Interface to core BigDigits "mp" functions using fixed-length arrays. More...

Typedefs
typedef uint32_t	DIGIT_T
	The basic BigDigit element, an unsigned 32-bit integer. More...

Functions
int	mpAbs (DIGIT_T x[], const DIGIT_T y[], size_t ndigits)
	Sets x = \|y\|, the absolute value of y. More...

DIGIT_T	mpAdd (DIGIT_T w[], const DIGIT_T u[], const DIGIT_T v[], size_t ndigits)
	Computes w = u + v, returns carry. More...

void	mpAndBits (DIGIT_T a[], const DIGIT_T b[], const DIGIT_T c[], size_t ndigits)
	Computes bitwise a = b AND c. More...

size_t	mpBitLength (const DIGIT_T a[], size_t ndigits)
	Returns number of significant bits in a. More...

int	mpChs (DIGIT_T x[], const DIGIT_T y[], size_t ndigits)
	Sets x = -y. More...

int	mpCompare (const DIGIT_T a[], const DIGIT_T b[], size_t ndigits)
	Returns sign of `(a-b)` as `{-1,0,+1}` More...

int	mpCompare_ct (const DIGIT_T a[], const DIGIT_T b[], size_t ndigits)
	Returns sign of `(a-b)` as `{-1,0,+1}` using constant-time algorithm. More...

const char *	mpCompileTime (void)
	Returns a pointer to a static string containing the time of compilation. More...

size_t	mpConvFromDecimal (DIGIT_T a[], size_t ndigits, const char *s)
	Converts a string in decimal format to a big digit. More...

size_t	mpConvFromHex (DIGIT_T a[], size_t ndigits, const char *s)
	Converts a string in hexadecimal format to a big digit. More...

size_t	mpConvFromOctets (DIGIT_T a[], size_t ndigits, const unsigned char *c, size_t nbytes)
	Converts nbytes octets into big digit a of max size ndigits. More...

size_t	mpConvFromStr (DIGIT_T a[], size_t ndigits, const char s, char *endptr, int base)
	Converts a string of digits in the specified radix `base` to a big digit array. More...

size_t	mpConvToDecimal (const DIGIT_T a[], size_t ndigits, char *s, size_t smax)
	Converts big digit a into a string in decimal format, where s has size smax including the terminating zero. More...

size_t	mpConvToHex (const DIGIT_T a[], size_t ndigits, char *s, size_t smax)
	Converts big digit a into a string in hexadecimal format, where s has size smax including the terminating zero. More...

size_t	mpConvToOctets (const DIGIT_T a[], size_t ndigits, unsigned char *c, size_t nbytes)
	Converts big digit a into string of octets, in big-endian order, padding to nbytes or truncating if necessary. More...

int	mpCubeRoot (DIGIT_T s[], const DIGIT_T x[], size_t ndigits)
	Computes integer cube root s = floor(cuberoot(x)) More...

int	mpDivide (DIGIT_T q[], DIGIT_T r[], const DIGIT_T u[], size_t udigits, DIGIT_T v[], size_t vdigits)
	Computes integer division of u by v such that u=qv+r. More...

int	mpEqual (const DIGIT_T a[], const DIGIT_T b[], size_t ndigits)
	Returns true if a == b, else false. More...

int	mpEqual_ct (const DIGIT_T a[], const DIGIT_T b[], size_t ndigits)
	Returns true if a == b, else false, using constant-time algorithm. More...

int	mpGcd (DIGIT_T g[], const DIGIT_T x[], const DIGIT_T y[], size_t ndigits)
	Computes g = gcd(x, y), the greatest common divisor of x and y. More...

int	mpGetBit (const DIGIT_T a[], size_t ndigits, size_t n)
	Returns value 1 or 0 of bit n (0..nbits-1) More...

int	mpIsNegative (const DIGIT_T x[], size_t ndigits)
	Returns true (1) if x < 0, else false (0) More...

int	mpIsPrime (DIGIT_T w[], size_t ndigits, size_t t)
	Returns true (1) if `w` is probably prime. More...

int	mpIsZero (const DIGIT_T a[], size_t ndigits)
	Returns true if a is zero, else false. More...

int	mpIsZero_ct (const DIGIT_T a[], size_t ndigits)
	Returns true if a is zero, else false, using constant-time algorithm. More...

int	mpJacobi (const DIGIT_T a[], const DIGIT_T n[], size_t ndigits)
	Returns the Jacobi symbol (a/n) in {-1, 0, +1}. More...

void	mpModAdd (DIGIT_T w[], const DIGIT_T u[], const DIGIT_T v[], const DIGIT_T m[], size_t ndigits)
	Computes w = u + v (mod m) More...

int	mpModExp (DIGIT_T y[], const DIGIT_T x[], const DIGIT_T e[], DIGIT_T m[], size_t ndigits)
	Computes y = x^e mod m. More...

int	mpModExp_ct (DIGIT_T yout[], const DIGIT_T x[], const DIGIT_T e[], DIGIT_T m[], size_t ndigits)
	Computes y = x^e mod m in constant time. More...

void	mpModHalve (DIGIT_T w[], const DIGIT_T u[], const DIGIT_T p[], size_t ndigits)
	Computes w = u/2 (mod p) for an odd prime p. More...

int	mpModInv (DIGIT_T inv[], const DIGIT_T u[], const DIGIT_T m[], size_t ndigits)
	Computes the inverse of `u` modulo `m`, inv = u^{-1} mod m. More...

int	mpModMult (DIGIT_T a[], const DIGIT_T x[], const DIGIT_T y[], DIGIT_T m[], size_t ndigits)
	Computes a = (x * y) mod m. More...

void	mpModPowerOf2 (DIGIT_T a[], size_t ndigits, size_t L)
	Computes a = a mod 2^L, ie clears all bits greater than L. More...

void	mpModSpecial (DIGIT_T u[], const DIGIT_T v[], const DIGIT_T m[], size_t ndigits)
	Computes u = v (mod m) in the special case where `0<=v<km` for small k. More...

int	mpModSqrt (DIGIT_T x[], const DIGIT_T a[], DIGIT_T p[], size_t ndigits)
	Computes x = one square root of an integer `a` modulo an odd prime `p` More...

int	mpModSquare (DIGIT_T a[], const DIGIT_T x[], DIGIT_T m[], size_t ndigits)
	Computes a = x^2 mod m. More...

void	mpModSub (DIGIT_T w[], const DIGIT_T u[], const DIGIT_T v[], const DIGIT_T m[], size_t ndigits)
	Computes w = u - v (mod m) More...

int	mpModulo (DIGIT_T r[], const DIGIT_T u[], size_t udigits, DIGIT_T v[], size_t vdigits)
	Computes remainder r = u mod v. More...

int	mpMultiply (DIGIT_T w[], const DIGIT_T u[], const DIGIT_T v[], size_t ndigits)
	Computes product w = u * v. More...

void	mpNotBits (DIGIT_T a[], const DIGIT_T b[], size_t ndigits)
	Computes bitwise a = NOT b. More...

void	mpOrBits (DIGIT_T a[], const DIGIT_T b[], const DIGIT_T c[], size_t ndigits)
	Computes bitwise a = b OR c. More...

void	mpPrint (const DIGIT_T *a, size_t ndigits)
	Print all digits in hex incl leading zero digits. More...

void	mpPrintBits (const char prefix, DIGIT_T a, size_t ndigits, const char *suffix)
	Print in bit (0/1) format with optional prefix and suffix strings. More...

void	mpPrintDecimal (const char prefix, const DIGIT_T a, size_t ndigits, const char *suffix)
	Print in decimal format with optional prefix and suffix strings. More...

void	mpPrintDecimalSigned (const char prefix, DIGIT_T a, size_t ndigits, const char *suffix)
	Print a signed integer in decimal format with optional prefix and suffix strings. More...

void	mpPrintHex (const char prefix, const DIGIT_T a, size_t ndigits, const char *suffix)
	Print in hex format with optional prefix and suffix strings. More...

void	mpPrintNL (const DIGIT_T *a, size_t ndigits)
	Print all digits in hex with newlines. More...

void	mpPrintTrim (const DIGIT_T *a, size_t ndigits)
	Print in hex but trim leading zero digits. More...

void	mpPrintTrimNL (const DIGIT_T *a, size_t ndigits)
	Print in hex, trim leading zeroes, add newlines. More...

size_t	mpQuickRandBits (DIGIT_T a[], size_t ndigits, size_t nbits)
	Generate a quick-and-dirty random mp number a of bit length at most `nbits` using plain-old-rand. More...

int	mpRabinMiller (DIGIT_T w[], size_t ndigits, size_t t)
	Returns true (1) if `w` is probably prime using just the Rabin-Miller test. More...

int	mpSetBit (DIGIT_T a[], size_t ndigits, size_t n, int value)
	Sets bit n of a (0..nbits-1) with value 1 or 0. More...

void	mpSetDigit (DIGIT_T a[], DIGIT_T d, size_t ndigits)
	Sets a = d where d is a single digit. More...

void	mpSetEqual (DIGIT_T a[], const DIGIT_T b[], size_t ndigits)
	Sets a = b. More...

volatile DIGIT_T	mpSetZero (volatile DIGIT_T a[], size_t ndigits)
	Sets a = 0. More...

DIGIT_T	mpShiftLeft (DIGIT_T a[], const DIGIT_T b[], size_t x, size_t ndigits)
	Computes a = b << x. More...

DIGIT_T	mpShiftRight (DIGIT_T a[], const DIGIT_T b[], size_t x, size_t ndigits)
	Computes a = b >> x. More...

DIGIT_T	mpShortAdd (DIGIT_T w[], const DIGIT_T u[], DIGIT_T d, size_t ndigits)
	Computes w = u + d, returns carry. More...

int	mpShortCmp (const DIGIT_T a[], DIGIT_T d, size_t ndigits)
	Returns sign of (a - d) where d is a single digit. More...

DIGIT_T	mpShortDiv (DIGIT_T q[], const DIGIT_T u[], DIGIT_T d, size_t ndigits)
	Computes quotient q = u div d, returns remainder. More...

int	mpShortIsEqual (const DIGIT_T a[], DIGIT_T d, size_t ndigits)
	Returns true if a == d, else false, where d is a single digit. More...

DIGIT_T	mpShortMod (const DIGIT_T a[], DIGIT_T d, size_t ndigits)
	Computes remainder r = a mod d. More...

DIGIT_T	mpShortMult (DIGIT_T p[], const DIGIT_T x[], DIGIT_T d, size_t ndigits)
	Computes product p = x * d. More...

DIGIT_T	mpShortSub (DIGIT_T w[], const DIGIT_T u[], DIGIT_T d, size_t ndigits)
	Computes w = u - d, returns borrow. More...

size_t	mpSizeof (const DIGIT_T a[], size_t ndigits)
	Returns number of significant non-zero digits in a. More...

int	mpSqrt (DIGIT_T s[], const DIGIT_T x[], size_t ndigits)
	Computes integer square root s = floor(sqrt(x)) More...

int	mpSquare (DIGIT_T w[], const DIGIT_T x[], size_t ndigits)
	Computes square w = x^2. More...

DIGIT_T	mpSubtract (DIGIT_T w[], const DIGIT_T u[], const DIGIT_T v[], size_t ndigits)
	Computes w = u - v, returns borrow. More...

DIGIT_T	mpToShort (const DIGIT_T a[], size_t ndigits)
	Returns the least significant digit in a. More...

int	mpVersion (void)
	Returns version number = major1000+minor100+release*10+PP_OPTIONS. More...

void	mpXorBits (DIGIT_T a[], const DIGIT_T b[], const DIGIT_T c[], size_t ndigits)
	Computes bitwise a = b XOR c. More...

DIGIT_T	spDivide (DIGIT_T q, DIGIT_T r, const DIGIT_T u[2], DIGIT_T v)
	Computes quotient q = u div v, remainder r = u mod v, where q, r and v are single digits. More...

int	spMultiply (DIGIT_T p[2], DIGIT_T x, DIGIT_T y)
	Computes p = x * y, where x and y are single digits. More...

DIGIT_T	spSimpleRand (DIGIT_T lower, DIGIT_T upper)
	Returns a simple pseudo-random digit between lower and upper. More...

Detailed Description

Interface to core BigDigits "mp" functions using fixed-length arrays.

Typedef Documentation

◆ DIGIT_T

typedef uint32_t DIGIT_T

The basic BigDigit element, an unsigned 32-bit integer.

Function Documentation

◆ mpAbs()

int mpAbs	(	DIGIT_T	x[],
		const DIGIT_T	y[],
		size_t	ndigits
	)

Sets x = |y|, the absolute value of y.

Remarks: Expects a negative number to be stored in two's-complement representation.

◆ mpAdd()

DIGIT_T mpAdd	(	DIGIT_T	w[],
		const DIGIT_T	u[],
		const DIGIT_T	v[],
		size_t	ndigits
	)

Computes w = u + v, returns carry.

Precondition: w and v must not overlap.

◆ mpAndBits()

void mpAndBits	(	DIGIT_T	a[],
		const DIGIT_T	b[],
		const DIGIT_T	c[],
		size_t	ndigits
	)

Computes bitwise a = b AND c.

◆ mpBitLength()

size_t mpBitLength	(	const DIGIT_T	a[],
		size_t	ndigits
	)

Returns number of significant bits in a.

◆ mpChs()

int mpChs	(	DIGIT_T	x[],
		const DIGIT_T	y[],
		size_t	ndigits
	)

Sets x = -y.

Remarks: Expects a negative number to be stored in two's-complement representation.

◆ mpCompare()

int mpCompare	(	const DIGIT_T	a[],
		const DIGIT_T	b[],
		size_t	ndigits
	)

Returns sign of (a-b) as {-1,0,+1}

Remarks: Not constant-time.

◆ mpCompare_ct()

int mpCompare_ct	(	const DIGIT_T	a[],
		const DIGIT_T	b[],
		size_t	ndigits
	)

Returns sign of (a-b) as {-1,0,+1} using constant-time algorithm.

◆ mpCompileTime()

const char* mpCompileTime ( void )

Returns a pointer to a static string containing the time of compilation.

◆ mpConvFromDecimal()

size_t mpConvFromDecimal	(	DIGIT_T	a[],
		size_t	ndigits,
		const char *	s
	)

Converts a string in decimal format to a big digit.

Returns: actual number of (possibly zero) digits set.

◆ mpConvFromHex()

size_t mpConvFromHex	(	DIGIT_T	a[],
		size_t	ndigits,
		const char *	s
	)

Converts a string in hexadecimal format to a big digit.

Returns: actual number of (possibly zero) digits set.

◆ mpConvFromOctets()

size_t mpConvFromOctets	(	DIGIT_T	a[],
		size_t	ndigits,
		const unsigned char *	c,
		size_t	nbytes
	)

Converts nbytes octets into big digit a of max size ndigits.

Returns: actual number of digits set

◆ mpConvFromStr()

size_t mpConvFromStr	(	DIGIT_T	a[],
		size_t	ndigits,
		const char *	s,
		char **	endptr,
		int	base
	)

Converts a string of digits in the specified radix base to a big digit array.

Supported bases are 10 (decimal), 16 (hexadecimal), and 2 (binary). The conversion stops at the first invalid character or end of string. Sets endptr to point to the first character that could not be converted, similar to ANSI strtoul. If base is 0 then base 10 is assumed unless the prefix 0x or 0b is present, denoting base 16 or base 2 respectively.

◆ mpConvToDecimal()

size_t mpConvToDecimal	(	const DIGIT_T	a[],
		size_t	ndigits,
		char *	s,
		size_t	smax
	)

Converts big digit a into a string in decimal format, where s has size smax including the terminating zero.

Returns: number of chars required excluding leading zeroes.

◆ mpConvToHex()

size_t mpConvToHex	(	const DIGIT_T	a[],
		size_t	ndigits,
		char *	s,
		size_t	smax
	)

Converts big digit a into a string in hexadecimal format, where s has size smax including the terminating zero.

Returns: number of chars required excluding leading zeroes.

◆ mpConvToOctets()

size_t mpConvToOctets	(	const DIGIT_T	a[],
		size_t	ndigits,
		unsigned char *	c,
		size_t	nbytes
	)

Converts big digit a into string of octets, in big-endian order, padding to nbytes or truncating if necessary.

Returns: number of non-zero octets required.

◆ mpCubeRoot()

int mpCubeRoot	(	DIGIT_T	s[],
		const DIGIT_T	x[],
		size_t	ndigits
	)

Computes integer cube root s = floor(cuberoot(x))

◆ mpDivide()

int mpDivide	(	DIGIT_T	q[],
		DIGIT_T	r[],
		const DIGIT_T	u[],
		size_t	udigits,
		DIGIT_T	v[],
		size_t	vdigits
	)

Computes integer division of u by v such that u=qv+r.

Parameters

[out]	q	to receive quotient = u div v, an array of size `udigits`
[out]	r	to receive divisor = u mod v, an array of size `udigits`
[in]	u	dividend of size `udigits`
[in]	udigits	size of arrays `q` `r` and `u`
[in]	v	divisor of size `vdigits`
[in]	vdigits	size of array `v`

Precondition: q and r must be independent of u and v.

Warning: Trashes q and r first

◆ mpEqual()

int mpEqual	(	const DIGIT_T	a[],
		const DIGIT_T	b[],
		size_t	ndigits
	)

Returns true if a == b, else false.

Remarks: Not constant-time.

◆ mpEqual_ct()

int mpEqual_ct	(	const DIGIT_T	a[],
		const DIGIT_T	b[],
		size_t	ndigits
	)

Returns true if a == b, else false, using constant-time algorithm.

◆ mpGcd()

int mpGcd	(	DIGIT_T	g[],
		const DIGIT_T	x[],
		const DIGIT_T	y[],
		size_t	ndigits
	)

Computes g = gcd(x, y), the greatest common divisor of x and y.

◆ mpGetBit()

int mpGetBit	(	const DIGIT_T	a[],
		size_t	ndigits,
		size_t	n
	)

Returns value 1 or 0 of bit n (0..nbits-1)

◆ mpIsNegative()

int mpIsNegative	(	const DIGIT_T	x[],
		size_t	ndigits
	)

Returns true (1) if x < 0, else false (0)

Remarks: Expects a negative number to be stored in two's-complement representation.

◆ mpIsPrime()

int mpIsPrime	(	DIGIT_T	w[],
		size_t	ndigits,
		size_t	t
	)

Returns true (1) if w is probably prime.

Parameters

[in]	w	Number to test
[in]	ndigits	size of array `w`
[in]	t	The count of Rabin-Miller primality tests to carry out (recommended at least 80)

Returns: true (1) if w is probably prime otherwise false (0)

Remarks: Uses FIPS-186-2/Rabin-Miller with trial division by small primes, which is faster in most cases than mpRabinMiller().

See also: mpRabinMiller().

◆ mpIsZero()

int mpIsZero	(	const DIGIT_T	a[],
		size_t	ndigits
	)

Returns true if a is zero, else false.

Remarks: Not constant-time.

◆ mpIsZero_ct()

int mpIsZero_ct	(	const DIGIT_T	a[],
		size_t	ndigits
	)

Returns true if a is zero, else false, using constant-time algorithm.

◆ mpJacobi()

int mpJacobi	(	const DIGIT_T	a[],
		const DIGIT_T	n[],
		size_t	ndigits
	)

Returns the Jacobi symbol (a/n) in {-1, 0, +1}.

Remarks

If n is prime then the Jacobi symbol becomes the Legendre symbol (a/p) defined to be

(a/p) = +1 if a is a quadratic residue modulo p
(a/p) = -1 if a is a quadratic non-residue modulo p
(a/p) = 0 if a is divisible by p

◆ mpModAdd()

void mpModAdd	(	DIGIT_T	w[],
		const DIGIT_T	u[],
		const DIGIT_T	v[],
		const DIGIT_T	m[],
		size_t	ndigits
	)

Computes w = u + v (mod m)

Precondition: Require u and v to be in the range [0, m-1]. The variables w and v must not overlap.

Remarks: Quicker than adding then using mpModulo()

◆ mpModExp()

int mpModExp	(	DIGIT_T	y[],
		const DIGIT_T	x[],
		const DIGIT_T	e[],
		DIGIT_T	m[],
		size_t	ndigits
	)

Computes y = x^e mod m.

◆ mpModExp_ct()

int mpModExp_ct	(	DIGIT_T	yout[],
		const DIGIT_T	x[],
		const DIGIT_T	e[],
		DIGIT_T	m[],
		size_t	ndigits
	)

Computes y = x^e mod m in constant time.

Remarks: Resistant to simple power analysis attack on private exponent. Slower than mpModExp().

◆ mpModHalve()

void mpModHalve	(	DIGIT_T	w[],
		const DIGIT_T	u[],
		const DIGIT_T	p[],
		size_t	ndigits
	)

Computes w = u/2 (mod p) for an odd prime p.

Precondition: Require u to be in the range [0,p-1]

◆ mpModInv()

int mpModInv	(	DIGIT_T	inv[],
		const DIGIT_T	u[],
		const DIGIT_T	m[],
		size_t	ndigits
	)

Computes the inverse of u modulo m, inv = u^{-1} mod m.

◆ mpModMult()

int mpModMult	(	DIGIT_T	a[],
		const DIGIT_T	x[],
		const DIGIT_T	y[],
		DIGIT_T	m[],
		size_t	ndigits
	)

Computes a = (x * y) mod m.

◆ mpModPowerOf2()

void mpModPowerOf2	(	DIGIT_T	a[],
		size_t	ndigits,
		size_t	L
	)

Computes a = a mod 2^L, ie clears all bits greater than L.

◆ mpModSpecial()

void mpModSpecial	(	DIGIT_T	u[],
		const DIGIT_T	v[],
		const DIGIT_T	m[],
		size_t	ndigits
	)

Computes u = v (mod m) in the special case where 0<=v<km for small k.

Remarks: Uses subtraction instead of division, so is much faster than mpModulo() in this case.

Precondition: v is in the range [0,km] where k is a small integer

Warning: Use only if you know k is small, say < 3.

◆ mpModSqrt()

int mpModSqrt	(	DIGIT_T	x[],
		const DIGIT_T	a[],
		DIGIT_T	p[],
		size_t	ndigits
	)

Computes x = one square root of an integer a modulo an odd prime p

Parameters

x	To receive the result
a	An integer expected to be a quadratic residue modulo p
p	An odd prime
ndigits	The number of digits in each of the parameters

Returns: 0 if successful, or -1 if square root does not exist

Remarks: More precisely, find an integer x such that x^2 mod p = a. Uses the Tonelli-Shanks algorithm. The other square root is p - x.

Warning: Check the return value before using the result x.

◆ mpModSquare()

int mpModSquare	(	DIGIT_T	a[],
		const DIGIT_T	x[],
		DIGIT_T	m[],
		size_t	ndigits
	)

Computes a = x^2 mod m.

◆ mpModSub()

void mpModSub	(	DIGIT_T	w[],
		const DIGIT_T	u[],
		const DIGIT_T	v[],
		const DIGIT_T	m[],
		size_t	ndigits
	)

Computes w = u - v (mod m)

Precondition: Require u and v to be in the range [0, m-1]. The variables w and v must not overlap.

Remarks: Quicker than subtracting then using mpModulo()

◆ mpModulo()

int mpModulo	(	DIGIT_T	r[],
		const DIGIT_T	u[],
		size_t	udigits,
		DIGIT_T	v[],
		size_t	vdigits
	)

Computes remainder r = u mod v.

Parameters

[out]	r	to receive divisor = u mod v, an array of size `vdigits`
[in]	u	dividend of size `udigits`
[in]	udigits	size of arrays `r` and `u`
[in]	v	divisor of size `vdigits`
[in]	vdigits	size of array `v`

Precondition: r and u must not overlap.

Remarks: Note that r is vdigits long here, but is udigits long in mpDivide().

◆ mpMultiply()

int mpMultiply	(	DIGIT_T	w[],
		const DIGIT_T	u[],
		const DIGIT_T	v[],
		size_t	ndigits
	)

Computes product w = u * v.

Parameters

[out]	w	To receive the product, an array of size 2 x `ndigits`
[in]	u	An array of size `ndigits`
[in]	v	An array of size `ndigits`
[in]	ndigits	size of arrays `u` and `v`

Precondition: w and u must not overlap.

Warning: The product must be of size 2 x ndigits

◆ mpNotBits()

void mpNotBits	(	DIGIT_T	a[],
		const DIGIT_T	b[],
		size_t	ndigits
	)

Computes bitwise a = NOT b.

◆ mpOrBits()

void mpOrBits	(	DIGIT_T	a[],
		const DIGIT_T	b[],
		const DIGIT_T	c[],
		size_t	ndigits
	)

Computes bitwise a = b OR c.

◆ mpPrint()

void mpPrint	(	const DIGIT_T *	a,
		size_t	ndigits
	)

Print all digits in hex incl leading zero digits.

◆ mpPrintBits()

void mpPrintBits	(	const char *	prefix,
		DIGIT_T *	a,
		size_t	ndigits,
		const char *	suffix
	)

Print in bit (0/1) format with optional prefix and suffix strings.

◆ mpPrintDecimal()

void mpPrintDecimal	(	const char *	prefix,
		const DIGIT_T *	a,
		size_t	ndigits,
		const char *	suffix
	)

Print in decimal format with optional prefix and suffix strings.

◆ mpPrintDecimalSigned()

void mpPrintDecimalSigned	(	const char *	prefix,
		DIGIT_T *	a,
		size_t	ndigits,
		const char *	suffix
	)

Print a signed integer in decimal format with optional prefix and suffix strings.

Remarks: Expects a negative number to be stored in two's-complement representation.

◆ mpPrintHex()

void mpPrintHex	(	const char *	prefix,
		const DIGIT_T *	a,
		size_t	ndigits,
		const char *	suffix
	)

Print in hex format with optional prefix and suffix strings.

◆ mpPrintNL()

void mpPrintNL	(	const DIGIT_T *	a,
		size_t	ndigits
	)

Print all digits in hex with newlines.

◆ mpPrintTrim()

void mpPrintTrim	(	const DIGIT_T *	a,
		size_t	ndigits
	)

Print in hex but trim leading zero digits.

Deprecated:: Use mpPrintHex()

◆ mpPrintTrimNL()

void mpPrintTrimNL	(	const DIGIT_T *	a,
		size_t	ndigits
	)

Print in hex, trim leading zeroes, add newlines.

Deprecated:: Use mpPrintHex()

◆ mpQuickRandBits()

size_t mpQuickRandBits	(	DIGIT_T	a[],
		size_t	ndigits,
		size_t	nbits
	)

Generate a quick-and-dirty random mp number a of bit length at most nbits using plain-old-rand.

Remarks: Not crypto secure.

See also: mpRandomBits()

◆ mpRabinMiller()

int mpRabinMiller	(	DIGIT_T	w[],
		size_t	ndigits,
		size_t	t
	)

Returns true (1) if w is probably prime using just the Rabin-Miller test.

See also: mpIsPrime() is preferred.

◆ mpSetBit()

int mpSetBit	(	DIGIT_T	a[],
		size_t	ndigits,
		size_t	n,
		int	value
	)

Sets bit n of a (0..nbits-1) with value 1 or 0.

◆ mpSetDigit()

void mpSetDigit	(	DIGIT_T	a[],
		DIGIT_T	d,
		size_t	ndigits
	)

Sets a = d where d is a single digit.

◆ mpSetEqual()

void mpSetEqual	(	DIGIT_T	a[],
		const DIGIT_T	b[],
		size_t	ndigits
	)

Sets a = b.

◆ mpSetZero()

volatile DIGIT_T mpSetZero	(	volatile DIGIT_T	a[],
		size_t	ndigits
	)

Sets a = 0.

◆ mpShiftLeft()

DIGIT_T mpShiftLeft	(	DIGIT_T	a[],
		const DIGIT_T	b[],
		size_t	x,
		size_t	ndigits
	)

Computes a = b << x.

◆ mpShiftRight()

DIGIT_T mpShiftRight	(	DIGIT_T	a[],
		const DIGIT_T	b[],
		size_t	x,
		size_t	ndigits
	)

Computes a = b >> x.

◆ mpShortAdd()

DIGIT_T mpShortAdd	(	DIGIT_T	w[],
		const DIGIT_T	u[],
		DIGIT_T	d,
		size_t	ndigits
	)

Computes w = u + d, returns carry.

◆ mpShortCmp()

int mpShortCmp	(	const DIGIT_T	a[],
		DIGIT_T	d,
		size_t	ndigits
	)

Returns sign of (a - d) where d is a single digit.

◆ mpShortDiv()

DIGIT_T mpShortDiv	(	DIGIT_T	q[],
		const DIGIT_T	u[],
		DIGIT_T	d,
		size_t	ndigits
	)

Computes quotient q = u div d, returns remainder.

◆ mpShortIsEqual()

int mpShortIsEqual	(	const DIGIT_T	a[],
		DIGIT_T	d,
		size_t	ndigits
	)

Returns true if a == d, else false, where d is a single digit.

◆ mpShortMod()

DIGIT_T mpShortMod	(	const DIGIT_T	a[],
		DIGIT_T	d,
		size_t	ndigits
	)

Computes remainder r = a mod d.

◆ mpShortMult()

DIGIT_T mpShortMult	(	DIGIT_T	p[],
		const DIGIT_T	x[],
		DIGIT_T	d,
		size_t	ndigits
	)

Computes product p = x * d.

◆ mpShortSub()

DIGIT_T mpShortSub	(	DIGIT_T	w[],
		const DIGIT_T	u[],
		DIGIT_T	d,
		size_t	ndigits
	)

Computes w = u - d, returns borrow.

◆ mpSizeof()

size_t mpSizeof	(	const DIGIT_T	a[],
		size_t	ndigits
	)

Returns number of significant non-zero digits in a.

◆ mpSqrt()

int mpSqrt	(	DIGIT_T	s[],
		const DIGIT_T	x[],
		size_t	ndigits
	)

Computes integer square root s = floor(sqrt(x))

◆ mpSquare()

int mpSquare	(	DIGIT_T	w[],
		const DIGIT_T	x[],
		size_t	ndigits
	)

Computes square w = x^2.

Parameters

[out]	w	array of size 2 x `ndigits` to receive square
[in]	x	array of size `ndigits`
[in]	ndigits	size of array `x`

Precondition: w and x must not overlap.

Warning: The product w must be of size 2 x ndigits

◆ mpSubtract()

DIGIT_T mpSubtract	(	DIGIT_T	w[],
		const DIGIT_T	u[],
		const DIGIT_T	v[],
		size_t	ndigits
	)

Computes w = u - v, returns borrow.

Precondition: w and v must not overlap.

◆ mpToShort()

DIGIT_T mpToShort	(	const DIGIT_T	a[],
		size_t	ndigits
	)

Returns the least significant digit in a.

◆ mpVersion()

int mpVersion ( void )

Returns version number = major*1000+minor*100+release*10+PP_OPTIONS.

◆ mpXorBits()

void mpXorBits	(	DIGIT_T	a[],
		const DIGIT_T	b[],
		const DIGIT_T	c[],
		size_t	ndigits
	)

Computes bitwise a = b XOR c.

◆ spDivide()

DIGIT_T spDivide	(	DIGIT_T *	q,
		DIGIT_T *	r,
		const DIGIT_T	u[2],
		DIGIT_T	v
	)

Computes quotient q = u div v, remainder r = u mod v, where q, r and v are single digits.

◆ spMultiply()

int spMultiply	(	DIGIT_T	p[2],
		DIGIT_T	x,
		DIGIT_T	y
	)

Computes p = x * y, where x and y are single digits.

◆ spSimpleRand()

DIGIT_T spSimpleRand	(	DIGIT_T	lower,
		DIGIT_T	upper
	)

Returns a simple pseudo-random digit between lower and upper.

Remarks: Not crypto secure.

See also: spBetterRand()

Typedefs

Functions

Detailed Description

Typedef Documentation

◆ DIGIT_T

Function Documentation

◆ mpAbs()

◆ mpAdd()

◆ mpAndBits()

◆ mpBitLength()

◆ mpChs()

◆ mpCompare()

◆ mpCompare_ct()

◆ mpCompileTime()

◆ mpConvFromDecimal()

◆ mpConvFromHex()

◆ mpConvFromOctets()

◆ mpConvFromStr()

◆ mpConvToDecimal()

◆ mpConvToHex()

◆ mpConvToOctets()

◆ mpCubeRoot()

◆ mpDivide()

◆ mpEqual()

◆ mpEqual_ct()

◆ mpGcd()

◆ mpGetBit()

◆ mpIsNegative()

◆ mpIsPrime()

◆ mpIsZero()

◆ mpIsZero_ct()

◆ mpJacobi()

◆ mpModAdd()

◆ mpModExp()

◆ mpModExp_ct()

◆ mpModHalve()

◆ mpModInv()

◆ mpModMult()

◆ mpModPowerOf2()

◆ mpModSpecial()

◆ mpModSqrt()

◆ mpModSquare()

◆ mpModSub()

◆ mpModulo()

◆ mpMultiply()

◆ mpNotBits()

◆ mpOrBits()

◆ mpPrint()

◆ mpPrintBits()

◆ mpPrintDecimal()

◆ mpPrintDecimalSigned()

◆ mpPrintHex()

◆ mpPrintNL()

◆ mpPrintTrim()

◆ mpPrintTrimNL()

◆ mpQuickRandBits()

◆ mpRabinMiller()

◆ mpSetBit()

◆ mpSetDigit()

◆ mpSetEqual()

◆ mpSetZero()

◆ mpShiftLeft()

◆ mpShiftRight()

◆ mpShortAdd()

◆ mpShortCmp()

◆ mpShortDiv()

◆ mpShortIsEqual()

◆ mpShortMod()

◆ mpShortMult()

◆ mpShortSub()

◆ mpSizeof()

◆ mpSqrt()

◆ mpSquare()

◆ mpSubtract()

◆ mpToShort()

◆ mpVersion()

◆ mpXorBits()

◆ spDivide()

◆ spMultiply()

◆ spSimpleRand()