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.
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class EC_Group¶
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EC_Group(const OID &oid)¶
Initialize an
EC_Group
using an OID referencing the curve parameters.
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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”)
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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.
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EC_Group(const std::vector<uint8_t> &ber_encoding)¶
Initialize an
EC_Group
by decoding a DER encoded parameter block.
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std::vector<uint8_t> DER_encode(EC_Group_Encoding form) const¶
Return the DER encoding of this group.
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std::string PEM_encode() const¶
Return the PEM encoding of this group (base64 of DER encoding plus header/trailer).
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bool a_is_minus_3() const¶
Return true if the
a
parameter is congruent to -3 mod p.
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bool a_is_zero() const¶
Return true if the
a
parameter is congruent to 0 mod p.
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size_t get_p_bits() const¶
Return size of the prime in bits.
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size_t get_p_bytes() const¶
Return size of the prime in bytes.
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size_t get_order_bits() const¶
Return size of the group order in bits.
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size_t get_order_bytes() const¶
Return size of the group order in bytes.
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BigInt inverse_mod_order(const BigInt &x) const¶
Return inverse of argument
x
modulo the curve order.
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BigInt multiply_mod_order(const BigInt &x, const BigInt &y) const¶
Multiply
x
andy
and reduce the result modulo the curve order.
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bool verify_public_element(const EC_Point &y) const¶
Return true if
y
seems to be a valid group element.
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const OID &get_curve_oid() const¶
Return the OID used to identify the curve. May be empty.
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EC_Point point(const BigInt &x, const BigInt &y) const¶
Create and return a point with affine elements
x
andy
. Note this function does not verify thatx
andy
satisfy the curve equation.
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EC_Point point_multiply(const BigInt &x, const EC_Point &pt, const BigInt &y) const¶
Multi-exponentiation. Returns base_point*x + pt*y. Not constant time. (Ordinarily used for signature verification.)
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EC_Point 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.
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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.
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EC_Point blinded_var_point_multiply(const EC_Point &point, const BigInt &k, RandomNumberGenerator &rng, std::vector<BigInt> &ws) const¶
Return
point*k
in a way that attempts to resist side channels.
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BigInt random_scalar(RandomNumberGenerator &rng) const¶
Return a random scalar (ie an integer between 1 and the group order).
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EC_Point 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.
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bool verify_group(RandomNumberGenerator &rng, bool strong = false) const¶
Attempt to verify the group seems valid.
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static const std::set<std::string> &known_named_groups()¶
Return a list of known groups, ie groups for which
EC_Group(name)
will succeed.
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EC_Group(const OID &oid)¶
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class EC_Point¶
Stores elliptic curve points in Jacobian representation.
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std::vector<uint8_t> encode(EC_Point::Compression_Type format) const¶
Encode a point in a way that can later be decoded with EC_Group::OS2ECP.
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EC_Point &operator*=(const BigInt &scalar)¶
Point multiplication using Montgomery ladder.
Warning
Prefer the blinded functions in
EC_Group
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void force_affine()¶
Convert the point to its equivalent affine coordinates. Throws if this is the point at infinity.
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static void force_all_affine(std::vector<EC_Point> &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.
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bool is_affine() const¶
Return true if this point is in affine coordinates.
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bool is_zero() const¶
Return true if this point is zero (aka point at infinity).
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bool on_the_curve() const¶
Return true if this point is on the curve.
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void randomize_repr(RandomNumberGenerator &rng)¶
Randomize the point representation.
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bool operator==(const EC_Point &other) const¶
Point equality. This compares the affine representations.
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void add(const EC_Point &other, std::vector<BigInt> &workspace)¶
Point addition, taking a workspace.
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void add_affine(const EC_Point &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.
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std::vector<uint8_t> encode(EC_Point::Compression_Type format) const¶