[PATCH v3 6/6] rslib: Fix integer overflow on large fcr or prim

From: Zhang Boyang
Date: Mon Jun 20 2022 - 02:21:10 EST

Current rslib support symsize up to 16, so the max value of rs->nn can
be 0xFFFF. Since fcr <= nn, prim <= nn, multiplications on them can
overflow easily, e.g. fcr*root[j], fcr*prim.

This patch fixes these problems by introducing rs_modnn_mul(a, b). This
function is same as rs_modnn(a*b) but it will avoid overflow when
calculating a*b. It requires 0 <= a <= nn && 0 <= b <= nn, because it
use uint32_t to do the multiplication internally, so there will be no
overflow as long as 0 <= a <= nn <= 0xFFFF && 0 <= b <= nn <= 0xFFFF. In
fact, if we use `unsigned int' everywhere, there is no need to have
rs_modnn_mul(). But the `unsigned int' approach has poor scalability and
it may bring us to the mess of signed and unsigned integers.

With rs_modnn(), the intermediate result is now restricted to [0, nn).
This enables us to use rs_modnn_fast(a+b) to replace rs_modnn(a+b), as
long as 0 <= a+b < 2*nn. The most common case is one addend in [0, nn]
and the other addend in [0, nn). The examples of values in [0, nn] are
fcr, prim, indexes taken from rs->index_of[0...nn], etc. The examples of
values in [0, nn) are results from rs_modnn(), indexes taken from
rs->index_of[1...nn], etc.

Since the roots of RS generator polynomial, i.e. (fcr+i)*prim%nn, is
often used. It's now precomputed into rs->genroot[], to avoid writing
rs_modnn_mul(rs, rs_modnn_fast(rs, fcr + i), prim) everywhere.

The algorithm of searching for rs->iprim is also changed. Instead of
searching for (1+what*nn)%prim == 0, then iprim = (1+what*nn)/prim, it
now searches for iprim*prim%nn == 1 directly.

A new test case is also added to test_rslib.c to ensure correctness.

Signed-off-by: Zhang Boyang <zhangboyang.id@xxxxxxxxx>
---
include/linux/rslib.h | 23 +++++++++++++
lib/reed_solomon/decode_rs.c | 60 +++++++++++++++++++--------------
lib/reed_solomon/reed_solomon.c | 30 ++++++++++++-----
lib/reed_solomon/test_rslib.c | 8 ++---
4 files changed, 83 insertions(+), 38 deletions(-)

diff --git a/include/linux/rslib.h b/include/linux/rslib.h
index a277a178157b..a11ea5e8eb14 100644
--- a/include/linux/rslib.h
+++ b/include/linux/rslib.h
@@ -22,6 +22,7 @@
* @alpha_to: exp() lookup table
* @index_of: log() lookup table
* @genpoly: Generator polynomial
+ * @genroot: Roots of generator polynomial, index form
* @nroots: Number of generator roots = number of parity symbols
* @fcr: First consecutive root, index form
* @prim: Primitive element, index form
@@ -37,6 +38,7 @@ struct rs_codec {
uint16_t *alpha_to;
uint16_t *index_of;
uint16_t *genpoly;
+ uint16_t *genroot;
int nroots;
int fcr;
int prim;
@@ -128,6 +130,27 @@ static inline int rs_modnn(struct rs_codec *rs, int x)
return x;
}

+/**
+ * rs_modnn_mul() - Modulo replacement for galois field arithmetics
+ *
+ * @rs: Pointer to the RS codec
+ * @a: 0 <= a <= nn ; a*b is the value to reduce
+ * @b: 0 <= b <= nn ; a*b is the value to reduce
+ *
+ * Same as rs_modnn(a*b), but avoid integer overflow when calculating a*b
+*/
+static inline int rs_modnn_mul(struct rs_codec *rs, int a, int b)
+{
+ /* nn <= 0xFFFF, so (a * b) will not overflow uint32_t */
+ uint32_t x = (uint32_t)a * (uint32_t)b;
+ uint32_t nn = (uint32_t)rs->nn;
+ while (x >= nn) {
+ x -= nn;
+ x = (x >> rs->mm) + (x & nn);
+ }
+ return (int)x;
+}
+
/**
* rs_modnn_fast() - Modulo replacement for galois field arithmetics
*
diff --git a/lib/reed_solomon/decode_rs.c b/lib/reed_solomon/decode_rs.c
index 6c1d53d1b702..3387465ab429 100644
--- a/lib/reed_solomon/decode_rs.c
+++ b/lib/reed_solomon/decode_rs.c
@@ -20,6 +20,7 @@
int iprim = rs->iprim;
uint16_t *alpha_to = rs->alpha_to;
uint16_t *index_of = rs->index_of;
+ uint16_t *genroot = rs->genroot;
uint16_t u, q, tmp, num1, num2, den, discr_r, syn_error;
int count = 0;
int num_corrected;
@@ -69,8 +70,8 @@
} else {
syn[i] = ((((uint16_t) data[j]) ^
invmsk) & msk) ^
- alpha_to[rs_modnn(rs, index_of[syn[i]] +
- (fcr + i) * prim)];
+ alpha_to[rs_modnn_fast(rs,
+ index_of[syn[i]] + genroot[i])];
}
}
}
@@ -81,8 +82,8 @@
syn[i] = ((uint16_t) par[j]) & msk;
} else {
syn[i] = (((uint16_t) par[j]) & msk) ^
- alpha_to[rs_modnn(rs, index_of[syn[i]] +
- (fcr+i)*prim)];
+ alpha_to[rs_modnn_fast(rs,
+ index_of[syn[i]] + genroot[i])];
}
}
}
@@ -108,15 +109,17 @@

if (no_eras > 0) {
/* Init lambda to be the erasure locator polynomial */
- lambda[1] = alpha_to[rs_modnn(rs,
- prim * (nn - 1 - (eras_pos[0] + pad)))];
+ lambda[1] = alpha_to[rs_modnn_mul(rs,
+ prim, (nn - 1 - (eras_pos[0] + pad)))];
for (i = 1; i < no_eras; i++) {
- u = rs_modnn(rs, prim * (nn - 1 - (eras_pos[i] + pad)));
+ u = rs_modnn_mul(rs,
+ prim, (nn - 1 - (eras_pos[i] + pad)));
for (j = i + 1; j > 0; j--) {
tmp = index_of[lambda[j - 1]];
if (tmp != nn) {
lambda[j] ^=
- alpha_to[rs_modnn(rs, u + tmp)];
+ alpha_to[rs_modnn_fast(rs,
+ u + tmp)];
}
}
}
@@ -137,9 +140,9 @@
for (i = 0; i < r; i++) {
if ((lambda[i] != 0) && (s[r - i - 1] != nn)) {
discr_r ^=
- alpha_to[rs_modnn(rs,
- index_of[lambda[i]] +
- s[r - i - 1])];
+ alpha_to[rs_modnn_fast(rs,
+ index_of[lambda[i]] +
+ s[r - i - 1])];
}
}
discr_r = index_of[discr_r]; /* Index form */
@@ -153,8 +156,8 @@
for (i = 0; i < nroots; i++) {
if (b[i] != nn) {
t[i + 1] = lambda[i + 1] ^
- alpha_to[rs_modnn(rs, discr_r +
- b[i])];
+ alpha_to[rs_modnn_fast(rs,
+ discr_r + b[i])];
} else
t[i + 1] = lambda[i + 1];
}
@@ -166,8 +169,9 @@
*/
for (i = 0; i <= nroots; i++) {
b[i] = (lambda[i] == 0) ? nn :
- rs_modnn(rs, index_of[lambda[i]]
- - discr_r + nn);
+ rs_modnn_fast(rs,
+ index_of[lambda[i]] +
+ nn - discr_r);
}
} else {
/* 2 lines below: B(x) <-- x*B(x) */
@@ -197,11 +201,11 @@
/* Find roots of error+erasure locator polynomial by Chien search */
memcpy(&reg[1], &lambda[1], nroots * sizeof(reg[0]));
count = 0; /* Number of roots of lambda(x) */
- for (i = 1, k = iprim - 1; i <= nn; i++, k = rs_modnn(rs, k + iprim)) {
+ for (i = 1, k = iprim-1; i <= nn; i++, k = rs_modnn_fast(rs, k+iprim)) {
q = alpha_to[0]; /* lambda[0] is always 0 */
for (j = deg_lambda; j > 0; j--) {
if (reg[j] != nn) {
- reg[j] = rs_modnn(rs, reg[j] + j);
+ reg[j] = rs_modnn_fast(rs, reg[j] + j);
q ^= alpha_to[reg[j]];
}
}
@@ -238,8 +242,8 @@
tmp = 0;
for (j = i; j >= 0; j--) {
if ((s[i - j] != nn) && (lambda[j] != nn))
- tmp ^=
- alpha_to[rs_modnn(rs, s[i - j] + lambda[j])];
+ tmp ^= alpha_to[rs_modnn_fast(rs,
+ s[i - j] + lambda[j])];
}
omega[i] = index_of[tmp];
}
@@ -254,8 +258,9 @@
num1 = 0;
for (i = deg_omega; i >= 0; i--) {
if (omega[i] != nn)
- num1 ^= alpha_to[rs_modnn(rs, omega[i] +
- i * root[j])];
+ num1 ^= alpha_to[rs_modnn_fast(rs,
+ omega[i] +
+ rs_modnn_mul(rs, i, root[j]))];
}

if (num1 == 0) {
@@ -264,15 +269,18 @@
continue;
}

- num2 = alpha_to[rs_modnn(rs, root[j] * (fcr - 1) + nn)];
+ num2 = alpha_to[rs_modnn_fast(rs,
+ rs_modnn_mul(rs, root[j], fcr) +
+ nn - root[j])];
den = 0;

/* lambda[i+1] for i even is the formal derivative
* lambda_pr of lambda[i] */
for (i = min(deg_lambda, nroots - 1) & ~1; i >= 0; i -= 2) {
if (lambda[i + 1] != nn) {
- den ^= alpha_to[rs_modnn(rs, lambda[i + 1] +
- i * root[j])];
+ den ^= alpha_to[rs_modnn_fast(rs,
+ lambda[i + 1] +
+ rs_modnn_mul(rs, i, root[j]))];
}
}

@@ -292,8 +300,8 @@
if (b[j] == 0)
continue;

- k = (fcr + i) * prim * (nn-loc[j]-1);
- tmp ^= alpha_to[rs_modnn(rs, index_of[b[j]] + k)];
+ k = rs_modnn_mul(rs, genroot[i], nn - loc[j] - 1);
+ tmp ^= alpha_to[rs_modnn_fast(rs, index_of[b[j]] + k)];
}

if (tmp != alpha_to[s[i]])
diff --git a/lib/reed_solomon/reed_solomon.c b/lib/reed_solomon/reed_solomon.c
index da46026a60b8..2c86e4dfcbaa 100644
--- a/lib/reed_solomon/reed_solomon.c
+++ b/lib/reed_solomon/reed_solomon.c
@@ -100,6 +100,10 @@ static struct rs_codec *codec_init(int symsize, int gfpoly, int (*gffunc)(int),
if(rs->genpoly == NULL)
goto err;

+ rs->genroot = kmalloc_array(rs->nroots, sizeof(uint16_t), gfp);
+ if(rs->genroot == NULL)
+ goto err;
+
/* Generate Galois field lookup tables */
rs->index_of[0] = rs->nn; /* log(zero) = -inf */
rs->alpha_to[rs->nn] = 0; /* alpha**-inf = 0 */
@@ -126,26 +130,34 @@ static struct rs_codec *codec_init(int symsize, int gfpoly, int (*gffunc)(int),
goto err;

/* Find prim-th root of 1, used in decoding */
- for(iprim = 1; (iprim % prim) != 0; iprim += rs->nn);
+ for (iprim = 1; rs_modnn_mul(rs, iprim, prim) != 1; iprim++);
/* prim-th root of 1, index form */
- rs->iprim = iprim / prim;
+ rs->iprim = iprim;
+
+ /* Precompute generator polynomial roots */
+ root = rs_modnn_mul(rs, fcr, prim);
+ for (i = 0; i < nroots; i++) {
+ rs->genroot[i] = root; /* = (fcr + i) * prim % nn */
+ root = rs_modnn_fast(rs, root + prim);
+ }

/* Form RS code generator polynomial from its roots */
rs->genpoly[0] = rs->alpha_to[0];
- for (i = 0, root = fcr * prim; i < nroots; i++, root += prim) {
+ for (i = 0; i < nroots; i++) {
+ root = rs->genroot[i];
rs->genpoly[i + 1] = rs->alpha_to[0];
/* Multiply rs->genpoly[] by @**(root + x) */
for (j = i; j > 0; j--) {
if (rs->genpoly[j] != 0) {
- rs->genpoly[j] = rs->genpoly[j -1] ^
- rs->alpha_to[rs_modnn(rs,
+ rs->genpoly[j] = rs->genpoly[j - 1] ^
+ rs->alpha_to[rs_modnn_fast(rs,
rs->index_of[rs->genpoly[j]] + root)];
} else
rs->genpoly[j] = rs->genpoly[j - 1];
}
/* rs->genpoly[0] can never be zero */
rs->genpoly[0] =
- rs->alpha_to[rs_modnn(rs,
+ rs->alpha_to[rs_modnn_fast(rs,
rs->index_of[rs->genpoly[0]] + root)];
}
/* convert rs->genpoly[] to index form for quicker encoding */
@@ -157,6 +169,7 @@ static struct rs_codec *codec_init(int symsize, int gfpoly, int (*gffunc)(int),
return rs;

err:
+ kfree(rs->genroot);
kfree(rs->genpoly);
kfree(rs->index_of);
kfree(rs->alpha_to);
@@ -188,6 +201,7 @@ void free_rs(struct rs_control *rs)
kfree(cd->alpha_to);
kfree(cd->index_of);
kfree(cd->genpoly);
+ kfree(cd->genroot);
kfree(cd);
}
mutex_unlock(&rslistlock);
@@ -340,7 +354,7 @@ EXPORT_SYMBOL_GPL(encode_rs8);
* @data: data field of a given type
* @par: received parity data field
* @len: data length
- * @s: syndrome data field, must be in index form
+ * @s: syndrome data field, must be in index form, 0 <= index <= nn
* (if NULL, syndrome is calculated)
* @no_eras: number of erasures
* @eras_pos: position of erasures, can be NULL
@@ -393,7 +407,7 @@ EXPORT_SYMBOL_GPL(encode_rs16);
* @data: data field of a given type
* @par: received parity data field
* @len: data length
- * @s: syndrome data field, must be in index form
+ * @s: syndrome data field, must be in index form, 0 <= index <= nn
* (if NULL, syndrome is calculated)
* @no_eras: number of erasures
* @eras_pos: position of erasures, can be NULL
diff --git a/lib/reed_solomon/test_rslib.c b/lib/reed_solomon/test_rslib.c
index d9d1c33aebda..a03c7249f920 100644
--- a/lib/reed_solomon/test_rslib.c
+++ b/lib/reed_solomon/test_rslib.c
@@ -55,6 +55,7 @@ static struct etab Tab[] = {
{8, 0x11d, 1, 1, 30, 100 },
{8, 0x187, 112, 11, 32, 100 },
{9, 0x211, 1, 1, 33, 80 },
+ {16, 0x1ffed, 65534, 65534, 50, 5 },
{0, 0, 0, 0, 0, 0},
};

@@ -232,9 +233,8 @@ static void compute_syndrome(struct rs_control *rsc, uint16_t *data,
struct rs_codec *rs = rsc->codec;
uint16_t *alpha_to = rs->alpha_to;
uint16_t *index_of = rs->index_of;
+ uint16_t *genroot = rs->genroot;
int nroots = rs->nroots;
- int prim = rs->prim;
- int fcr = rs->fcr;
int i, j;

/* Calculating syndrome */
@@ -245,8 +245,8 @@ static void compute_syndrome(struct rs_control *rsc, uint16_t *data,
syn[i] = data[j];
} else {
syn[i] = data[j] ^
- alpha_to[rs_modnn(rs, index_of[syn[i]]
- + (fcr + i) * prim)];
+ alpha_to[rs_modnn_fast(rs,
+ index_of[syn[i]] + genroot[i])];
}
}
}
--
2.30.2