return CRYPTO_get_ex_data(&r->ex_data, idx);
}
+/*
+ * Define a scaling constant for our fixed point arithmetic.
+ * This value must be a power of two because the base two logarithm code
+ * makes this assumption. The exponent must also be a multiple of three so
+ * that the scale factor has an exact cube root. Finally, the scale factor
+ * should not be so large that a multiplication of two scaled numbers
+ * overflows a 64 bit unsigned integer.
+ */
+static const unsigned int scale = 1 << 18;
+static const unsigned int cbrt_scale = 1 << (2 * 18 / 3);
+
+/* Define some constants, none exceed 32 bits */
+static const unsigned int log_2 = 0x02c5c8; /* scale * log(2) */
+static const unsigned int log_e = 0x05c551; /* scale * log2(M_E) */
+static const unsigned int c1_923 = 0x07b126; /* scale * 1.923 */
+static const unsigned int c4_690 = 0x12c28f; /* scale * 4.690 */
+
+/*
+ * Multiply two scale integers together and rescale the result.
+ */
+static ossl_inline uint64_t mul2(uint64_t a, uint64_t b)
+{
+ return a * b / scale;
+}
+
+/*
+ * Calculate the cube root of a 64 bit scaled integer.
+ * Although the cube root of a 64 bit number does fit into a 32 bit unsigned
+ * integer, this is not guaranteed after scaling, so this function has a
+ * 64 bit return. This uses the shifting nth root algorithm with some
+ * algebraic simplifications.
+ */
+static uint64_t icbrt64(uint64_t x)
+{
+ uint64_t r = 0;
+ uint64_t b;
+ int s;
+
+ for (s = 63; s >= 0; s -= 3) {
+ r <<= 1;
+ b = 3 * r * (r + 1) + 1;
+ if ((x >> s) >= b) {
+ x -= b << s;
+ r++;
+ }
+ }
+ return r * cbrt_scale;
+}
+
+/*
+ * Calculate the natural logarithm of a 64 bit scaled integer.
+ * This is done by calculating a base two logarithm and scaling.
+ * The maximum logarithm (base 2) is 64 and this reduces base e, so
+ * a 32 bit result should not overflow. The argument passed must be
+ * greater than unity so we don't need to handle negative results.
+ */
+static uint32_t ilog_e(uint64_t v)
+{
+ uint32_t i, r = 0;
+
+ /*
+ * Scale down the value into the range 1 .. 2.
+ *
+ * If fractional numbers need to be processed, another loop needs
+ * to go here that checks v < scale and if so multiplies it by 2 and
+ * reduces r by scale. This also means making r signed.
+ */
+ while (v >= 2 * scale) {
+ v >>= 1;
+ r += scale;
+ }
+ for (i = scale / 2; i != 0; i /= 2) {
+ v = mul2(v, v);
+ if (v >= 2 * scale) {
+ v >>= 1;
+ r += i;
+ }
+ }
+ r = (r * (uint64_t)scale) / log_e;
+ return r;
+}
+
+/*
+ * NIST SP 800-56B rev 2 Appendix D: Maximum Security Strength Estimates for IFC
+ * Modulus Lengths.
+ *
+ * E = \frac{1.923 \sqrt[3]{nBits \cdot log_e(2)}
+ * \cdot(log_e(nBits \cdot log_e(2))^{2/3} - 4.69}{log_e(2)}
+ * The two cube roots are merged together here.
+ */
+static uint16_t rsa_compute_security_bits(int n)
+{
+ uint64_t x;
+ uint32_t lx;
+ uint16_t y;
+
+ /* Look for common values as listed in SP 800-56B rev 2 Appendix D */
+ switch (n) {
+ case 2048:
+ return 112;
+ case 3072:
+ return 128;
+ case 4096:
+ return 152;
+ case 6144:
+ return 176;
+ case 8192:
+ return 200;
+ }
+ /*
+ * The first incorrect result (i.e. not accurate or off by one low) occurs
+ * for n = 699668. The true value here is 1200. Instead of using this n
+ * as the check threshold, the smallest n such that the correct result is
+ * 1200 is used instead.
+ */
+ if (n >= 687737)
+ return 1200;
+ if (n < 8)
+ return 0;
+
+ x = n * (uint64_t)log_2;
+ lx = ilog_e(x);
+ y = (uint16_t)((mul2(c1_923, icbrt64(mul2(mul2(x, lx), lx))) - c4_690)
+ / log_2);
+ return (y + 4) & ~7;
+}
+
int RSA_security_bits(const RSA *rsa)
{
int bits = BN_num_bits(rsa->n);
if (ex_primes <= 0 || (ex_primes + 2) > rsa_multip_cap(bits))
return 0;
}
- return BN_security_bits(bits, -1);
+ return rsa_compute_security_bits(bits);
}
int RSA_set0_key(RSA *r, BIGNUM *n, BIGNUM *e, BIGNUM *d)