Class Ed448

java.lang.Object

org.bouncycastle.math.ec.rfc8032.Ed448

public abstract class Ed448
extends 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	Description
static final class	Ed448.Algorithm
static final class	Ed448.PublicPoint

Field Summary

Fields

Modifier and Type	Field	Description
static final int	PREHASH_SIZE
static final int	PUBLIC_KEY_SIZE
static final int	SECRET_KEY_SIZE
static final int	SIGNATURE_SIZE

Constructor Summary

Constructors

Constructor	Description
Ed448()

Method Summary

Modifier and Type	Method	Description
static Xof	createPrehash()
static void	encodePublicPoint(Ed448.PublicPoint publicPoint, byte[] pk, int pkOff)
static void	generatePrivateKey(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 Object

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

Field Details

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 Details

Ed448

public Ed448()

Method Details

createPrehash

public static Xof createPrehash()

encodePublicPoint

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

generatePrivateKey

public static void generatePrivateKey(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)