Overview

This section describes the programming interface of the CAU3 PKHA driver.

Data Structures
struct	_cau3_pkha_ecc_point_t
	PKHA ECC point structure. More...

Typedefs
typedef struct _cau3_pkha_ecc_point_t	cau3_pkha_ecc_point_t
	PKHA ECC point structure.

typedef enum _cau3_pkha_timing_t	cau3_pkha_timing_t
	Use of timing equalized version of a PKHA function. More...

typedef enum _cau3_pkha_f2m_t	cau3_pkha_f2m_t
	Integer vs binary polynomial arithmetic selection. More...

typedef enum _cau3_pkha_montgomery_form_t	cau3_pkha_montgomery_form_t
	Montgomery or normal PKHA input format. More...

Enumerations
enum	_cau3_pkha_timing_t { kCAU3_PKHA_NoTimingEqualized = 0U, kCAU3_PKHA_TimingEqualized = 1U }
	Use of timing equalized version of a PKHA function. More...

enum	_cau3_pkha_f2m_t { kCAU3_PKHA_IntegerArith = 0U, kCAU3_PKHA_F2mArith = 1U }
	Integer vs binary polynomial arithmetic selection. More...

enum	_cau3_pkha_montgomery_form_t { kCAU3_PKHA_NormalValue = 0U, kCAU3_PKHA_MontgomeryFormat = 1U }
	Montgomery or normal PKHA input format. More...

Functions
status_t	CAU3_PKHA_NormalToMontgomery (CAU3_Type base, const uint8_t N, size_t sizeN, uint8_t A, size_t sizeA, uint8_t B, size_t sizeB, uint8_t R2, size_t sizeR2, cau3_pkha_timing_t equalTime, cau3_pkha_f2m_t arithType)
	Converts from integer to Montgomery format. More...

status_t	CAU3_PKHA_MontgomeryToNormal (CAU3_Type base, const uint8_t N, size_t sizeN, uint8_t A, size_t sizeA, uint8_t B, size_t sizeB, cau3_pkha_timing_t equalTime, cau3_pkha_f2m_t arithType)
	Converts from Montgomery format to int. More...

status_t	CAU3_PKHA_ModAdd (CAU3_Type base, const uint8_t A, size_t sizeA, const uint8_t B, size_t sizeB, const uint8_t N, size_t sizeN, uint8_t result, size_t resultSize, cau3_pkha_f2m_t arithType)
	Performs modular addition - (A + B) mod N. More...

status_t	CAU3_PKHA_ModSub1 (CAU3_Type base, const uint8_t A, size_t sizeA, const uint8_t B, size_t sizeB, const uint8_t N, size_t sizeN, uint8_t result, size_t resultSize)
	Performs modular subtraction - (A - B) mod N. More...

status_t	CAU3_PKHA_ModSub2 (CAU3_Type base, const uint8_t A, size_t sizeA, const uint8_t B, size_t sizeB, const uint8_t N, size_t sizeN, uint8_t result, size_t resultSize)
	Performs modular subtraction - (B - A) mod N. More...

status_t	CAU3_PKHA_ModMul (CAU3_Type base, const uint8_t A, size_t sizeA, const uint8_t B, size_t sizeB, const uint8_t N, size_t sizeN, uint8_t result, size_t resultSize, cau3_pkha_f2m_t arithType, cau3_pkha_montgomery_form_t montIn, cau3_pkha_montgomery_form_t montOut, cau3_pkha_timing_t equalTime)
	Performs modular multiplication - (A x B) mod N. More...

status_t	CAU3_PKHA_ModExp (CAU3_Type base, const uint8_t A, size_t sizeA, const uint8_t N, size_t sizeN, const uint8_t E, size_t sizeE, uint8_t result, size_t resultSize, cau3_pkha_f2m_t arithType, cau3_pkha_montgomery_form_t montIn, cau3_pkha_timing_t equalTime)
	Performs modular exponentiation - (A^E) mod N. More...

status_t	CAU3_PKHA_ModSqrt (CAU3_Type base, const uint8_t A, size_t sizeA, const uint8_t N, size_t sizeN, uint8_t result, size_t *resultSize)
	Performs Modular Square Root. More...

status_t	CAU3_PKHA_ModRed (CAU3_Type base, const uint8_t A, size_t sizeA, const uint8_t N, size_t sizeN, uint8_t result, size_t *resultSize, cau3_pkha_f2m_t arithType)
	Performs modular reduction - (A) mod N. More...

status_t	CAU3_PKHA_ModInv (CAU3_Type base, const uint8_t A, size_t sizeA, const uint8_t N, size_t sizeN, uint8_t result, size_t *resultSize, cau3_pkha_f2m_t arithType)
	Performs modular inversion - (A^-1) mod N. More...

status_t	CAU3_PKHA_ModR2 (CAU3_Type base, const uint8_t N, size_t sizeN, uint8_t result, size_t resultSize, cau3_pkha_f2m_t arithType)
	Computes integer Montgomery factor R^2 mod N. More...

status_t	CAU3_PKHA_ModRR (CAU3_Type base, const uint8_t P, size_t sizeP, size_t sizeE, uint8_t result, size_t resultSize)
	Performs Integer RERP mod P. More...

status_t	CAU3_PKHA_ModGcd (CAU3_Type base, const uint8_t A, size_t sizeA, const uint8_t N, size_t sizeN, uint8_t result, size_t *resultSize, cau3_pkha_f2m_t arithType)
	Calculates the greatest common divisor - GCD (A, N). More...

status_t	CAU3_PKHA_PrimalityTest (CAU3_Type base, const uint8_t A, size_t sizeA, const uint8_t B, size_t sizeB, const uint8_t N, size_t sizeN, bool *res)
	Executes Miller-Rabin primality test. More...

status_t	CAU3_PKHA_ECC_PointAdd (CAU3_Type base, const cau3_pkha_ecc_point_t A, const cau3_pkha_ecc_point_t B, const uint8_t N, const uint8_t R2modN, const uint8_t aCurveParam, const uint8_t bCurveParam, size_t size, cau3_pkha_f2m_t arithType, cau3_pkha_ecc_point_t result)
	Adds elliptic curve points - A + B. More...

status_t	CAU3_PKHA_ECC_PointDouble (CAU3_Type base, const cau3_pkha_ecc_point_t B, const uint8_t N, const uint8_t aCurveParam, const uint8_t bCurveParam, size_t size, cau3_pkha_f2m_t arithType, cau3_pkha_ecc_point_t result)
	Doubles elliptic curve points - B + B. More...

status_t	CAU3_PKHA_ECC_PointMul (CAU3_Type base, const cau3_pkha_ecc_point_t A, const uint8_t E, size_t sizeE, const uint8_t N, const uint8_t R2modN, const uint8_t aCurveParam, const uint8_t bCurveParam, size_t size, cau3_pkha_timing_t equalTime, cau3_pkha_f2m_t arithType, cau3_pkha_ecc_point_t result)
	Multiplies an elliptic curve point by a scalar - E x (A0, A1). More...

status_t	CAU3_PKHA_ECM_PointMul (CAU3_Type base, const uint8_t E, size_t sizeE, const uint8_t inputCoordinate, const uint8_t A24, const uint8_t N, const uint8_t R2modN, size_t size, cau3_pkha_timing_t equalTime, uint8_t *outputCoordinate)
	Computes scalar multiplication of a point on an elliptic curve in Montgomery form. More...

status_t	CAU3_PKHA_ECT_PointMul (CAU3_Type base, const cau3_pkha_ecc_point_t A, const uint8_t E, size_t sizeE, const uint8_t N, const uint8_t R2modN, const uint8_t aCurveParam, const uint8_t dCurveParam, size_t size, cau3_pkha_timing_t equalTime, cau3_pkha_ecc_point_t result)
	Multiplies an Edwards-form elliptic curve point by a scalar - E x (A0, A1). More...

status_t	CAU3_PKHA_ECT_PointAdd (CAU3_Type base, const cau3_pkha_ecc_point_t A, const cau3_pkha_ecc_point_t B, const uint8_t N, const uint8_t R2modN, const uint8_t aCurveParam, const uint8_t dCurveParam, size_t size, cau3_pkha_ecc_point_t result)
	Adds an Edwards-form elliptic curve points - A + B. More...

Data Structure Documentation

struct _cau3_pkha_ecc_point_t

Data Fields
uint8_t *	X
	X coordinate (affine)

uint8_t *	Y
	Y coordinate (affine)

Typedef Documentation

typedef enum _cau3_pkha_timing_t cau3_pkha_timing_t

typedef enum _cau3_pkha_f2m_t cau3_pkha_f2m_t

typedef enum _cau3_pkha_montgomery_form_t cau3_pkha_montgomery_form_t

Enumeration Type Documentation

enum _cau3_pkha_timing_t

Enumerator
kCAU3_PKHA_NoTimingEqualized	Normal version of a PKHA operation.
kCAU3_PKHA_TimingEqualized	Timing-equalized version of a PKHA operation.

enum _cau3_pkha_f2m_t

Enumerator
kCAU3_PKHA_IntegerArith	Use integer arithmetic.
kCAU3_PKHA_F2mArith	Use binary polynomial arithmetic.

enum _cau3_pkha_montgomery_form_t

Enumerator
kCAU3_PKHA_NormalValue	PKHA number is normal integer.
kCAU3_PKHA_MontgomeryFormat	PKHA number is in montgomery format.

Function Documentation

status_t CAU3_PKHA_NormalToMontgomery	(	CAU3_Type *	base,
		const uint8_t *	N,
		size_t	sizeN,
		uint8_t *	A,
		size_t *	sizeA,
		uint8_t *	B,
		size_t *	sizeB,
		uint8_t *	R2,
		size_t *	sizeR2,
		cau3_pkha_timing_t	equalTime,
		cau3_pkha_f2m_t	arithType
	)

This function computes R2 mod N and optionally converts A or B into Montgomery format of A or B.

Parameters

	base	CAU3 peripheral base address
	N	modulus
	sizeN	size of N in bytes
[in,out]	A	The first input in non-Montgomery format. Output Montgomery format of the first input.
[in,out]	sizeA	pointer to size variable. On input it holds size of input A in bytes. On output it holds size of Montgomery format of A in bytes.
[in,out]	B	Second input in non-Montgomery format. Output Montgomery format of the second input.
[in,out]	sizeB	pointer to size variable. On input it holds size of input B in bytes. On output it holds size of Montgomery format of B in bytes.
[out]	R2	Output Montgomery factor R2 mod N.
[out]	sizeR2	pointer to size variable. On output it holds size of Montgomery factor R2 mod N in bytes.
	equalTime	Run the function time equalized or no timing equalization.
	arithType	Type of arithmetic to perform (integer or F2m)

Returns: Operation status.

status_t CAU3_PKHA_MontgomeryToNormal	(	CAU3_Type *	base,
		const uint8_t *	N,
		size_t	sizeN,
		uint8_t *	A,
		size_t *	sizeA,
		uint8_t *	B,
		size_t *	sizeB,
		cau3_pkha_timing_t	equalTime,
		cau3_pkha_f2m_t	arithType
	)

This function converts Montgomery format of A or B into int A or B.

Parameters

	base	CAU3 peripheral base address
	N	modulus.
	sizeN	size of N modulus in bytes.
[in,out]	A	Input first number in Montgomery format. Output is non-Montgomery format.
[in,out]	sizeA	pointer to size variable. On input it holds size of the input A in bytes. On output it holds size of non-Montgomery A in bytes.
[in,out]	B	Input first number in Montgomery format. Output is non-Montgomery format.
[in,out]	sizeB	pointer to size variable. On input it holds size of the input B in bytes. On output it holds size of non-Montgomery B in bytes.
	equalTime	Run the function time equalized or no timing equalization.
	arithType	Type of arithmetic to perform (integer or F2m)

Returns: Operation status.

status_t CAU3_PKHA_ModAdd	(	CAU3_Type *	base,
		const uint8_t *	A,
		size_t	sizeA,
		const uint8_t *	B,
		size_t	sizeB,
		const uint8_t *	N,
		size_t	sizeN,
		uint8_t *	result,
		size_t *	resultSize,
		cau3_pkha_f2m_t	arithType
	)

This function performs modular addition of (A + B) mod N, with either integer or binary polynomial (F2m) inputs. In the F2m form, this function is equivalent to a bitwise XOR and it is functionally the same as subtraction.

Parameters

	base	CAU3 peripheral base address
	A	first addend (integer or binary polynomial)
	sizeA	Size of A in bytes
	B	second addend (integer or binary polynomial)
	sizeB	Size of B in bytes
	N	modulus.
	sizeN	Size of N in bytes.
[out]	result	Output array to store result of operation
[out]	resultSize	Output size of operation in bytes
	arithType	Type of arithmetic to perform (integer or F2m)

Returns: Operation status.

status_t CAU3_PKHA_ModSub1	(	CAU3_Type *	base,
		const uint8_t *	A,
		size_t	sizeA,
		const uint8_t *	B,
		size_t	sizeB,
		const uint8_t *	N,
		size_t	sizeN,
		uint8_t *	result,
		size_t *	resultSize
	)

This function performs modular subtraction of (A - B) mod N with integer inputs.

Parameters

	base	CAU3 peripheral base address
	A	first addend (integer or binary polynomial)
	sizeA	Size of A in bytes
	B	second addend (integer or binary polynomial)
	sizeB	Size of B in bytes
	N	modulus
	sizeN	Size of N in bytes
[out]	result	Output array to store result of operation
[out]	resultSize	Output size of operation in bytes

Returns: Operation status.

status_t CAU3_PKHA_ModSub2	(	CAU3_Type *	base,
		const uint8_t *	A,
		size_t	sizeA,
		const uint8_t *	B,
		size_t	sizeB,
		const uint8_t *	N,
		size_t	sizeN,
		uint8_t *	result,
		size_t *	resultSize
	)

This function performs modular subtraction of (B - A) mod N, with integer inputs.

Parameters

	base	CAU3 peripheral base address
	A	first addend (integer or binary polynomial)
	sizeA	Size of A in bytes
	B	second addend (integer or binary polynomial)
	sizeB	Size of B in bytes
	N	modulus
	sizeN	Size of N in bytes
[out]	result	Output array to store result of operation
[out]	resultSize	Output size of operation in bytes

Returns: Operation status.

status_t CAU3_PKHA_ModMul	(	CAU3_Type *	base,
		const uint8_t *	A,
		size_t	sizeA,
		const uint8_t *	B,
		size_t	sizeB,
		const uint8_t *	N,
		size_t	sizeN,
		uint8_t *	result,
		size_t *	resultSize,
		cau3_pkha_f2m_t	arithType,
		cau3_pkha_montgomery_form_t	montIn,
		cau3_pkha_montgomery_form_t	montOut,
		cau3_pkha_timing_t	equalTime
	)

This function performs modular multiplication with either integer or binary polynomial (F2m) inputs. It can optionally specify whether inputs and/or outputs will be in Montgomery form or not.

Parameters

	base	CAU3 peripheral base address
	A	first addend (integer or binary polynomial)
	sizeA	Size of A in bytes
	B	second addend (integer or binary polynomial)
	sizeB	Size of B in bytes
	N	modulus.
	sizeN	Size of N in bytes
[out]	result	Output array to store result of operation
[out]	resultSize	Output size of operation in bytes
	arithType	Type of arithmetic to perform (integer or F2m)
	montIn	Format of inputs
	montOut	Format of output
	equalTime	Run the function time equalized or no timing equalization. This argument is ignored for F2m modular multiplication.

Returns: Operation status.

status_t CAU3_PKHA_ModExp	(	CAU3_Type *	base,
		const uint8_t *	A,
		size_t	sizeA,
		const uint8_t *	N,
		size_t	sizeN,
		const uint8_t *	E,
		size_t	sizeE,
		uint8_t *	result,
		size_t *	resultSize,
		cau3_pkha_f2m_t	arithType,
		cau3_pkha_montgomery_form_t	montIn,
		cau3_pkha_timing_t	equalTime
	)

This function performs modular exponentiation with either integer or binary polynomial (F2m) inputs.

Parameters

	base	CAU3 peripheral base address
	A	first addend (integer or binary polynomial)
	sizeA	Size of A in bytes
	N	modulus
	sizeN	Size of N in bytes
	E	exponent
	sizeE	Size of E in bytes
[out]	result	Output array to store result of operation
[out]	resultSize	Output size of operation in bytes
	montIn	Format of A input (normal or Montgomery)
	arithType	Type of arithmetic to perform (integer or F2m)
	equalTime	Run the function time equalized or no timing equalization.

Returns: Operation status.

status_t CAU3_PKHA_ModSqrt	(	CAU3_Type *	base,
		const uint8_t *	A,
		size_t	sizeA,
		const uint8_t *	N,
		size_t	sizeN,
		uint8_t *	result,
		size_t *	resultSize
	)

This function performs modular square root with integer inputs. The modular square root function computes output result B, such that ( B x B ) mod N = input A. If no such B result exists, the result will be set to 0 and the PKHA "prime" flag will be set. Input values A and B are limited to a maximum size of 128 bytes. Note that two such square root values may exist. This algorithm will find either one of them, if any exist. The second possible square root (B') can be found by calculating B' = N - B.

Parameters

	base	CAU3 peripheral base address
	A	input value, for which a square root is to be calculated
	sizeA	Size of A in bytes
	N	modulus
	sizeN	Size of N in bytes
[out]	result	Output array to store result of operation
[out]	resultSize	Output size of operation in bytes

Returns: Operation status.

status_t CAU3_PKHA_ModRed	(	CAU3_Type *	base,
		const uint8_t *	A,
		size_t	sizeA,
		const uint8_t *	N,
		size_t	sizeN,
		uint8_t *	result,
		size_t *	resultSize,
		cau3_pkha_f2m_t	arithType
	)

This function performs modular reduction with either integer or binary polynomial (F2m) inputs.

Parameters

	base	CAU3 peripheral base address
	A	first addend (integer or binary polynomial)
	sizeA	Size of A in bytes
	N	modulus
	sizeN	Size of N in bytes
[out]	result	Output array to store result of operation
[out]	resultSize	Output size of operation in bytes
	arithType	Type of arithmetic to perform (integer or F2m)

Returns: Operation status.

status_t CAU3_PKHA_ModInv	(	CAU3_Type *	base,
		const uint8_t *	A,
		size_t	sizeA,
		const uint8_t *	N,
		size_t	sizeN,
		uint8_t *	result,
		size_t *	resultSize,
		cau3_pkha_f2m_t	arithType
	)

This function performs modular inversion with either integer or binary polynomial (F2m) inputs.

Parameters

	base	CAU3 peripheral base address
	A	first addend (integer or binary polynomial)
	sizeA	Size of A in bytes
	N	modulus
	sizeN	Size of N in bytes
[out]	result	Output array to store result of operation
[out]	resultSize	Output size of operation in bytes
	arithType	Type of arithmetic to perform (integer or F2m)

Returns: Operation status.

status_t CAU3_PKHA_ModR2	(	CAU3_Type *	base,
		const uint8_t *	N,
		size_t	sizeN,
		uint8_t *	result,
		size_t *	resultSize,
		cau3_pkha_f2m_t	arithType
	)

This function computes a constant to assist in converting operands into the Montgomery residue system representation.

Parameters

	base	CAU3 peripheral base address
	N	modulus
	sizeN	Size of N in bytes
[out]	result	Output array to store result of operation
[out]	resultSize	Output size of operation in bytes
	arithType	Type of arithmetic to perform (integer or F2m)

Returns: Operation status.

status_t CAU3_PKHA_ModRR	(	CAU3_Type *	base,
		const uint8_t *	P,
		size_t	sizeP,
		size_t	sizeE,
		uint8_t *	result,
		size_t *	resultSize
	)

This function is used to compute a constant to assist in converting operands into the Montgomery residue system representation specifically for Chinese Remainder Theorem while performing RSA with a CRT implementation where a modulus E=P x Q, and P and Q are prime numbers. Although labeled RERP mod P, this routine (function) can also compute RERQ mod Q.

Parameters

	base	CAU3 peripheral base address
	P	modulus P or Q of CRT, an odd integer
	sizeP	Size of P in bytes
	sizeE	Number of bytes of E = P x Q (this size must be given, though content of E itself is not used).
[out]	result	Output array to store result of operation
[out]	resultSize	Output size of operation in bytes

Returns: Operation status.

status_t CAU3_PKHA_ModGcd	(	CAU3_Type *	base,
		const uint8_t *	A,
		size_t	sizeA,
		const uint8_t *	N,
		size_t	sizeN,
		uint8_t *	result,
		size_t *	resultSize,
		cau3_pkha_f2m_t	arithType
	)

This function calculates the greatest common divisor of two inputs with either integer or binary polynomial (F2m) inputs.

Parameters

	base	CAU3 peripheral base address
	A	first value (must be smaller than or equal to N)
	sizeA	Size of A in bytes
	N	second value (must be non-zero)
	sizeN	Size of N in bytes
[out]	result	Output array to store result of operation
[out]	resultSize	Output size of operation in bytes
	arithType	Type of arithmetic to perform (integer or F2m)

Returns: Operation status.

status_t CAU3_PKHA_PrimalityTest	(	CAU3_Type *	base,
		const uint8_t *	A,
		size_t	sizeA,
		const uint8_t *	B,
		size_t	sizeB,
		const uint8_t *	N,
		size_t	sizeN,
		bool *	res
	)

This function calculates whether or not a candidate prime number is likely to be a prime.

Parameters

	base	CAU3 peripheral base address
	A	initial random seed
	sizeA	Size of A in bytes
	B	number of trial runs
	sizeB	Size of B in bytes
	N	candidate prime integer
	sizeN	Size of N in bytes
[out]	res	True if the value is likely prime or false otherwise

Returns: Operation status.

status_t CAU3_PKHA_ECC_PointAdd	(	CAU3_Type *	base,
		const cau3_pkha_ecc_point_t *	A,
		const cau3_pkha_ecc_point_t *	B,
		const uint8_t *	N,
		const uint8_t *	R2modN,
		const uint8_t *	aCurveParam,
		const uint8_t *	bCurveParam,
		size_t	size,
		cau3_pkha_f2m_t	arithType,
		cau3_pkha_ecc_point_t *	result
	)

This function performs ECC point addition over a prime field (Fp) or binary field (F2m) using affine coordinates.

Parameters

	base	CAU3 peripheral base address
	A	Left-hand point
	B	Right-hand point
	N	Prime modulus of the field
	R2modN	NULL (the function computes R2modN internally) or pointer to pre-computed R2modN (obtained from CAU3_PKHA_ModR2() function).
	aCurveParam	A parameter from curve equation
	bCurveParam	B parameter from curve equation (constant)
	size	Size in bytes of curve points and parameters
	arithType	Type of arithmetic to perform (integer or F2m)
[out]	result	Result point

Returns: Operation status.

status_t CAU3_PKHA_ECC_PointDouble	(	CAU3_Type *	base,
		const cau3_pkha_ecc_point_t *	B,
		const uint8_t *	N,
		const uint8_t *	aCurveParam,
		const uint8_t *	bCurveParam,
		size_t	size,
		cau3_pkha_f2m_t	arithType,
		cau3_pkha_ecc_point_t *	result
	)

This function performs ECC point doubling over a prime field (Fp) or binary field (F2m) using affine coordinates.

Parameters

	base	CAU3 peripheral base address
	B	Point to double
	N	Prime modulus of the field
	aCurveParam	A parameter from curve equation
	bCurveParam	B parameter from curve equation (constant)
	size	Size in bytes of curve points and parameters
	arithType	Type of arithmetic to perform (integer or F2m)
[out]	result	Result point

Returns: Operation status.

status_t CAU3_PKHA_ECC_PointMul	(	CAU3_Type *	base,
		const cau3_pkha_ecc_point_t *	A,
		const uint8_t *	E,
		size_t	sizeE,
		const uint8_t *	N,
		const uint8_t *	R2modN,
		const uint8_t *	aCurveParam,
		const uint8_t *	bCurveParam,
		size_t	size,
		cau3_pkha_timing_t	equalTime,
		cau3_pkha_f2m_t	arithType,
		cau3_pkha_ecc_point_t *	result
	)

This function performs ECC point multiplication to multiply an ECC point by a scalar integer multiplier over a prime field (Fp) or a binary field (F2m).

Parameters

	base	CAU3 peripheral base address
	A	Point as multiplicand
	E	Scalar multiple
	sizeE	The size of E, in bytes
	N	Modulus, a prime number for the Fp field or Irreducible polynomial for F2m field.
	R2modN	NULL (the function computes R2modN internally) or pointer to pre-computed R2modN (obtained from CAU3_PKHA_ModR2() function).
	aCurveParam	A parameter from curve equation
	bCurveParam	B parameter from curve equation (C parameter for operation over F2m).
	size	Size in bytes of curve points and parameters
	equalTime	Run the function time equalized or no timing equalization.
	arithType	Type of arithmetic to perform (integer or F2m)
[out]	result	Result point

Returns: Operation status.

status_t CAU3_PKHA_ECM_PointMul	(	CAU3_Type *	base,
		const uint8_t *	E,
		size_t	sizeE,
		const uint8_t *	inputCoordinate,
		const uint8_t *	A24,
		const uint8_t *	N,
		const uint8_t *	R2modN,
		size_t	size,
		cau3_pkha_timing_t	equalTime,
		uint8_t *	outputCoordinate
	)

This function computes the scalar multiplication of a point on an elliptic curve in Montgomery form. The input and output are just the x coordinates of the points. The points on a curve are defined by the equation E: B*y^2 = x^3 + A*x^2 + x mod p This function computes a point multiplication on a Montgomery curve, using Montgomery values, by means of a Montgomery ladder. At the end of the ladder, P2 = P3 + P1, where P1 is the input and P3 is the result.

Parameters

	base	CAU3 peripheral base address
	E	Scalar multiplier, any integer
	sizeE	The size of E, in bytes
	inputCoordinate	Point as multiplicand, an input point's affine x coordinate
	A24	elliptic curve a24 parameter, that is, (A+2)/4
	N	Modulus, a prime number.
	R2modN	NULL (the function computes R2modN internally) or pointer to pre-computed R2modN (obtained from CAU3_PKHA_ModR2() function).
	size	Size in bytes of curve points and parameters
	equalTime	Run the function time equalized or no timing equalization.
[out]	outputCoordinate	Resulting poin's x affine coordinate.

Returns: Operation status.

status_t CAU3_PKHA_ECT_PointMul	(	CAU3_Type *	base,
		const cau3_pkha_ecc_point_t *	A,
		const uint8_t *	E,
		size_t	sizeE,
		const uint8_t *	N,
		const uint8_t *	R2modN,
		const uint8_t *	aCurveParam,
		const uint8_t *	dCurveParam,
		size_t	size,
		cau3_pkha_timing_t	equalTime,
		cau3_pkha_ecc_point_t *	result
	)

This function performs scalar multiplication of an Edwards-form elliptic curve point in affine coordinates. The points on a curve are defined by the equation E: a*X^2 + d^2 = 1 + D^2*X^2*Y^2 mod N

Parameters

	base	CAU3 peripheral base address
	A	Point as multiplicand
	E	Scalar multiple
	sizeE	The size of E, in bytes
	N	Modulus, a prime number for the Fp field.
	R2modN	NULL (the function computes R2modN internally) or pointer to pre-computed R2modN (obtained from CAU3_PKHA_ModR2() function).
	aCurveParam	A parameter from curve equation
	dCurveParam	D parameter from curve equation.
	size	Size in bytes of curve points and parameters
	equalTime	Run the function time equalized or no timing equalization.
[out]	result	Result point

Returns: Operation status.

status_t CAU3_PKHA_ECT_PointAdd	(	CAU3_Type *	base,
		const cau3_pkha_ecc_point_t *	A,
		const cau3_pkha_ecc_point_t *	B,
		const uint8_t *	N,
		const uint8_t *	R2modN,
		const uint8_t *	aCurveParam,
		const uint8_t *	dCurveParam,
		size_t	size,
		cau3_pkha_ecc_point_t *	result
	)

This function performs Edwards-form elliptic curve point addition over a prime field (Fp) using affine coordinates. The points on a curve are defined by the equation E: a*X^2 + Y^2 = 1 + d^2*X^2*Y^2 mod N

Parameters

	base	CAU3 peripheral base address
	A	Left-hand point
	B	Right-hand point
	N	Prime modulus of the field
	R2modN	NULL (the function computes R2modN internally) or pointer to pre-computed R2modN (obtained from CAU3_PKHA_ModR2() function).
	aCurveParam	A parameter from curve equation
	dCurveParam	D parameter from curve equation
	size	Size in bytes of curve points and parameters
[out]	result	Result point

Returns: Operation status.

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