docs/fp24.md - incubator-milagro-crypto-js - Git at Google

 <a name="FP24"></a>

 ## FP24
 **Kind**: global class
 **this**: <code>{FP24}</code>

 * [FP24](#FP24)
     * [new FP24()](#new_FP24_new)
     * _instance_
         * [.reduce()](#FP24+reduce)
         * [.norm()](#FP24+norm)
         * [.iszilch()](#FP24+iszilch)
         * [.isunity()](#FP24+isunity)
         * [.cmove(g, d)](#FP24+cmove)
         * [.select()](#FP24+select)
         * [.geta()](#FP24+geta)
         * [.getb()](#FP24+getb)
         * [.getc()](#FP24+getc)
         * [.equals(x)](#FP24+equals)
         * [.copy(x)](#FP24+copy)
         * [.one(x)](#FP24+one)
         * [.zero()](#FP24+zero)
         * [.conj()](#FP24+conj)
         * [.set(d, e, f)](#FP24+set)
         * [.seta(c)](#FP24+seta)
         * [.usqr()](#FP24+usqr)
         * [.sqr()](#FP24+sqr)
         * [.mul(y)](#FP24+mul)
         * [.smul(y)](#FP24+smul)
         * [.ssmul(y)](#FP24+ssmul)
         * [.inverse()](#FP24+inverse)
         * [.frob(f)](#FP24+frob)
         * [.trace()](#FP24+trace)
         * [.toString()](#FP24+toString)
         * [.toBytes(w)](#FP24+toBytes)
         * [.pow(e)](#FP24+pow)
         * [.pinpow(e, bts)](#FP24+pinpow)
         * [.compow(e, r)](#FP24+compow)
     * _static_
         * [.fromBytes(w)](#FP24.fromBytes)
         * [.teq()](#FP24.teq)
         * [.pow8()](#FP24.pow8)

 <a name="new_FP24_new"></a>

 ### new FP24()
 Creates an instance of FP24.

 <a name="FP24+reduce"></a>

 ### fP24.reduce()
 Reduces all components of possibly unreduced FP24 mod Modulus

 **Kind**: instance method of [<code>FP24</code>](#FP24)
 **this**: <code>{FP24}</code>
 <a name="FP24+norm"></a>

 ### fP24.norm()
 Normalises the components of an FP24

 **Kind**: instance method of [<code>FP24</code>](#FP24)
 **this**: <code>{FP24}</code>
 <a name="FP24+iszilch"></a>

 ### fP24.iszilch()
 Tests for FP24 equal to zero

 **Kind**: instance method of [<code>FP24</code>](#FP24)
 **this**: <code>{FP24}</code>
 <a name="FP24+isunity"></a>

 ### fP24.isunity()
 Tests for FP24 equal to unity

 **Kind**: instance method of [<code>FP24</code>](#FP24)
 **this**: <code>{FP24}</code>
 <a name="FP24+cmove"></a>

 ### fP24.cmove(g, d)
 Conditional copy of FP24 number

 **Kind**: instance method of [<code>FP24</code>](#FP24)
 **this**: <code>{FP24}</code>

 | Param | Description |
 | --- | --- |
 | g | FP24 instance |
 | d | copy depends on this value |

 <a name="FP24+select"></a>

 ### fP24.select()
 Constant time select from pre-computed table

 **Kind**: instance method of [<code>FP24</code>](#FP24)
 **this**: <code>{FP24}</code>
 <a name="FP24+geta"></a>

 ### fP24.geta()
 extract a from this

 **Kind**: instance method of [<code>FP24</code>](#FP24)
 **this**: <code>{FP24}</code>
 <a name="FP24+getb"></a>

 ### fP24.getb()
 extract b from this

 **Kind**: instance method of [<code>FP24</code>](#FP24)
 **this**: <code>{FP24}</code>
 <a name="FP24+getc"></a>

 ### fP24.getc()
 extract c from this

 **Kind**: instance method of [<code>FP24</code>](#FP24)
 **this**: <code>{FP24}</code>
 <a name="FP24+equals"></a>

 ### fP24.equals(x)
 Tests for equality of two FP24s

 **Kind**: instance method of [<code>FP24</code>](#FP24)
 **this**: <code>{FP24}</code>

 | Param | Description |
 | --- | --- |
 | x | FP24 instance to compare |

 <a name="FP24+copy"></a>

 ### fP24.copy(x)
 Copy FP24 to another FP24

 **Kind**: instance method of [<code>FP24</code>](#FP24)
 **this**: <code>{FP24}</code>

 | Param | Description |
 | --- | --- |
 | x | FP24 instance to be copied |

 <a name="FP24+one"></a>

 ### fP24.one(x)
 Set FP24 to unity

 **Kind**: instance method of [<code>FP24</code>](#FP24)
 **this**: <code>{FP24}</code>

 | Param | Description |
 | --- | --- |
 | x | FP24 instance to be set to one |

 <a name="FP24+zero"></a>

 ### fP24.zero()
 Set FP24 to zero

 **Kind**: instance method of [<code>FP24</code>](#FP24)
 **this**: <code>{FP24}</code>
 <a name="FP24+conj"></a>

 ### fP24.conj()
 Conjugation of FP24

 **Kind**: instance method of [<code>FP24</code>](#FP24)
 **this**: <code>{FP24}</code>
 <a name="FP24+set"></a>

 ### fP24.set(d, e, f)
 Set FP24 from three FP8 values

 **Kind**: instance method of [<code>FP24</code>](#FP24)
 **this**: <code>{FP24}</code>

 | Param | Description |
 | --- | --- |
 | d | FP8 instance |
 | e | FP8 instance |
 | f | FP8 instance |

 <a name="FP24+seta"></a>

 ### fP24.seta(c)
 Set FP24 from one FP8 value

 **Kind**: instance method of [<code>FP24</code>](#FP24)
 **this**: <code>{FP24}</code>

 | Param | Description |
 | --- | --- |
 | c | FP8 instance |

 <a name="FP24+usqr"></a>

 ### fP24.usqr()
 Fast Squaring of an FP24 in "unitary" form

 **Kind**: instance method of [<code>FP24</code>](#FP24)
 **this**: <code>{FP24}</code>
 <a name="FP24+sqr"></a>

 ### fP24.sqr()
 Fast Squaring of an FP24

 **Kind**: instance method of [<code>FP24</code>](#FP24)
 **this**: <code>{FP24}</code>
 <a name="FP24+mul"></a>

 ### fP24.mul(y)
 Full unconditional Multiplication of two FP24s

 **Kind**: instance method of [<code>FP24</code>](#FP24)
 **this**: <code>{FP24}</code>

 | Param | Description |
 | --- | --- |
 | y | FP24 instance, the multiplier |

 <a name="FP24+smul"></a>

 ### fP24.smul(y)
 Fast multiplication of two sparse FP24s that arises from ATE pairing line functions

 **Kind**: instance method of [<code>FP24</code>](#FP24)
 **this**: <code>{FP24}</code>

 | Param | Description |
 | --- | --- |
 | y | FP24 instance, the multiplier |

 <a name="FP24+ssmul"></a>

 ### fP24.ssmul(y)
 Fast multiplication of what may be sparse multiplicands

 **Kind**: instance method of [<code>FP24</code>](#FP24)
 **this**: <code>{FP24}</code>

 | Param | Description |
 | --- | --- |
 | y | FP24 instance, the multiplier |

 <a name="FP24+inverse"></a>

 ### fP24.inverse()
 Inverting an FP24

 **Kind**: instance method of [<code>FP24</code>](#FP24)
 **this**: <code>{FP24}</code>
 <a name="FP24+frob"></a>

 ### fP24.frob(f)
 Raises an FP24 to the power of the internal modulus p, using the Frobenius

 **Kind**: instance method of [<code>FP24</code>](#FP24)
 **this**: <code>{FP24}</code>

 | Param | Description |
 | --- | --- |
 | f | Modulus |

 <a name="FP24+trace"></a>

 ### fP24.trace()
 Calculate the trace of an FP24

 **Kind**: instance method of [<code>FP24</code>](#FP24)
 **this**: <code>{FP24}</code>
 <a name="FP24+toString"></a>

 ### fP24.toString()
 convert this to hex string

 **Kind**: instance method of [<code>FP24</code>](#FP24)
 **this**: <code>{FP24}</code>
 <a name="FP24+toBytes"></a>

 ### fP24.toBytes(w)
 convert this to byte array

 **Kind**: instance method of [<code>FP24</code>](#FP24)
 **this**: <code>{FP24}</code>

 | Param | Description |
 | --- | --- |
 | w | Byte array |

 <a name="FP24+pow"></a>

 ### fP24.pow(e)
 Raises an FP24 to the power of a BIG

 **Kind**: instance method of [<code>FP24</code>](#FP24)
 **this**: <code>{FP24}</code>

 | Param | Description |
 | --- | --- |
 | e | BIG instance exponent |

 <a name="FP24+pinpow"></a>

 ### fP24.pinpow(e, bts)
 Raises an FP24 instance x to a small integer power, side-channel resistant

 **Kind**: instance method of [<code>FP24</code>](#FP24)
 **this**: <code>{FP24}</code>

 | Param | Description |
 | --- | --- |
 | e | small integer exponent |
 | bts | maximum number of bits in exponent |

 <a name="FP24+compow"></a>

 ### fP24.compow(e, r)
 Raises an FP24 instance to a BIG power, compressed to FP4

 **Kind**: instance method of [<code>FP24</code>](#FP24)
 **this**: <code>{FP24}</code>

 | Param | Description |
 | --- | --- |
 | e | BIG exponent |
 | r | BIG group order |

 <a name="FP24.fromBytes"></a>

 ### FP24.fromBytes(w)
 convert from byte array to FP24

 **Kind**: static method of [<code>FP24</code>](#FP24)
 **this**: <code>{FP24}</code>

 | Param | Description |
 | --- | --- |
 | w | Byte array |

 <a name="FP24.teq"></a>

 ### FP24.teq()
 return 1 if b==c, no branching

 **Kind**: static method of [<code>FP24</code>](#FP24)
 **this**: <code>{FP24}</code>
 <a name="FP24.pow8"></a>

 ### FP24.pow8()
 p=q0^u0.q1^u1.q2^u2.q3^u3...

 **Kind**: static method of [<code>FP24</code>](#FP24)
 **this**: <code>{FP24}</code>
	<a name="FP24"></a>

	## FP24
	Kind: global class
	this: <code>{FP24}</code>

	* [FP24](#FP24)
	* [new FP24()](#new_FP24_new)
	* _instance_
	* [.reduce()](#FP24+reduce)
	* [.norm()](#FP24+norm)
	* [.iszilch()](#FP24+iszilch)
	* [.isunity()](#FP24+isunity)
	* [.cmove(g, d)](#FP24+cmove)
	* [.select()](#FP24+select)
	* [.geta()](#FP24+geta)
	* [.getb()](#FP24+getb)
	* [.getc()](#FP24+getc)
	* [.equals(x)](#FP24+equals)
	* [.copy(x)](#FP24+copy)
	* [.one(x)](#FP24+one)
	* [.zero()](#FP24+zero)
	* [.conj()](#FP24+conj)
	* [.set(d, e, f)](#FP24+set)
	* [.seta(c)](#FP24+seta)
	* [.usqr()](#FP24+usqr)
	* [.sqr()](#FP24+sqr)
	* [.mul(y)](#FP24+mul)
	* [.smul(y)](#FP24+smul)
	* [.ssmul(y)](#FP24+ssmul)
	* [.inverse()](#FP24+inverse)
	* [.frob(f)](#FP24+frob)
	* [.trace()](#FP24+trace)
	* [.toString()](#FP24+toString)
	* [.toBytes(w)](#FP24+toBytes)
	* [.pow(e)](#FP24+pow)
	* [.pinpow(e, bts)](#FP24+pinpow)
	* [.compow(e, r)](#FP24+compow)
	* _static_
	* [.fromBytes(w)](#FP24.fromBytes)
	* [.teq()](#FP24.teq)
	* [.pow8()](#FP24.pow8)

	<a name="new_FP24_new"></a>

	### new FP24()
	Creates an instance of FP24.

	<a name="FP24+reduce"></a>

	### fP24.reduce()
	Reduces all components of possibly unreduced FP24 mod Modulus

	Kind: instance method of [<code>FP24</code>](#FP24)
	this: <code>{FP24}</code>
	<a name="FP24+norm"></a>

	### fP24.norm()
	Normalises the components of an FP24

	Kind: instance method of [<code>FP24</code>](#FP24)
	this: <code>{FP24}</code>
	<a name="FP24+iszilch"></a>

	### fP24.iszilch()
	Tests for FP24 equal to zero

	Kind: instance method of [<code>FP24</code>](#FP24)
	this: <code>{FP24}</code>
	<a name="FP24+isunity"></a>

	### fP24.isunity()
	Tests for FP24 equal to unity

	Kind: instance method of [<code>FP24</code>](#FP24)
	this: <code>{FP24}</code>
	<a name="FP24+cmove"></a>

	### fP24.cmove(g, d)
	Conditional copy of FP24 number

	Kind: instance method of [<code>FP24</code>](#FP24)
	this: <code>{FP24}</code>

	\| Param \| Description \|
	\| --- \| --- \|
	\| g \| FP24 instance \|
	\| d \| copy depends on this value \|

	<a name="FP24+select"></a>

	### fP24.select()
	Constant time select from pre-computed table

	Kind: instance method of [<code>FP24</code>](#FP24)
	this: <code>{FP24}</code>
	<a name="FP24+geta"></a>

	### fP24.geta()
	extract a from this

	Kind: instance method of [<code>FP24</code>](#FP24)
	this: <code>{FP24}</code>
	<a name="FP24+getb"></a>

	### fP24.getb()
	extract b from this

	Kind: instance method of [<code>FP24</code>](#FP24)
	this: <code>{FP24}</code>
	<a name="FP24+getc"></a>

	### fP24.getc()
	extract c from this

	Kind: instance method of [<code>FP24</code>](#FP24)
	this: <code>{FP24}</code>
	<a name="FP24+equals"></a>

	### fP24.equals(x)
	Tests for equality of two FP24s

	Kind: instance method of [<code>FP24</code>](#FP24)
	this: <code>{FP24}</code>

	\| Param \| Description \|
	\| --- \| --- \|
	\| x \| FP24 instance to compare \|

	<a name="FP24+copy"></a>

	### fP24.copy(x)
	Copy FP24 to another FP24

	Kind: instance method of [<code>FP24</code>](#FP24)
	this: <code>{FP24}</code>

	\| Param \| Description \|
	\| --- \| --- \|
	\| x \| FP24 instance to be copied \|

	<a name="FP24+one"></a>

	### fP24.one(x)
	Set FP24 to unity

	Kind: instance method of [<code>FP24</code>](#FP24)
	this: <code>{FP24}</code>

	\| Param \| Description \|
	\| --- \| --- \|
	\| x \| FP24 instance to be set to one \|

	<a name="FP24+zero"></a>

	### fP24.zero()
	Set FP24 to zero

	Kind: instance method of [<code>FP24</code>](#FP24)
	this: <code>{FP24}</code>
	<a name="FP24+conj"></a>

	### fP24.conj()
	Conjugation of FP24

	Kind: instance method of [<code>FP24</code>](#FP24)
	this: <code>{FP24}</code>
	<a name="FP24+set"></a>

	### fP24.set(d, e, f)
	Set FP24 from three FP8 values

	Kind: instance method of [<code>FP24</code>](#FP24)
	this: <code>{FP24}</code>

	\| Param \| Description \|
	\| --- \| --- \|
	\| d \| FP8 instance \|
	\| e \| FP8 instance \|
	\| f \| FP8 instance \|

	<a name="FP24+seta"></a>

	### fP24.seta(c)
	Set FP24 from one FP8 value

	Kind: instance method of [<code>FP24</code>](#FP24)
	this: <code>{FP24}</code>

	\| Param \| Description \|
	\| --- \| --- \|
	\| c \| FP8 instance \|

	<a name="FP24+usqr"></a>

	### fP24.usqr()
	Fast Squaring of an FP24 in "unitary" form

	Kind: instance method of [<code>FP24</code>](#FP24)
	this: <code>{FP24}</code>
	<a name="FP24+sqr"></a>

	### fP24.sqr()
	Fast Squaring of an FP24

	Kind: instance method of [<code>FP24</code>](#FP24)
	this: <code>{FP24}</code>
	<a name="FP24+mul"></a>

	### fP24.mul(y)
	Full unconditional Multiplication of two FP24s

	Kind: instance method of [<code>FP24</code>](#FP24)
	this: <code>{FP24}</code>

	\| Param \| Description \|
	\| --- \| --- \|
	\| y \| FP24 instance, the multiplier \|

	<a name="FP24+smul"></a>

	### fP24.smul(y)
	Fast multiplication of two sparse FP24s that arises from ATE pairing line functions

	Kind: instance method of [<code>FP24</code>](#FP24)
	this: <code>{FP24}</code>

	\| Param \| Description \|
	\| --- \| --- \|
	\| y \| FP24 instance, the multiplier \|

	<a name="FP24+ssmul"></a>

	### fP24.ssmul(y)
	Fast multiplication of what may be sparse multiplicands

	Kind: instance method of [<code>FP24</code>](#FP24)
	this: <code>{FP24}</code>

	\| Param \| Description \|
	\| --- \| --- \|
	\| y \| FP24 instance, the multiplier \|

	<a name="FP24+inverse"></a>

	### fP24.inverse()
	Inverting an FP24

	Kind: instance method of [<code>FP24</code>](#FP24)
	this: <code>{FP24}</code>
	<a name="FP24+frob"></a>

	### fP24.frob(f)
	Raises an FP24 to the power of the internal modulus p, using the Frobenius

	Kind: instance method of [<code>FP24</code>](#FP24)
	this: <code>{FP24}</code>

	\| Param \| Description \|
	\| --- \| --- \|
	\| f \| Modulus \|

	<a name="FP24+trace"></a>

	### fP24.trace()
	Calculate the trace of an FP24

	Kind: instance method of [<code>FP24</code>](#FP24)
	this: <code>{FP24}</code>
	<a name="FP24+toString"></a>

	### fP24.toString()
	convert this to hex string

	Kind: instance method of [<code>FP24</code>](#FP24)
	this: <code>{FP24}</code>
	<a name="FP24+toBytes"></a>

	### fP24.toBytes(w)
	convert this to byte array

	Kind: instance method of [<code>FP24</code>](#FP24)
	this: <code>{FP24}</code>

	\| Param \| Description \|
	\| --- \| --- \|
	\| w \| Byte array \|

	<a name="FP24+pow"></a>

	### fP24.pow(e)
	Raises an FP24 to the power of a BIG

	Kind: instance method of [<code>FP24</code>](#FP24)
	this: <code>{FP24}</code>

	\| Param \| Description \|
	\| --- \| --- \|
	\| e \| BIG instance exponent \|

	<a name="FP24+pinpow"></a>

	### fP24.pinpow(e, bts)
	Raises an FP24 instance x to a small integer power, side-channel resistant

	Kind: instance method of [<code>FP24</code>](#FP24)
	this: <code>{FP24}</code>

	\| Param \| Description \|
	\| --- \| --- \|
	\| e \| small integer exponent \|
	\| bts \| maximum number of bits in exponent \|

	<a name="FP24+compow"></a>

	### fP24.compow(e, r)
	Raises an FP24 instance to a BIG power, compressed to FP4

	Kind: instance method of [<code>FP24</code>](#FP24)
	this: <code>{FP24}</code>

	\| Param \| Description \|
	\| --- \| --- \|
	\| e \| BIG exponent \|
	\| r \| BIG group order \|

	<a name="FP24.fromBytes"></a>

	### FP24.fromBytes(w)
	convert from byte array to FP24

	Kind: static method of [<code>FP24</code>](#FP24)
	this: <code>{FP24}</code>

	\| Param \| Description \|
	\| --- \| --- \|
	\| w \| Byte array \|

	<a name="FP24.teq"></a>

	### FP24.teq()
	return 1 if b==c, no branching

	Kind: static method of [<code>FP24</code>](#FP24)
	this: <code>{FP24}</code>
	<a name="FP24.pow8"></a>

	### FP24.pow8()
	p=q0^u0.q1^u1.q2^u2.q3^u3...

	Kind: static method of [<code>FP24</code>](#FP24)
	this: <code>{FP24}</code>