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diff --git a/comm/third_party/botan/doc/api_ref/ecc.rst b/comm/third_party/botan/doc/api_ref/ecc.rst new file mode 100644 index 0000000000..f522bbe3df --- /dev/null +++ b/comm/third_party/botan/doc/api_ref/ecc.rst @@ -0,0 +1,284 @@ +Elliptic Curve Operations +============================ + +In addition to high level operations for signatures, key agreement, +and message encryption using elliptic curve cryptography, the library +contains lower level interfaces for performing operations such as +elliptic curve point multiplication. + +Only curves over prime fields are supported. + +Many of these functions take a workspace, either a vector of words or +a vector of BigInts. These are used to minimize memory allocations +during common operations. + +.. warning:: + You should only use these interfaces if you know what you are doing. + +.. cpp:class:: EC_Group + + .. cpp:function:: EC_Group(const OID& oid) + + Initialize an ``EC_Group`` using an OID referencing the curve + parameters. + + .. cpp:function:: EC_Group(const std::string& name) + + Initialize an ``EC_Group`` using a name or OID (for example + "secp256r1", or "1.2.840.10045.3.1.7") + + .. cpp:function:: EC_Group(const BigInt& p, \ + const BigInt& a, \ + const BigInt& b, \ + const BigInt& base_x, \ + const BigInt& base_y, \ + const BigInt& order, \ + const BigInt& cofactor, \ + const OID& oid = OID()) + + Initialize an elliptic curve group from the relevant parameters. This + is used for example to create custom (application-specific) curves. + + .. cpp:function:: EC_Group(const std::vector<uint8_t>& ber_encoding) + + Initialize an ``EC_Group`` by decoding a DER encoded parameter block. + + .. cpp:function:: std::vector<uint8_t> DER_encode(EC_Group_Encoding form) const + + Return the DER encoding of this group. + + .. cpp:function:: std::string PEM_encode() const + + Return the PEM encoding of this group (base64 of DER encoding plus + header/trailer). + + .. cpp:function:: bool a_is_minus_3() const + + Return true if the ``a`` parameter is congruent to -3 mod p. + + .. cpp:function:: bool a_is_zero() const + + Return true if the ``a`` parameter is congruent to 0 mod p. + + .. cpp:function:: size_t get_p_bits() const + + Return size of the prime in bits. + + .. cpp:function:: size_t get_p_bytes() const + + Return size of the prime in bytes. + + .. cpp:function:: size_t get_order_bits() const + + Return size of the group order in bits. + + .. cpp:function:: size_t get_order_bytes() const + + Return size of the group order in bytes. + + .. cpp:function:: const BigInt& get_p() const + + Return the prime modulus. + + .. cpp:function:: const BigInt& get_a() const + + Return the ``a`` parameter of the elliptic curve equation. + + .. cpp:function:: const BigInt& get_b() const + + Return the ``b`` parameter of the elliptic curve equation. + + .. cpp:function:: const PointGFp& get_base_point() const + + Return the groups base point element. + + .. cpp:function:: const BigInt& get_g_x() const + + Return the x coordinate of the base point element. + + .. cpp:function:: const BigInt& get_g_y() const + + Return the y coordinate of the base point element. + + .. cpp:function:: const BigInt& get_order() const + + Return the order of the group generated by the base point. + + .. cpp:function:: const BigInt& get_cofactor() const + + Return the cofactor of the curve. In most cases this will be 1. + + .. cpp:function:: BigInt mod_order(const BigInt& x) const + + Reduce argument ``x`` modulo the curve order. + + .. cpp:function:: BigInt inverse_mod_order(const BigInt& x) const + + Return inverse of argument ``x`` modulo the curve order. + + .. cpp:function:: BigInt multiply_mod_order(const BigInt& x, const BigInt& y) const + + Multiply ``x`` and ``y`` and reduce the result modulo the curve order. + + .. cpp:function:: bool verify_public_element(const PointGFp& y) const + + Return true if ``y`` seems to be a valid group element. + + .. cpp:function:: const OID& get_curve_oid() const + + Return the OID used to identify the curve. May be empty. + + .. cpp:function:: PointGFp point(const BigInt& x, const BigInt& y) const + + Create and return a point with affine elements ``x`` and ``y``. Note + this function *does not* verify that ``x`` and ``y`` satisfy the curve + equation. + + .. cpp:function:: PointGFp point_multiply(const BigInt& x, const PointGFp& pt, const BigInt& y) const + + Multi-exponentiation. Returns base_point*x + pt*y. Not constant time. + (Ordinarily used for signature verification.) + + .. cpp:function:: PointGFp blinded_base_point_multiply(const BigInt& k, \ + RandomNumberGenerator& rng, \ + std::vector<BigInt>& ws) const + + Return ``base_point*k`` in a way that attempts to resist side channels. + + .. cpp:function:: BigInt blinded_base_point_multiply_x(const BigInt& k, \ + RandomNumberGenerator& rng, \ + std::vector<BigInt>& ws) const + + Like `blinded_base_point_multiply` but returns only the x coordinate. + + .. cpp:function:: PointGFp blinded_var_point_multiply(const PointGFp& point, \ + const BigInt& k, \ + RandomNumberGenerator& rng, \ + std::vector<BigInt>& ws) const + + Return ``point*k`` in a way that attempts to resist side channels. + + .. cpp:function:: BigInt random_scalar(RandomNumberGenerator& rng) const + + Return a random scalar (ie an integer between 1 and the group order). + + .. cpp:function:: PointGFp zero_point() const + + Return the zero point (aka the point at infinity). + + .. cpp:function:: PointGFp OS2ECP(const uint8_t bits[], size_t len) const + + Decode a point from the binary encoding. This function verifies that + the decoded point is a valid element on the curve. + + .. cpp:function:: bool verify_group(RandomNumberGenerator& rng, bool strong = false) const + + Attempt to verify the group seems valid. + + .. cpp:function:: static const std::set<std::string>& known_named_groups() + + Return a list of known groups, ie groups for which ``EC_Group(name)`` + will succeed. + +.. cpp:class:: PointGFp + + Stores elliptic curve points in Jacobian representation. + + .. cpp:function:: std::vector<uint8_t> encode(PointGFp::Compression_Type format) const + + Encode a point in a way that can later be decoded with `EC_Group::OS2ECP`. + + .. cpp:function:: PointGFp& operator+=(const PointGFp& rhs) + + Point addition. + + .. cpp:function:: PointGFp& operator-=(const PointGFp& rhs) + + Point subtraction. + + .. cpp:function:: PointGFp& operator*=(const BigInt& scalar) + + Point multiplication using Montgomery ladder. + + .. warning:: + Prefer the blinded functions in ``EC_Group`` + + .. cpp:function:: PointGFp& negate() + + Negate this point. + + .. cpp:function:: BigInt get_affine_x() const + + Return the affine ``x`` coordinate of the point. + + .. cpp:function:: BigInt get_affine_y() const + + Return the affine ``y`` coordinate of the point. + + .. cpp:function:: void force_affine() + + Convert the point to its equivalent affine coordinates. Throws + if this is the point at infinity. + + .. cpp:function:: static void force_all_affine(std::vector<PointGFp>& points, \ + secure_vector<word>& ws) + + Force several points to be affine at once. Uses Montgomery's + trick to reduce number of inversions required, so this is much + faster than calling ``force_affine`` on each point in sequence. + + .. cpp:function:: bool is_affine() const + + Return true if this point is in affine coordinates. + + .. cpp:function:: bool is_zero() const + + Return true if this point is zero (aka point at infinity). + + .. cpp:function:: bool on_the_curve() const + + Return true if this point is on the curve. + + .. cpp:function:: void randomize_repr(RandomNumberGenerator& rng) + + Randomize the point representation. + + .. cpp:function:: bool operator==(const PointGFp& other) const + + Point equality. This compares the affine representations. + + .. cpp:function:: void add(const PointGFp& other, std::vector<BigInt>& workspace) + + Point addition, taking a workspace. + + .. cpp:function:: void add_affine(const PointGFp& other, std::vector<BigInt>& workspace) + + Mixed (Jacobian+affine) addition, taking a workspace. + + .. warning:: + + This function assumes that ``other`` is affine, if this is + not correct the result will be invalid. + + .. cpp:function:: void mult2(std::vector<BigInt>& workspace) + + Point doubling. + + .. cpp:function:: void mult2i(size_t i, std::vector<BigInt>& workspace) + + Repeated point doubling. + + .. cpp:function:: PointGFp plus(const PointGFp& other, std::vector<BigInt>& workspace) const + + Point addition, returning the result. + + .. cpp:function:: PointGFp double_of(std::vector<BigInt>& workspace) const + + Point doubling, returning the result. + + .. cpp:function:: PointGFp zero() const + + Return the point at infinity + + + |