0x12BF2D5B, 0x0B7474D6, 0xE694F91E, 0x6DBE1159, 0x74A3926F, 0x12FEE5E4,
    0x38777CB6, 0xA932DF8C, 0xD8BEC4D0, 0x73B931BA, 0x3BC832B6, 0x8D9DD300,
    0x741FA7BF, 0x8AFC47ED, 0x2576F693, 0x6BA42466, 0x3AAB639C, 0x5AE4F568,
    0x3423B474, 0x2BF1C978, 0x238F16CB, 0xE39D652D, 0xE3FDB8BE, 0xFC848AD9,
    0x22222E04, 0xA4037C07, 0x13EB57A8, 0x1A23F0C7, 0x3473FC64, 0x6CEA306B,
    0x4BCBC886, 0x2F8385DD, 0xFA9D4B7F, 0xA2C087E8, 0x79683303, 0xED5BDD3A,
    0x062B3CF5, 0xB3A278A6, 0x6D2A13F8, 0x3F44F82D, 0xDF310EE0, 0x74AB6A36,
    0x4597E899, 0xA0255DC1, 0x64F31CC5, 0x0846851D, 0xF9AB4819, 0x5DED7EA1,
    0xB1D510BD, 0x7EE74D73, 0xFAF36BC3, 0x1ECFA268, 0x359046F4, 0xEB879F92,
    0x4009438B, 0x481C6CD7, 0x889A002E, 0xD5EE382B, 0xC9190DA6, 0xFC026E47,
    0x9558E447, 0x5677E9AA, 0x9E3050E2, 0x765694DF, 0xC81F56E8, 0x80B96E71,
    0x60C980DD, 0x98EDD3DF, 0xFFFFFFFF, 0xFFFFFFFF,
  ];
}

#[cfg(test)]
mod tests {
  use super::*;

  fn assert_group_private_exponent_uses_bits<G>(expected_bits: usize)
  where
    G: DiffieHellmanGroup,
  {
    assert_eq!(G::EXPONENT_BITS, expected_bits);
    let exponent_bits = DiffieHellman::group::<G>().private_key.0.bits();
    assert!(
      exponent_bits > expected_bits / 2,
      "expected an exponent near {expected_bits} bits, got {exponent_bits} bits"
    );
  }

  #[test]
  fn predefined_group_private_exponents_use_bits() {
    assert_group_private_exponent_uses_bits::<Modp1536>(200);
    assert_group_private_exponent_uses_bits::<Modp2048>(225);
    assert_group_private_exponent_uses_bits::<Modp3072>(275);
    assert_group_private_exponent_uses_bits::<Modp4096>(325);
    assert_group_private_exponent_uses_bits::<Modp6144>(375);
    assert_group_private_exponent_uses_bits::<Modp8192>(400);
  }
}