Add Reed-Solomon user-space decoding lib.

lib/Makemodule.am

@@ -77,6 +77,7 @@ libcryptsetup_la_SOURCES = \
 	lib/verity/verity.c		\
 	lib/verity/verity.h		\
 	lib/verity/rs_encode_char.c	\
+	lib/verity/rs_decode_char.c	\
 	lib/verity/rs.h                 \
 	lib/luks2/luks2_disk_metadata.c	\
 	lib/luks2/luks2_json_format.c	\

lib/verity/rs.h

@@ -23,13 +23,41 @@
 #ifndef _LIBFEC_RS_H
 #define _LIBFEC_RS_H
 
+/* Special reserved value encoding zero in index form. */
+#define A0 (rs->nn)
+
+#define RS_MIN(a, b) ((a) < (b) ? (a) : (b))
+
 typedef unsigned char data_t;
-struct rs;
+
+/* Reed-Solomon codec control block */
+struct rs {
+	int mm;          /* Bits per symbol */
+	int nn;          /* Symbols per block (= (1<<mm)-1) */
+	data_t *alpha_to;/* log lookup table */
+	data_t *index_of;/* Antilog lookup table */
+	data_t *genpoly; /* Generator polynomial */
+	int nroots;      /* Number of generator roots = number of parity symbols */
+	int fcr;         /* First consecutive root, index form */
+	int prim;        /* Primitive element, index form */
+	int iprim;       /* prim-th root of 1, index form */
+	int pad;         /* Padding bytes in shortened block */
+};
+
+static inline int modnn(struct rs *rs, int x)
+{
+	while (x >= rs->nn) {
+		x -= rs->nn;
+		x = (x >> rs->mm) + (x & rs->nn);
+	}
+	return x;
+}
 
 struct rs *init_rs_char(int symsize, int gfpoly, int fcr, int prim, int nroots, int pad);
 void free_rs_char(struct rs *rs);
 
 /* General purpose RS codec, 8-bit symbols */
 void encode_rs_char(struct rs *rs, data_t *data, data_t *parity);
+int decode_rs_char(struct rs *rs, data_t *data);
 
 #endif

lib/verity/rs_decode_char.c

@@ -0,0 +1,197 @@
+/*
+ * Reed-Solomon decoder, based on libfec
+ *
+ * Copyright (C) 2002, Phil Karn, KA9Q
+ * libcryptsetup modifications
+ *   Copyright (C) 2017-2018, Red Hat, Inc. All rights reserved.
+ *
+ * This file is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU Lesser General Public
+ * License as published by the Free Software Foundation; either
+ * version 2.1 of the License, or (at your option) any later version.
+ *
+ * This file is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * Lesser General Public License for more details.
+ *
+ * You should have received a copy of the GNU Lesser General Public
+ * License along with this file; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+ */
+
+#include <string.h>
+#include <stdlib.h>
+
+#include "rs.h"
+
+int decode_rs_char(struct rs* rs, data_t* data)
+{
+	int deg_lambda, el, deg_omega, syn_error, count;
+	int i, j, r, k;
+	data_t q, tmp, num1, num2, den, discr_r;
+	/* FIXME: remove VLAs here */
+	data_t lambda[rs->nroots + 1], s[rs->nroots]; /* Err+Eras Locator poly and syndrome poly */
+	data_t b[rs->nroots + 1], t[rs->nroots + 1], omega[rs->nroots + 1];
+	data_t root[rs->nroots], reg[rs->nroots + 1], loc[rs->nroots];
+
+	memset(s, 0, rs->nroots * sizeof(data_t));
+	memset(b, 0, (rs->nroots + 1) * sizeof(data_t));
+
+	/* form the syndromes; i.e., evaluate data(x) at roots of g(x) */
+	for (i = 0; i < rs->nroots; i++)
+		s[i] = data[0];
+
+	for (j = 1; j < rs->nn - rs->pad; j++) {
+		for (i = 0; i < rs->nroots; i++) {
+			if (s[i] == 0) {
+				s[i] = data[j];
+			} else {
+				s[i] = data[j] ^ rs->alpha_to[modnn(rs, rs->index_of[s[i]] + (rs->fcr + i) * rs->prim)];
+			}
+		}
+	}
+
+	/* Convert syndromes to index form, checking for nonzero condition */
+	syn_error = 0;
+	for (i = 0; i < rs->nroots; i++) {
+		syn_error |= s[i];
+		s[i] = rs->index_of[s[i]];
+	}
+
+	/*
+	 * if syndrome is zero, data[] is a codeword and there are no
+	 * errors to correct. So return data[] unmodified
+	 */
+	if (!syn_error)
+		return 0;
+
+	memset(&lambda[1], 0, rs->nroots * sizeof(lambda[0]));
+	lambda[0] = 1;
+
+	for (i   = 0; i < rs->nroots + 1; i++)
+		b[i] = rs->index_of[lambda[i]];
+
+	/*
+	 * Begin Berlekamp-Massey algorithm to determine error+erasure
+	 * locator polynomial
+	 */
+	r  = 0;
+	el = 0;
+	while (++r <= rs->nroots) { /* r is the step number */
+		/* Compute discrepancy at the r-th step in poly-form */
+		discr_r = 0;
+		for (i = 0; i < r; i++) {
+			if ((lambda[i] != 0) && (s[r - i - 1] != A0)) {
+				discr_r ^= rs->alpha_to[modnn(rs, rs->index_of[lambda[i]] + s[r - i - 1])];
+			}
+		}
+		discr_r = rs->index_of[discr_r]; /* Index form */
+		if (discr_r == A0) {
+			/* 2 lines below: B(x) <-- x*B(x) */
+			memmove(&b[1], b, rs->nroots * sizeof(b[0]));
+			b[0] = A0;
+		} else {
+			/* 7 lines below: T(x) <-- lambda(x) - discr_r*x*b(x) */
+			t[0] = lambda[0];
+			for (i = 0; i < rs->nroots; i++) {
+				if (b[i] != A0)
+					t[i + 1] = lambda[i + 1] ^ rs->alpha_to[modnn(rs, discr_r + b[i])];
+				else
+					t[i + 1] = lambda[i + 1];
+			}
+			if (2 * el <= r - 1) {
+				el = r - el;
+				/*
+				 * 2 lines below: B(x) <-- inv(discr_r) *
+				 * lambda(x)
+				 */
+				for (i   = 0; i <= rs->nroots; i++)
+					b[i] = (lambda[i] == 0) ? A0 : modnn(rs, rs->index_of[lambda[i]] - discr_r + rs->nn);
+			} else {
+				/* 2 lines below: B(x) <-- x*B(x) */
+				memmove(&b[1], b, rs->nroots * sizeof(b[0]));
+				b[0] = A0;
+			}
+			memcpy(lambda, t, (rs->nroots + 1) * sizeof(t[0]));
+		}
+	}
+
+	/* Convert lambda to index form and compute deg(lambda(x)) */
+	deg_lambda = 0;
+	for (i = 0; i < rs->nroots + 1; i++) {
+		lambda[i] = rs->index_of[lambda[i]];
+		if (lambda[i] != A0)
+			deg_lambda = i;
+	}
+	/* Find roots of the error+erasure locator polynomial by Chien search */
+	memcpy(&reg[1], &lambda[1], rs->nroots * sizeof(reg[0]));
+	count = 0; /* Number of roots of lambda(x) */
+	for (i = 1, k = rs->iprim - 1; i <= rs->nn; i++, k = modnn(rs, k + rs->iprim)) {
+		q = 1; /* lambda[0] is always 0 */
+		for (j = deg_lambda; j > 0; j--) {
+			if (reg[j] != A0) {
+				reg[j] = modnn(rs, reg[j] + j);
+				q ^= rs->alpha_to[reg[j]];
+			}
+		}
+		if (q != 0)
+			continue; /* Not a root */
+
+		/* store root (index-form) and error location number */
+		root[count] = i;
+		loc[count]  = k;
+		/* If we've already found max possible roots, abort the search to save time */
+		if (++count == deg_lambda)
+			break;
+	}
+
+	/*
+	 * deg(lambda) unequal to number of roots => uncorrectable
+	 * error detected
+	 */
+	if (deg_lambda != count)
+		return -1;
+
+	/*
+	 * Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo
+	 * x**rs->nroots). in index form. Also find deg(omega).
+	 */
+	deg_omega = deg_lambda - 1;
+	for (i = 0; i <= deg_omega; i++) {
+		tmp = 0;
+		for (j = i; j >= 0; j--) {
+			if ((s[i - j] != A0) && (lambda[j] != A0))
+				tmp ^= rs->alpha_to[modnn(rs, s[i - j] + lambda[j])];
+		}
+		omega[i] = rs->index_of[tmp];
+	}
+
+	/*
+	 * Compute error values in poly-form. num1 = omega(inv(X(l))), num2 =
+	 * inv(X(l))**(rs->fcr-1) and den = lambda_pr(inv(X(l))) all in poly-form
+	 */
+	for (j = count - 1; j >= 0; j--) {
+		num1 = 0;
+		for (i = deg_omega; i >= 0; i--) {
+			if (omega[i] != A0)
+				num1 ^= rs->alpha_to[modnn(rs, omega[i] + i * root[j])];
+		}
+		num2 = rs->alpha_to[modnn(rs, root[j] * (rs->fcr - 1) + rs->nn)];
+		den  = 0;
+
+		/* lambda[i+1] for i even is the formal derivative lambda_pr of lambda[i] */
+		for (i = RS_MIN(deg_lambda, rs->nroots - 1) & ~1; i >= 0; i -= 2) {
+			if (lambda[i + 1] != A0)
+				den ^= rs->alpha_to[modnn(rs, lambda[i + 1] + i * root[j])];
+		}
+
+		/* Apply error to data */
+		if (num1 != 0 && loc[j] >= rs->pad) {
+			data[loc[j] - rs->pad] ^= rs->alpha_to[modnn(rs, rs->index_of[num1] +
+						  rs->index_of[num2] + rs->nn - rs->index_of[den])];
+		}
+	}
+
+	return count;
+}

lib/verity/rs_encode_char.c

@@ -25,32 +25,6 @@
 
 #include "rs.h"
 
-/* Special reserved value encoding zero in index form. */
-#define A0 (rs->nn)
-
-/* Reed-Solomon codec control block */
-struct rs {
-	int mm;          /* Bits per symbol */
-	int nn;          /* Symbols per block (= (1<<mm)-1) */
-	data_t *alpha_to;/* log lookup table */
-	data_t *index_of;/* Antilog lookup table */
-	data_t *genpoly; /* Generator polynomial */
-	int nroots;      /* Number of generator roots = number of parity symbols */
-	int fcr;         /* First consecutive root, index form */
-	int prim;        /* Primitive element, index form */
-	int iprim;       /* prim-th root of 1, index form */
-	int pad;         /* Padding bytes in shortened block */
-};
-
-static inline int modnn(struct rs *rs, int x)
-{
-	while (x >= rs->nn) {
-		x -= rs->nn;
-		x = (x >> rs->mm) + (x & rs->nn);
-	}
-	return x;
-}
-
 /* Initialize a Reed-Solomon codec
  * symsize = symbol size, bits
  * gfpoly = Field generator polynomial coefficients