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3599 \chapter{Elliptic Curve Cryptography}
3602 The library provides a set of core ECC functions as well that are designed to be the Elliptic Curve analogy of all of the
3671 keySize INTEGER, -- Curve size (in bits) divided by eight
3679 keySize INTEGER, -- Curve size (in bits) divided by eight
3692 \mysection{ECC Curve Parameters}
3693 The library uses the following structure to describe an elliptic curve. This is used internally, as well as by the new
3698 /** Structure defines a NIST GF(p) curve */
3700 /** The size of the curve in octets */
3703 curve */
3712 /** The order of the curve (hex) */
3715 /** The x co-ordinate of the base point on the curve (hex) */
3718 /** The y co-ordinate of the base point on the curve (hex) */
3723 The curve must be of the form $y^2 = x^3 - 3x + b$, and all of the integer parameters are encoded in hexadecimal format.
3743 As of v1.16, the library supports an extended key generation routine which allows the user to specify their own curve. It is specified as follows:
3754 This function generates a random ECC key over the curve specified by the parameters by \textit{dp}. The rest of the parameters are equivalent to
3788 The following function imports a LibTomCrypt format ECC key using a specified set of curve parameters:
3797 the ECC structure pointed to by \textit{key}. The curve is specified by the parameters pointed to by \textit{dp}. The function will free
6349 @param modulus Modulus for curve
6413 /** A point on a ECC curve, stored in Jacobian format such