From 2926484de15cfa6f26ff5a3c55ead699f3fba123 Mon Sep 17 00:00:00 2001 From: Gilles Peskine Date: Tue, 27 Sep 2022 13:19:50 +0200 Subject: [PATCH] Describe generic conventions for the bignum core module This commit codifies some conventions that result from the original design goals and others that have emerged after starting the implementation. * Value ranges * Bignum parameter naming and ordering * Sizes * Aliasing and overlap * Error handling Signed-off-by: Gilles Peskine --- library/bignum_core.h | 51 ++++++++++++++++++++++++++++++++++++++++--- 1 file changed, 48 insertions(+), 3 deletions(-) diff --git a/library/bignum_core.h b/library/bignum_core.h index d64111b18e..2274a8a904 100644 --- a/library/bignum_core.h +++ b/library/bignum_core.h @@ -11,6 +11,51 @@ * as the principal representation of a number modulo 2^#biL or a smaller * bound. * + * The functions in this module obey the following conventions unless + * explicitly indicated otherwise: + * + * - **Overflow**: some functions indicate overflow from the range + * [0, 2^#biL-1] by returning carry parameters, while others operate + * modulo and so cannot overflow. This should be clear from the function + * documentation. + * - **Bignum parameters**: Bignums are passed as pointers to an array of + * limbs. A limb has the type #mbedtls_mpi_uint. Unless otherwise specified: + * - Bignum parameters called \p A, \p B, ... are inputs, and are + * not modified by the function. + * - For operations modulo some number, the modulus is called \p N + * and is input-only. + * - Bignum parameters called \p X, \p Y are outputs or input-output. + * The initial content of output-only parameters is ignored. + * - Some functions use different names that reflect traditional + * naming of operands of certain operations (e.g. + * divisor/dividend/quotient/remainder). + * - \p T is a temporary storage area. The initial content of such + * parameter is ignored and the final content is unspecified. + * - **Bignum sizes**: bignum sizes are always expressed in limbs. + * Most functions work on bignums of a given size and take a single + * \p limbs parameter that applies to all parameters that are limb arrays. + * All bignum sizes must be at least 1 and must be significantly less than + * #SIZE_MAX. The behavior if a size is 0 is undefined. The behavior if the + * total size of all parameters overflows #SIZE_MAX is undefined. + * - **Parameter ordering**: for bignum parameters, outputs come before inputs. + * Temporaries come last. + * - **Aliasing**: in general, output bignums may be aliased to one or more + * inputs. As an exception, parameters that are documented as a modulus value + * may not be aliased to an output. Temporaries may not be aliased to + * any other parameter. + * - **Overlap**: apart from aliasing of limb array pointers (where two + * arguments are equal pointers), overlap is not supported and may result + * in undefined behavior. + * - **Error handling**: This is a low-level module. Functions generally do not + * try to protect against invalid arguments such as nonsensical sizes or + * null pointers. Note that some functions that operate on bignums of + * different sizes have constraints about their size, and violating those + * constraints may lead to buffer overflows. + * - **Modular representatives**: functions that operate modulo \p N expect + * all modular inputs to be in the range [0, \p N - 1] and guarantee outputs + * in the range [0, \p N - 1]. If an input is out of range, outputs are + * fully unspecified, though bignum values out of range should not cause + * buffer overflows (beware that this is not extensively tested). */ /* @@ -39,9 +84,9 @@ #include "mbedtls/bignum.h" #endif -#define ciL ( sizeof(mbedtls_mpi_uint) ) /* chars in limb */ -#define biL ( ciL << 3 ) /* bits in limb */ -#define biH ( ciL << 2 ) /* half limb size */ +#define ciL ( sizeof(mbedtls_mpi_uint) ) /** chars in limb */ +#define biL ( ciL << 3 ) /** bits in limb */ +#define biH ( ciL << 2 ) /** half limb size */ /* * Convert between bits/chars and number of limbs