Feature/hors signature (#7635)

* feat(ciphers): add HORS few-time signature scheme

* test(ciphers): add tests for HORS signature

* fix(ciphers): require k as a verify parameter in HORS

Author: dilaraacetin

src/main/java/com/thealgorithms/ciphers/HorsSignature.java

@@ -0,0 +1,211 @@
+package com.thealgorithms.ciphers;
+
+import java.security.MessageDigest;
+import java.security.NoSuchAlgorithmException;
+import java.security.SecureRandom;
+
+/**
+ * HORS (Hash to Obtain Random Subset) is a hash-based few-time signature scheme by Reyzin and
+ * Reyzin (2002).
+ *
+ * <p>The private key consists of {@code t = 2^τ} random 32-byte secrets and the public key contains
+ * their SHA-256 hashes. To sign, the SHA-256 digest of the message is split into {@code k} chunks of
+ * {@code τ} bits (most significant bit first); each chunk is an index into the key, and the secrets
+ * at those {@code k} indices form the signature. The verifier derives the same indices and checks
+ * that each revealed secret hashes to the matching public-key value. The same index may appear more
+ * than once, as in the original scheme. Signing is deterministic.
+ *
+ * <p>HORS is a few-time scheme: each signature reveals {@code k} secrets, so after {@code r}
+ * signatures an attacker knows at most {@code r·k} of them. If all indices of another message fall
+ * into that set, its signature can be forged, so security decreases with every signature.
+ *
+ * <p>HORST compresses the large public key with a Merkle tree. FORS, used in SPHINCS+ and SLH-DSA
+ * (FIPS 205), uses a forest of trees instead, which also removes the repeated-index weakness. This
+ * implementation is educational and must not be used in production.
+ *
+ * <p>References: <a href="https://eprint.iacr.org/2002/014">Reyzin and Reyzin, Better than BiBa</a>,
+ * <a href="https://en.wikipedia.org/wiki/Hash-based_cryptography">Wikipedia: Hash-based cryptography</a>
+ *
+ * @author dilaraacetin
+ * @see LamportSignature
+ * @see WinternitzSignature
+ * @see MerkleSignatureScheme
+ */
+public final class HorsSignature {
+
+    // SHA-256 output length in bytes
+    private static final int HASH_BYTES = 32;
+    private static final int DIGEST_BITS = 256;
+    private static final int MIN_T = 16;
+    private static final int MAX_T = 65536;
+    private static final int DEFAULT_T = 1024;
+    private static final int DEFAULT_K = 16;
+
+    private final int k;
+    private final int tau;
+    private final byte[][] privateKey;
+    private final byte[][] publicKey;
+
+    /**
+     * Generates a new key pair with {@code t = 1024} and {@code k = 16}.
+     */
+    public HorsSignature() {
+        this(DEFAULT_T, DEFAULT_K);
+    }
+
+    /**
+     * Generates a new key pair.
+     *
+     * @param t the number of secrets; a power of two between 16 and 65536
+     * @param k the number of secrets revealed per signature; {@code k·log2(t)} must not exceed 256
+     * @throws IllegalArgumentException if {@code t} or {@code k} is not supported
+     */
+    public HorsSignature(int t, int k) {
+        this.tau = tauOf(t);
+        validateK(k, tau);
+        this.k = k;
+        SecureRandom secureRandom = new SecureRandom();
+        privateKey = new byte[t][HASH_BYTES];
+        publicKey = new byte[t][];
+        for (int i = 0; i < t; i++) {
+            secureRandom.nextBytes(privateKey[i]);
+            publicKey[i] = hash(privateKey[i]);
+        }
+    }
+
+    /**
+     * Returns a copy of the public key.
+     *
+     * @return {@code t} hash values, each 32 bytes long
+     */
+    public byte[][] getPublicKey() {
+        return deepCopy(publicKey);
+    }
+
+    /**
+     * Returns the number of secrets revealed per signature. Like {@code t}, it is part of the public
+     * key and is needed for verification.
+     *
+     * @return the parameter {@code k}
+     */
+    public int getK() {
+        return k;
+    }
+
+    /**
+     * Signs a message. Every signature reveals {@code k} secrets, so a key pair should only sign a
+     * few messages.
+     *
+     * @param message the message to sign
+     * @return the signature: {@code k} secrets of 32 bytes each
+     * @throws IllegalArgumentException if the message is null
+     */
+    public byte[][] sign(byte[] message) {
+        if (message == null) {
+            throw new IllegalArgumentException("message must not be null");
+        }
+        int[] indices = messageIndices(hash(message), k, tau);
+        byte[][] signature = new byte[k][];
+        for (int j = 0; j < k; j++) {
+            signature[j] = privateKey[indices[j]].clone();
+        }
+        return signature;
+    }
+
+    /**
+     * Verifies a signature against a public key. {@code t} is taken from the public key length.
+     * {@code k} is part of the public key and must be supplied by the verifier: taking it from the
+     * signature would let an attacker submit a shorter signature that reveals fewer secrets.
+     *
+     * @param message the signed message
+     * @param signature the signature to check
+     * @param publicKey the public key of the signer
+     * @param k the number of secrets per signature used by the signer (see {@link #getK()})
+     * @return true if the signature is valid for the message and public key, false otherwise
+     * @throws IllegalArgumentException if an argument is null, the public key length is not a
+     *     supported {@code t}, {@code k} is not supported for this {@code t}, a value is not 32
+     *     bytes long, or the signature does not contain exactly {@code k} values
+     */
+    public static boolean verify(byte[] message, byte[][] signature, byte[][] publicKey, int k) {
+        if (message == null) {
+            throw new IllegalArgumentException("message must not be null");
+        }
+        validateValues(publicKey, "publicKey");
+        validateValues(signature, "signature");
+        int tau = tauOf(publicKey.length);
+        validateK(k, tau);
+        if (signature.length != k) {
+            throw new IllegalArgumentException("signature must contain exactly " + k + " values, got " + signature.length);
+        }
+
+        int[] indices = messageIndices(hash(message), k, tau);
+        for (int j = 0; j < k; j++) {
+            if (!MessageDigest.isEqual(hash(signature[j]), publicKey[indices[j]])) {
+                return false;
+            }
+        }
+        return true;
+    }
+
+    /**
+     * Splits the first {@code k·τ} bits of a digest into {@code k} unsigned {@code τ}-bit indices,
+     * most significant bit first. Shared by sign and verify.
+     */
+    static int[] messageIndices(byte[] digest, int k, int tau) {
+        if ((long) k * tau > digest.length * 8L) {
+            throw new IllegalArgumentException("digest is too short for " + k + " indices of " + tau + " bits");
+        }
+        int[] indices = new int[k];
+        for (int j = 0; j < k; j++) {
+            int index = 0;
+            for (int i = 0; i < tau; i++) {
+                int bit = j * tau + i;
+                // bit 0 is the most significant bit of digest[0]; & 0xFF reads the byte as unsigned
+                index = (index << 1) | (((digest[bit / 8] & 0xFF) >> (7 - bit % 8)) & 1);
+            }
+            indices[j] = index;
+        }
+        return indices;
+    }
+
+    private static int tauOf(int t) {
+        if (t < MIN_T || t > MAX_T || (t & (t - 1)) != 0) {
+            throw new IllegalArgumentException("t must be a power of two between " + MIN_T + " and " + MAX_T + ", got " + t);
+        }
+        return Integer.numberOfTrailingZeros(t);
+    }
+
+    private static void validateK(int k, int tau) {
+        // k > DIGEST_BITS / tau is the same as k * tau > DIGEST_BITS, but cannot overflow
+        if (k < 1 || k > DIGEST_BITS / tau) {
+            throw new IllegalArgumentException("k must be at least 1 and k * log2(t) at most " + DIGEST_BITS + ", got k = " + k);
+        }
+    }
+
+    private static void validateValues(byte[][] values, String name) {
+        if (values == null) {
+            throw new IllegalArgumentException(name + " must not be null");
+        }
+        for (byte[] value : values) {
+            if (value == null || value.length != HASH_BYTES) {
+                throw new IllegalArgumentException(name + " values must be exactly " + HASH_BYTES + " bytes long");
+            }
+        }
+    }
+
+    private static byte[] hash(byte[] data) {
+        try {
+            return MessageDigest.getInstance("SHA-256").digest(data);
+        } catch (NoSuchAlgorithmException e) {
+            throw new AssertionError("SHA-256 is required by the Java SE specification", e);
+        }
+    }
+
+    private static byte[][] deepCopy(byte[][] values) {
+        byte[][] copy = new byte[values.length][];
+        for (int i = 0; i < values.length; i++) {
+            copy[i] = values[i].clone();
+        }
+        return copy;
+    }
+}