diff --git a/library/constant_time.h b/library/constant_time.h
index cdc5f85..3c7502f 100644
--- a/library/constant_time.h
+++ b/library/constant_time.h
@@ -30,53 +30,241 @@
 #include <stddef.h>
 
 
+/** Constant-time buffer comparison without branches.
+ *
+ * This is equivalent to the standard memncmp function, but is likely to be
+ * compiled to code using bitwise operation rather than a branch.
+ *
+ * This function can be used to write constant-time code by replacing branches
+ * with bit operations using masks.
+ *
+ * This function is implemented without using comparison operators, as those
+ * might be translated to branches by some compilers on some platforms.
+ *
+ * \param a     Pointer to the first buffer.
+ * \param b     Pointer to the second buffer.
+ * \param n     The number of bytes to compare in the buffer.
+ *
+ * \return      Zero if the content of the two buffer is the same,
+ *              otherwise non-zero.
+ */
 int mbedtls_cf_memcmp( const void *a,
                        const void *b,
                        size_t n );
 
+/** Turn a value into a mask:
+ * - if \p value == 0, return the all-bits 0 mask, aka 0
+ * - otherwise, return the all-bits 1 mask, aka (size_t) -1
+ *
+ * This function can be used to write constant-time code by replacing branches
+ * with bit operations using masks.
+ *
+ * This function is implemented without using comparison operators, as those
+ * might be translated to branches by some compilers on some platforms.
+ *
+ * \param value     The value to analyze.
+ *
+ * \return          Zero if \p value is zero, otherwise all-bits-one.
+ */
 unsigned mbedtls_cf_uint_mask( unsigned value );
 
+/** Turn a value into a mask:
+ * - if \p value == 0, return the all-bits 0 mask, aka 0
+ * - otherwise, return the all-bits 1 mask, aka (size_t) -1
+ *
+ * This function can be used to write constant-time code by replacing branches
+ * with bit operations using masks.
+ *
+ * This function is implemented without using comparison operators, as those
+ * might be translated to branches by some compilers on some platforms.
+ *
+ * \param value     The value to analyze.
+ *
+ * \return          Zero if \p value is zero, otherwise all-bits-one.
+ */
 size_t mbedtls_cf_size_mask( size_t value );
 
 #if defined(MBEDTLS_BIGNUM_C)
 
+/** Turn a value into a mask:
+ * - if \p value == 0, return the all-bits 0 mask, aka 0
+ * - otherwise, return the all-bits 1 mask, aka (size_t) -1
+ *
+ * This function can be used to write constant-time code by replacing branches
+ * with bit operations using masks.
+ *
+ * This function is implemented without using comparison operators, as those
+ * might be translated to branches by some compilers on some platforms.
+ *
+ * \param value     The value to analyze.
+ *
+ * \return          Zero if \p value is zero, otherwise all-bits-one.
+ */
 mbedtls_mpi_uint mbedtls_cf_mpi_uint_mask( mbedtls_mpi_uint value );
 
 #endif /* MBEDTLS_BIGNUM_C */
 
+/** Constant-flow mask generation for "less than" comparison:
+ * - if \p x < \p y, return all-bits 1, that is (size_t) -1
+ * - otherwise, return all bits 0, that is 0
+ *
+ * This function can be used to write constant-time code by replacing branches
+ * with bit operations using masks.
+ *
+ * This function is implemented without using comparison operators, as those
+ * might be translated to branches by some compilers on some platforms.
+ *
+ * \param x     The first value to analyze.
+ * \param y     The second value to analyze.
+ *
+ * \return      All-bits-one if \p x is less than \p y, otherwise zero.
+ */
 size_t mbedtls_cf_size_mask_lt( size_t x,
                                 size_t y );
 
+/** Constant-flow mask generation for "greater or equal" comparison:
+ * - if \p x >= \p y, return all-bits 1, that is (size_t) -1
+ * - otherwise, return all bits 0, that is 0
+ *
+ * This function can be used to write constant-time code by replacing branches
+ * with bit operations using masks.
+ *
+ * This function is implemented without using comparison operators, as those
+ * might be translated to branches by some compilers on some platforms.
+ *
+ * \param x     The first value to analyze.
+ * \param y     The second value to analyze.
+ *
+ * \return      All-bits-one if \p x is greater or equal than \p y,
+ *              otherwise zero.
+ */
 size_t mbedtls_cf_size_mask_ge( size_t x,
                                 size_t y );
 
+/** Constant-flow boolean "equal" comparison:
+ * return x == y
+ *
+ * This is equivalent to \p x == \p y, but is likely to be compiled
+ * to code using bitwise operation rather than a branch.
+ *
+ * This function is implemented without using comparison operators, as those
+ * might be translated to branches by some compilers on some platforms.
+ *
+ * \param x     The first value to analyze.
+ * \param y     The second value to analyze.
+ *
+ * \return      1 if \p x equals to \p y, otherwise 0.
+ */
 unsigned mbedtls_cf_size_bool_eq( size_t x,
                                   size_t y );
 
+/** Constant-flow "greater than" comparison:
+ * return x > y
+ *
+ * This is equivalent to \p x > \p y, but is likely to be compiled
+ * to code using bitwise operation rather than a branch.
+ *
+ * This function is implemented without using comparison operators, as those
+ * might be translated to branches by some compilers on some platforms.
+ *
+ * \param x     The first value to analyze.
+ * \param y     The second value to analyze.
+ *
+ * \return      1 if \p x greater than \p y, otherwise 0.
+ */
 unsigned mbedtls_cf_size_gt( size_t x,
                              size_t y );
 
 #if defined(MBEDTLS_BIGNUM_C)
 
+/** Decide if an integer is less than the other, without branches.
+ *
+ * This is equivalent to \p x < \p y, but is likely to be compiled
+ * to code using bitwise operation rather than a branch.
+ *
+ * This function is implemented without using comparison operators, as those
+ * might be translated to branches by some compilers on some platforms.
+ *
+ * \param x     The first value to analyze.
+ * \param y     The second value to analyze.
+ *
+ * \return      1 if \p x is less than \p y, otherwise 0.
+ */
 unsigned mbedtls_cf_mpi_uint_lt( const mbedtls_mpi_uint x,
                                  const mbedtls_mpi_uint y );
 
 #endif /* MBEDTLS_BIGNUM_C */
 
+/** Choose between two integer values without branches.
+ *
+ * This is equivalent to `condition ? if1 : if0`, but is likely to be compiled
+ * to code using bitwise operation rather than a branch.
+ *
+ * This function is implemented without using comparison operators, as those
+ * might be translated to branches by some compilers on some platforms.
+ *
+ * \param condition     Condition to test.
+ * \param if1           Value to use if \p condition is nonzero.
+ * \param if0           Value to use if \p condition is zero.
+ *
+ * \return  \c if1 if \p condition is nonzero, otherwise \c if0.
+ */
 unsigned mbedtls_cf_uint_if( unsigned condition,
                              unsigned if1,
                              unsigned if0 );
 
+/** Choose between two integer values without branches.
+ *
+ * This is equivalent to `condition ? if1 : if0`, but is likely to be compiled
+ * to code using bitwise operation rather than a branch.
+ *
+ * This function is implemented without using comparison operators, as those
+ * might be translated to branches by some compilers on some platforms.
+ *
+ * \param condition     Condition to test.
+ * \param if1           Value to use if \p condition is nonzero.
+ * \param if0           Value to use if \p condition is zero.
+ *
+ * \return  \c if1 if \p condition is nonzero, otherwise \c if0.
+ */
 size_t mbedtls_cf_size_if( unsigned condition,
                            size_t if1,
                            size_t if0 );
 
+/** Select between two sign values witout branches.
+ *
+ * This is functionally equivalent to `condition ? if1 : if0` but uses only bit
+ * operations in order to avoid branches.
+ *
+ * This function is implemented without using comparison operators, as those
+ * might be translated to branches by some compilers on some platforms.
+ *
+ * \param condition     Condition to test.
+ * \param if1           The first sign; must be either +1 or -1.
+ * \param if0           The second sign; must be either +1 or -1.
+ *
+ * \return  \c if1 if \p condition is nonzero, otherwise \c if0. */
 int mbedtls_cf_cond_select_sign( unsigned char condition,
                                  int if1,
                                  int if0 );
 
 #if defined(MBEDTLS_BIGNUM_C)
 
+/** Conditionally assign a value without branches.
+ *
+ * This is equivalent to `if ( condition ) dest = src`, but is likely
+ * to be compiled to code using bitwise operation rather than a branch.
+ *
+ * This function is implemented without using comparison operators, as those
+ * might be translated to branches by some compilers on some platforms.
+ *
+ * \param n             \p dest and \p src must be arrays of limbs of size n.
+ * \param dest          The MPI to conditionally assign to. This must point
+ *                      to an initialized MPI.
+ * \param src           The MPI to be assigned from. This must point to an
+ *                      initialized MPI.
+ * \param condition     Condition to test, must be 0 or 1.
+ */
 void mbedtls_cf_mpi_uint_cond_assign( size_t n,
                                       mbedtls_mpi_uint *dest,
                                       const mbedtls_mpi_uint *src,
@@ -84,10 +272,41 @@
 
 #endif /* MBEDTLS_BIGNUM_C */
 
+
+/** Shift some data towards the left inside a buffer.
+ *
+ * `mbedtls_cf_mem_move_to_left(start, total, offset)` is functionally
+ * equivalent to
+ * ```
+ * memmove(start, start + offset, total - offset);
+ * memset(start + offset, 0, total - offset);
+ * ```
+ * but it strives to use a memory access pattern (and thus total timing)
+ * that does not depend on \p offset. This timing independence comes at
+ * the expense of performance.
+ *
+ * \param start     Pointer to the start of the buffer.
+ * \param total     Total size of the buffer.
+ * \param offset    Offset from which to copy \p total - \p offset bytes.
+ */
 void mbedtls_cf_mem_move_to_left( void *start,
                                   size_t total,
                                   size_t offset );
 
+/** Conditional memcpy without branches.
+ *
+ * This is equivalent to `if ( c1 == c2 ) memcpy(dst, src, len)`, but is likely
+ * to be compiled to code using bitwise operation rather than a branch.
+ *
+ * This function is implemented without using comparison operators, as those
+ * might be translated to branches by some compilers on some platforms.
+ *
+ * \param dest      The pointer to conditionally copy to.
+ * \param src       The pointer to copy from.
+ * \param len       The number of bytes to copy.
+ * \param c1        The first value to analyze in the condition.
+ * \param c2        The second value to analyze in the condition.
+ */
 void mbedtls_cf_memcpy_if_eq( unsigned char *dest,
                               const unsigned char *src,
                               size_t len,
@@ -98,6 +317,7 @@
  * This function copies \p len bytes from \p src_base + \p offset_secret to \p
  * dst, with a code flow and memory access pattern that does not depend on \p
  * offset_secret, but only on \p offset_min, \p offset_max and \p len.
+ * Functionally equivalent to memcpy(dst, src + offset_secret, len).
  *
  * \param dst           The destination buffer. This must point to a writable
  *                      buffer of at least \p len bytes.
@@ -166,6 +386,27 @@
 
 #if defined(MBEDTLS_PKCS1_V15) && defined(MBEDTLS_RSA_C) && !defined(MBEDTLS_RSA_ALT)
 
+/** This function performs the unpadding part of a PKCS#1 v1.5 decryption
+ *  operation (RSAES-PKCS1-v1_5-DECRYPT).
+ *
+ * \note           The output buffer length \c output_max_len should be
+ *                 as large as the size \p ctx->len of \p ctx->N, for example,
+ *                 128 Bytes if RSA-1024 is used, to be able to hold an
+ *                 arbitrary decrypted message. If it is not large enough to
+ *                 hold the decryption of the particular ciphertext provided,
+ *                 the function returns #MBEDTLS_ERR_RSA_OUTPUT_TOO_LARGE.
+ *
+ * \param ilen           The length of the ciphertext.
+ * \param olen           The address at which to store the length of
+ *                       the plaintext. This must not be \c NULL.
+ * \param output         The buffer used to hold the plaintext. This must
+ *                       be a writable buffer of length \p output_max_len Bytes.
+ * \param output_max_len The length in Bytes of the output buffer \p output.
+ * \param buf            The input buffer for the unpadding operation.
+ *
+ * \return         \c 0 on success.
+ * \return         An \c MBEDTLS_ERR_RSA_XXX error code on failure.
+ */
 int mbedtls_cf_rsaes_pkcs1_v15_unpadding( size_t ilen,
                                           size_t *olen,
                                           unsigned char *output,