org.bouncycastle.math.ec.rfc8032

## Class Ed448

- java.lang.Object
- - org.bouncycastle.math.ec.rfc8032.Ed448

-     public abstract class Ed448
      extends java.lang.Object

  A low-level implementation of the Ed448 and Ed448ph instantiations of the Edwards-Curve Digital Signature Algorithm specified in RFC 8032.

  The implementation uses the "signed mult-comb" algorithm (for scalar multiplication by a fixed point) from Mike Hamburg, "Fast and compact elliptic-curve cryptography". Standard projective coordinates are used for most point arithmetic.

  Algorithm map.

  - Key generation — `generatePrivateKey` returns a 57-byte seed; `generatePublicKey` (via `scalarMultBaseEncoded`) computes `A = s * B` where `s` is the SHAKE-256-expanded clamped secret scalar (RFC 8032 sec. 5.2.5), using the constant-time signed multi-comb `scalarMultBase`.
  - Signing — `sign` computes `R = r * B` (signed multi-comb) where `r = SHAKE-256(dom4(F, C) || prefix || M, 912 bits) mod L`, then `S = (r + k * s) mod L` (RFC 8032 sec. 5.2.6). Reduction modulo `L` uses `Scalar448.reduce912` (Barrett-style, straight-line). No variable-base scalar multiplication is performed.
  - Verification — `verify` uses the basis reduction algorithm of Pornin via `Scalar448.reduceBasisVar` then evaluates the combined relation with Strauss-Shamir's trick in `scalarMultStraus225Var`. Both routines are deliberately variable-time and operate only on public material (signature, message, public key).
  - Coordinates — the precomputed base-point comb table lives in affine form (matching `PointAffine` in `pointLookup`); the signing-side accumulator is projective (X : Y : Z). Verification uses projective coordinates throughout.

  Side-channel scope. The signing path (which operates on the secret seed, the derived secret scalar, and the secret per-message nonce) is written to be constant-time at the Java level: the comb `scalarMultBase` walks all precomputed entries via mask-based `cmov` rather than a secret-indexed array load, conditional sign application uses XOR-with-mask `cnegate`, scalar recoding via `toSignedDigits` uses mask-driven `caddTo`, and `Scalar448.reduce912` is fully unrolled straight-line arithmetic. This is sufficient against a remote network timing attacker but is not a substitute for a constant-time native implementation against a co-located cache-line-resolution adversary — JVM-level timing variance from JIT, GC and cache eviction is not addressable in pure Java. Verification routines (those suffixed `Var`) are deliberately variable-time and operate only on public material.

- - ### Nested Class Summary

    Nested Classes
    Modifier and Type | Class and Description
    --- | ---
    `static class` | `Ed448.Algorithm`
    `static class` | `Ed448.PublicPoint`

  - ### Field Summary

    Fields
    Modifier and Type | Field and Description
    --- | ---
    `static int` | `PREHASH_SIZE`
    `static int` | `PUBLIC_KEY_SIZE`
    `static int` | `SECRET_KEY_SIZE`
    `static int` | `SIGNATURE_SIZE`

  - ### Constructor Summary

    Constructors
    Constructor and Description
    `Ed448()`

  - ### Method Summary

    All Methods Static Methods Concrete Methods
    Modifier and Type | Method and Description
    --- | ---
    `static Xof` | `createPrehash()`
    `static void` | `encodePublicPoint(Ed448.PublicPoint publicPoint, byte[] pk, int pkOff)`
    `static void` | `generatePrivateKey(java.security.SecureRandom random, byte[] k)`
    `static Ed448.PublicPoint` | `generatePublicKey(byte[] sk, int skOff)`
    `static void` | `generatePublicKey(byte[] sk, int skOff, byte[] pk, int pkOff)`
    `static void` | `precompute()`
    `static void` | `scalarMultBaseXY(X448.Friend friend, byte[] k, int kOff, int[] x, int[] y)` NOTE: Only for use by X448
    `static void` | `sign(byte[] sk, int skOff, byte[] ctx, byte[] m, int mOff, int mLen, byte[] sig, int sigOff)`
    `static void` | `sign(byte[] sk, int skOff, byte[] pk, int pkOff, byte[] ctx, byte[] m, int mOff, int mLen, byte[] sig, int sigOff)`
    `static void` | `signPrehash(byte[] sk, int skOff, byte[] ctx, byte[] ph, int phOff, byte[] sig, int sigOff)`
    `static void` | `signPrehash(byte[] sk, int skOff, byte[] pk, int pkOff, byte[] ctx, byte[] ph, int phOff, byte[] sig, int sigOff)`
    `static void` | `signPrehash(byte[] sk, int skOff, byte[] pk, int pkOff, byte[] ctx, Xof ph, byte[] sig, int sigOff)`
    `static void` | `signPrehash(byte[] sk, int skOff, byte[] ctx, Xof ph, byte[] sig, int sigOff)`
    `static boolean` | `validatePublicKeyFull(byte[] pk, int pkOff)`
    `static Ed448.PublicPoint` | `validatePublicKeyFullExport(byte[] pk, int pkOff)`
    `static boolean` | `validatePublicKeyPartial(byte[] pk, int pkOff)`
    `static Ed448.PublicPoint` | `validatePublicKeyPartialExport(byte[] pk, int pkOff)`
    `static boolean` | `verify(byte[] sig, int sigOff, byte[] pk, int pkOff, byte[] ctx, byte[] m, int mOff, int mLen)`
    `static boolean` | `verify(byte[] sig, int sigOff, Ed448.PublicPoint publicPoint, byte[] ctx, byte[] m, int mOff, int mLen)`
    `static boolean` | `verifyPrehash(byte[] sig, int sigOff, byte[] pk, int pkOff, byte[] ctx, byte[] ph, int phOff)`
    `static boolean` | `verifyPrehash(byte[] sig, int sigOff, byte[] pk, int pkOff, byte[] ctx, Xof ph)`
    `static boolean` | `verifyPrehash(byte[] sig, int sigOff, Ed448.PublicPoint publicPoint, byte[] ctx, byte[] ph, int phOff)`
    `static boolean` | `verifyPrehash(byte[] sig, int sigOff, Ed448.PublicPoint publicPoint, byte[] ctx, Xof ph)`

    - ### Methods inherited from class java.lang.Object

      `clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

- - ### Field Detail

    - #### PREHASH_SIZE

          public static final int PREHASH_SIZE

      See Also:
        Constant Field Values

    - #### PUBLIC_KEY_SIZE

          public static final int PUBLIC_KEY_SIZE

      See Also:
        Constant Field Values

    - #### SECRET_KEY_SIZE

          public static final int SECRET_KEY_SIZE

      See Also:
        Constant Field Values

    - #### SIGNATURE_SIZE

          public static final int SIGNATURE_SIZE

      See Also:
        Constant Field Values

  - ### Constructor Detail

    - #### Ed448

          public Ed448()

  - ### Method Detail

    - #### createPrehash

          public static Xof createPrehash()

    - #### encodePublicPoint

          public static void encodePublicPoint(Ed448.PublicPoint publicPoint,
                                               byte[] pk,
                                               int pkOff)

    - #### generatePrivateKey

          public static void generatePrivateKey(java.security.SecureRandom random,
                                                byte[] k)

    - #### generatePublicKey

          public static void generatePublicKey(byte[] sk,
                                               int skOff,
                                               byte[] pk,
                                               int pkOff)

    - #### generatePublicKey

          public static Ed448.PublicPoint generatePublicKey(byte[] sk,
                                                            int skOff)

    - #### precompute

          public static void precompute()

    - #### scalarMultBaseXY

          public static void scalarMultBaseXY(X448.Friend friend,
                                              byte[] k,
                                              int kOff,
                                              int[] x,
                                              int[] y)

      NOTE: Only for use by X448

    - #### sign

          public static void sign(byte[] sk,
                                  int skOff,
                                  byte[] ctx,
                                  byte[] m,
                                  int mOff,
                                  int mLen,
                                  byte[] sig,
                                  int sigOff)

    - #### sign

          public static void sign(byte[] sk,
                                  int skOff,
                                  byte[] pk,
                                  int pkOff,
                                  byte[] ctx,
                                  byte[] m,
                                  int mOff,
                                  int mLen,
                                  byte[] sig,
                                  int sigOff)

    - #### signPrehash

          public static void signPrehash(byte[] sk,
                                         int skOff,
                                         byte[] ctx,
                                         byte[] ph,
                                         int phOff,
                                         byte[] sig,
                                         int sigOff)

    - #### signPrehash

          public static void signPrehash(byte[] sk,
                                         int skOff,
                                         byte[] pk,
                                         int pkOff,
                                         byte[] ctx,
                                         byte[] ph,
                                         int phOff,
                                         byte[] sig,
                                         int sigOff)

    - #### signPrehash

          public static void signPrehash(byte[] sk,
                                         int skOff,
                                         byte[] ctx,
                                         Xof ph,
                                         byte[] sig,
                                         int sigOff)

    - #### signPrehash

          public static void signPrehash(byte[] sk,
                                         int skOff,
                                         byte[] pk,
                                         int pkOff,
                                         byte[] ctx,
                                         Xof ph,
                                         byte[] sig,
                                         int sigOff)

    - #### validatePublicKeyFull

          public static boolean validatePublicKeyFull(byte[] pk,
                                                      int pkOff)

    - #### validatePublicKeyFullExport

          public static Ed448.PublicPoint validatePublicKeyFullExport(byte[] pk,
                                                                      int pkOff)

    - #### validatePublicKeyPartial

          public static boolean validatePublicKeyPartial(byte[] pk,
                                                         int pkOff)

    - #### validatePublicKeyPartialExport

          public static Ed448.PublicPoint validatePublicKeyPartialExport(byte[] pk,
                                                                         int pkOff)

    - #### verify

          public static boolean verify(byte[] sig,
                                       int sigOff,
                                       byte[] pk,
                                       int pkOff,
                                       byte[] ctx,
                                       byte[] m,
                                       int mOff,
                                       int mLen)

    - #### verify

          public static boolean verify(byte[] sig,
                                       int sigOff,
                                       Ed448.PublicPoint publicPoint,
                                       byte[] ctx,
                                       byte[] m,
                                       int mOff,
                                       int mLen)

    - #### verifyPrehash

          public static boolean verifyPrehash(byte[] sig,
                                              int sigOff,
                                              byte[] pk,
                                              int pkOff,
                                              byte[] ctx,
                                              byte[] ph,
                                              int phOff)

    - #### verifyPrehash

          public static boolean verifyPrehash(byte[] sig,
                                              int sigOff,
                                              Ed448.PublicPoint publicPoint,
                                              byte[] ctx,
                                              byte[] ph,
                                              int phOff)

    - #### verifyPrehash

          public static boolean verifyPrehash(byte[] sig,
                                              int sigOff,
                                              byte[] pk,
                                              int pkOff,
                                              byte[] ctx,
                                              Xof ph)

    - #### verifyPrehash

          public static boolean verifyPrehash(byte[] sig,
                                              int sigOff,
                                              Ed448.PublicPoint publicPoint,
                                              byte[] ctx,
                                              Xof ph)