docs/fp2.md - incubator-milagro-crypto-js - Git at Google

 <a name="FP2"></a>

 ## FP2
 **Kind**: global class
 **this**: <code>{FP2}</code>

 * [FP2](#FP2)
     * [new FP2()](#new_FP2_new)
     * [.reduce()](#FP2+reduce)
     * [.norm()](#FP2+norm)
     * [.iszilch()](#FP2+iszilch)
     * [.isunity()](#FP2+isunity)
     * [.cmove(g, d)](#FP2+cmove)
     * [.equals(x)](#FP2+equals)
     * [.getA()](#FP2+getA)
     * [.getB()](#FP2+getB)
     * [.set(c, d)](#FP2+set)
     * [.seta(c)](#FP2+seta)
     * [.bset(c, d)](#FP2+bset)
     * [.bseta(c)](#FP2+bseta)
     * [.copy(x)](#FP2+copy)
     * [.zero()](#FP2+zero)
     * [.one(x)](#FP2+one)
     * [.neg(x)](#FP2+neg)
     * [.conj()](#FP2+conj)
     * [.add(x)](#FP2+add)
     * [.sub(x)](#FP2+sub)
     * [.pmul(s)](#FP2+pmul)
     * [.imul(s)](#FP2+imul)
     * [.sqr()](#FP2+sqr)
     * [.mul(y)](#FP2+mul)
     * [.sqrt()](#FP2+sqrt) ⇒
     * [.toString()](#FP2+toString)
     * [.inverse()](#FP2+inverse)
     * [.div2()](#FP2+div2)
     * [.times_i()](#FP2+times_i)
     * [.mul_ip()](#FP2+mul_ip)
     * [.div_ip2()](#FP2+div_ip2)
     * [.div_ip()](#FP2+div_ip)
     * [.pow(e)](#FP2+pow)

 <a name="new_FP2_new"></a>

 ### new FP2()
 Creates an instance of FP2.

 <a name="FP2+reduce"></a>

 ### fP2.reduce()
 Reduces all components of possibly unreduced FP2 mod Modulus

 **Kind**: instance method of [<code>FP2</code>](#FP2)
 **this**: <code>{FP2}</code>
 <a name="FP2+norm"></a>

 ### fP2.norm()
 Normalises the components of an FP2

 **Kind**: instance method of [<code>FP2</code>](#FP2)
 **this**: <code>{FP2}</code>
 <a name="FP2+iszilch"></a>

 ### fP2.iszilch()
 Tests for FP2 equal to zero

 **Kind**: instance method of [<code>FP2</code>](#FP2)
 **this**: <code>{FP2}</code>
 <a name="FP2+isunity"></a>

 ### fP2.isunity()
 Tests for FP2 equal to unity

 **Kind**: instance method of [<code>FP2</code>](#FP2)
 **this**: <code>{FP2}</code>
 <a name="FP2+cmove"></a>

 ### fP2.cmove(g, d)
 Conditional copy of FP2 number

 **Kind**: instance method of [<code>FP2</code>](#FP2)
 **this**: <code>{FP2}</code>

 | Param | Description |
 | --- | --- |
 | g | FP2 instance |
 | d | copy depends on this value |

 <a name="FP2+equals"></a>

 ### fP2.equals(x)
 Tests for equality of two FP2 instances

 **Kind**: instance method of [<code>FP2</code>](#FP2)
 **this**: <code>{FP2}</code>

 | Param | Description |
 | --- | --- |
 | x | FP2 instance to compare |

 <a name="FP2+getA"></a>

 ### fP2.getA()
 extract a from this

 **Kind**: instance method of [<code>FP2</code>](#FP2)
 **this**: <code>{FP2}</code>
 <a name="FP2+getB"></a>

 ### fP2.getB()
 extract b from this

 **Kind**: instance method of [<code>FP2</code>](#FP2)
 **this**: <code>{FP2}</code>
 <a name="FP2+set"></a>

 ### fP2.set(c, d)
 Set FP2 from two FP values

 **Kind**: instance method of [<code>FP2</code>](#FP2)
 **this**: <code>{FP2}</code>

 | Param | Description |
 | --- | --- |
 | c | FP instance |
 | d | FP instance |

 <a name="FP2+seta"></a>

 ### fP2.seta(c)
 Set FP2 from one FP value

 **Kind**: instance method of [<code>FP2</code>](#FP2)
 **this**: <code>{FP2}</code>

 | Param | Description |
 | --- | --- |
 | c | FP instance |

 <a name="FP2+bset"></a>

 ### fP2.bset(c, d)
 Set FP2 from two BIG values

 **Kind**: instance method of [<code>FP2</code>](#FP2)
 **this**: <code>{FP2}</code>

 | Param | Description |
 | --- | --- |
 | c | BIG instance |
 | d | BIG instance |

 <a name="FP2+bseta"></a>

 ### fP2.bseta(c)
 Set FP2 from one BIG value

 **Kind**: instance method of [<code>FP2</code>](#FP2)
 **this**: <code>{FP2}</code>

 | Param | Description |
 | --- | --- |
 | c | BIG instance |

 <a name="FP2+copy"></a>

 ### fP2.copy(x)
 Copy FP2 to another FP2

 **Kind**: instance method of [<code>FP2</code>](#FP2)
 **this**: <code>{FP2}</code>

 | Param | Description |
 | --- | --- |
 | x | FP2 instance to be copied |

 <a name="FP2+zero"></a>

 ### fP2.zero()
 Set FP2 to zero

 **Kind**: instance method of [<code>FP2</code>](#FP2)
 **this**: <code>{FP2}</code>
 <a name="FP2+one"></a>

 ### fP2.one(x)
 Set FP2 to unity

 **Kind**: instance method of [<code>FP2</code>](#FP2)
 **this**: <code>{FP2}</code>

 | Param | Description |
 | --- | --- |
 | x | FP2 instance to be set to one |

 <a name="FP2+neg"></a>

 ### fP2.neg(x)
 negate this

 **Kind**: instance method of [<code>FP2</code>](#FP2)
 **this**: <code>{FP2}</code>

 | Param | Description |
 | --- | --- |
 | x | FP2 instance to be set to one |

 <a name="FP2+conj"></a>

 ### fP2.conj()
 Conjugation of FP2

 **Kind**: instance method of [<code>FP2</code>](#FP2)
 **this**: <code>{FP2}</code>
 <a name="FP2+add"></a>

 ### fP2.add(x)
 addition of two FP2s

 **Kind**: instance method of [<code>FP2</code>](#FP2)
 **this**: <code>{FP2}</code>

 | Param | Description |
 | --- | --- |
 | x | FP2 instance |

 <a name="FP2+sub"></a>

 ### fP2.sub(x)
 subtraction of two FP2s

 **Kind**: instance method of [<code>FP2</code>](#FP2)
 **this**: <code>{FP2}</code>

 | Param | Description |
 | --- | --- |
 | x | FP2 instance |

 <a name="FP2+pmul"></a>

 ### fP2.pmul(s)
 Multiplication of an FP2 by an FP8

 **Kind**: instance method of [<code>FP2</code>](#FP2)
 **this**: <code>{FP2}</code>

 | Param | Description |
 | --- | --- |
 | s | FP8 instance |

 <a name="FP2+imul"></a>

 ### fP2.imul(s)
 Multiplication of an FP2 by a small integer

 **Kind**: instance method of [<code>FP2</code>](#FP2)
 **this**: <code>{FP2}</code>

 | Param | Description |
 | --- | --- |
 | s | integer |

 <a name="FP2+sqr"></a>

 ### fP2.sqr()
 Fast Squaring of an FP2

 **Kind**: instance method of [<code>FP2</code>](#FP2)
 **this**: <code>{FP2}</code>
 <a name="FP2+mul"></a>

 ### fP2.mul(y)
 Full unconditional Multiplication of two FP2s

 **Kind**: instance method of [<code>FP2</code>](#FP2)
 **this**: <code>{FP2}</code>

 | Param | Description |
 | --- | --- |
 | y | FP2 instance, the multiplier |

 <a name="FP2+sqrt"></a>

 ### fP2.sqrt() ⇒
 sqrt(a+ib) = sqrt(a+sqrt(a*a-n*b*b)/2)+ib/(2*sqrt(a+sqrt(a*a-n*b*b)/2))

 **Kind**: instance method of [<code>FP2</code>](#FP2)
 **Returns**: true if this is QR
 **this**: <code>{FP2}</code>
 <a name="FP2+toString"></a>

 ### fP2.toString()
 convert this to hex string

 **Kind**: instance method of [<code>FP2</code>](#FP2)
 **this**: <code>{FP2}</code>
 <a name="FP2+inverse"></a>

 ### fP2.inverse()
 Inverting an FP2

 **Kind**: instance method of [<code>FP2</code>](#FP2)
 **this**: <code>{FP2}</code>
 <a name="FP2+div2"></a>

 ### fP2.div2()
 Divide an FP2 by 2

 **Kind**: instance method of [<code>FP2</code>](#FP2)
 **this**: <code>{FP2}</code>
 <a name="FP2+times_i"></a>

 ### fP2.times\_i()
 Multiply an FP2 by sqrt(-1)

 **Kind**: instance method of [<code>FP2</code>](#FP2)
 **this**: <code>{FP2}</code>
 <a name="FP2+mul_ip"></a>

 ### fP2.mul\_ip()
 Multiply an FP2 by (1+sqrt(-1))

 **Kind**: instance method of [<code>FP2</code>](#FP2)
 **this**: <code>{FP2}</code>
 <a name="FP2+div_ip2"></a>

 ### fP2.div\_ip2()
 Divide an FP2 by (1+sqrt(-1))/2

 **Kind**: instance method of [<code>FP2</code>](#FP2)
 **this**: <code>{FP2}</code>
 <a name="FP2+div_ip"></a>

 ### fP2.div\_ip()
 Divide an FP2 by (1+sqrt(-1))

 **Kind**: instance method of [<code>FP2</code>](#FP2)
 **this**: <code>{FP2}</code>
 <a name="FP2+pow"></a>

 ### fP2.pow(e)
 Raises an FP2 to the power of a BIG

 **Kind**: instance method of [<code>FP2</code>](#FP2)
 **this**: <code>{FP2}</code>

 | Param | Description |
 | --- | --- |
 | e | BIG instance exponent |
	<a name="FP2"></a>

	## FP2
	Kind: global class
	this: <code>{FP2}</code>

	* [FP2](#FP2)
	* [new FP2()](#new_FP2_new)
	* [.reduce()](#FP2+reduce)
	* [.norm()](#FP2+norm)
	* [.iszilch()](#FP2+iszilch)
	* [.isunity()](#FP2+isunity)
	* [.cmove(g, d)](#FP2+cmove)
	* [.equals(x)](#FP2+equals)
	* [.getA()](#FP2+getA)
	* [.getB()](#FP2+getB)
	* [.set(c, d)](#FP2+set)
	* [.seta(c)](#FP2+seta)
	* [.bset(c, d)](#FP2+bset)
	* [.bseta(c)](#FP2+bseta)
	* [.copy(x)](#FP2+copy)
	* [.zero()](#FP2+zero)
	* [.one(x)](#FP2+one)
	* [.neg(x)](#FP2+neg)
	* [.conj()](#FP2+conj)
	* [.add(x)](#FP2+add)
	* [.sub(x)](#FP2+sub)
	* [.pmul(s)](#FP2+pmul)
	* [.imul(s)](#FP2+imul)
	* [.sqr()](#FP2+sqr)
	* [.mul(y)](#FP2+mul)
	* [.sqrt()](#FP2+sqrt) ⇒
	* [.toString()](#FP2+toString)
	* [.inverse()](#FP2+inverse)
	* [.div2()](#FP2+div2)
	* [.times_i()](#FP2+times_i)
	* [.mul_ip()](#FP2+mul_ip)
	* [.div_ip2()](#FP2+div_ip2)
	* [.div_ip()](#FP2+div_ip)
	* [.pow(e)](#FP2+pow)

	<a name="new_FP2_new"></a>

	### new FP2()
	Creates an instance of FP2.

	<a name="FP2+reduce"></a>

	### fP2.reduce()
	Reduces all components of possibly unreduced FP2 mod Modulus

	Kind: instance method of [<code>FP2</code>](#FP2)
	this: <code>{FP2}</code>
	<a name="FP2+norm"></a>

	### fP2.norm()
	Normalises the components of an FP2

	Kind: instance method of [<code>FP2</code>](#FP2)
	this: <code>{FP2}</code>
	<a name="FP2+iszilch"></a>

	### fP2.iszilch()
	Tests for FP2 equal to zero

	Kind: instance method of [<code>FP2</code>](#FP2)
	this: <code>{FP2}</code>
	<a name="FP2+isunity"></a>

	### fP2.isunity()
	Tests for FP2 equal to unity

	Kind: instance method of [<code>FP2</code>](#FP2)
	this: <code>{FP2}</code>
	<a name="FP2+cmove"></a>

	### fP2.cmove(g, d)
	Conditional copy of FP2 number

	Kind: instance method of [<code>FP2</code>](#FP2)
	this: <code>{FP2}</code>

	\| Param \| Description \|
	\| --- \| --- \|
	\| g \| FP2 instance \|
	\| d \| copy depends on this value \|

	<a name="FP2+equals"></a>

	### fP2.equals(x)
	Tests for equality of two FP2 instances

	Kind: instance method of [<code>FP2</code>](#FP2)
	this: <code>{FP2}</code>

	\| Param \| Description \|
	\| --- \| --- \|
	\| x \| FP2 instance to compare \|

	<a name="FP2+getA"></a>

	### fP2.getA()
	extract a from this

	Kind: instance method of [<code>FP2</code>](#FP2)
	this: <code>{FP2}</code>
	<a name="FP2+getB"></a>

	### fP2.getB()
	extract b from this

	Kind: instance method of [<code>FP2</code>](#FP2)
	this: <code>{FP2}</code>
	<a name="FP2+set"></a>

	### fP2.set(c, d)
	Set FP2 from two FP values

	Kind: instance method of [<code>FP2</code>](#FP2)
	this: <code>{FP2}</code>

	\| Param \| Description \|
	\| --- \| --- \|
	\| c \| FP instance \|
	\| d \| FP instance \|

	<a name="FP2+seta"></a>

	### fP2.seta(c)
	Set FP2 from one FP value

	Kind: instance method of [<code>FP2</code>](#FP2)
	this: <code>{FP2}</code>

	\| Param \| Description \|
	\| --- \| --- \|
	\| c \| FP instance \|

	<a name="FP2+bset"></a>

	### fP2.bset(c, d)
	Set FP2 from two BIG values

	Kind: instance method of [<code>FP2</code>](#FP2)
	this: <code>{FP2}</code>

	\| Param \| Description \|
	\| --- \| --- \|
	\| c \| BIG instance \|
	\| d \| BIG instance \|

	<a name="FP2+bseta"></a>

	### fP2.bseta(c)
	Set FP2 from one BIG value

	Kind: instance method of [<code>FP2</code>](#FP2)
	this: <code>{FP2}</code>

	\| Param \| Description \|
	\| --- \| --- \|
	\| c \| BIG instance \|

	<a name="FP2+copy"></a>

	### fP2.copy(x)
	Copy FP2 to another FP2

	Kind: instance method of [<code>FP2</code>](#FP2)
	this: <code>{FP2}</code>

	\| Param \| Description \|
	\| --- \| --- \|
	\| x \| FP2 instance to be copied \|

	<a name="FP2+zero"></a>

	### fP2.zero()
	Set FP2 to zero

	Kind: instance method of [<code>FP2</code>](#FP2)
	this: <code>{FP2}</code>
	<a name="FP2+one"></a>

	### fP2.one(x)
	Set FP2 to unity

	Kind: instance method of [<code>FP2</code>](#FP2)
	this: <code>{FP2}</code>

	\| Param \| Description \|
	\| --- \| --- \|
	\| x \| FP2 instance to be set to one \|

	<a name="FP2+neg"></a>

	### fP2.neg(x)
	negate this

	Kind: instance method of [<code>FP2</code>](#FP2)
	this: <code>{FP2}</code>

	\| Param \| Description \|
	\| --- \| --- \|
	\| x \| FP2 instance to be set to one \|

	<a name="FP2+conj"></a>

	### fP2.conj()
	Conjugation of FP2

	Kind: instance method of [<code>FP2</code>](#FP2)
	this: <code>{FP2}</code>
	<a name="FP2+add"></a>

	### fP2.add(x)
	addition of two FP2s

	Kind: instance method of [<code>FP2</code>](#FP2)
	this: <code>{FP2}</code>

	\| Param \| Description \|
	\| --- \| --- \|
	\| x \| FP2 instance \|

	<a name="FP2+sub"></a>

	### fP2.sub(x)
	subtraction of two FP2s

	Kind: instance method of [<code>FP2</code>](#FP2)
	this: <code>{FP2}</code>

	\| Param \| Description \|
	\| --- \| --- \|
	\| x \| FP2 instance \|

	<a name="FP2+pmul"></a>

	### fP2.pmul(s)
	Multiplication of an FP2 by an FP8

	Kind: instance method of [<code>FP2</code>](#FP2)
	this: <code>{FP2}</code>

	\| Param \| Description \|
	\| --- \| --- \|
	\| s \| FP8 instance \|

	<a name="FP2+imul"></a>

	### fP2.imul(s)
	Multiplication of an FP2 by a small integer

	Kind: instance method of [<code>FP2</code>](#FP2)
	this: <code>{FP2}</code>

	\| Param \| Description \|
	\| --- \| --- \|
	\| s \| integer \|

	<a name="FP2+sqr"></a>

	### fP2.sqr()
	Fast Squaring of an FP2

	Kind: instance method of [<code>FP2</code>](#FP2)
	this: <code>{FP2}</code>
	<a name="FP2+mul"></a>

	### fP2.mul(y)
	Full unconditional Multiplication of two FP2s

	Kind: instance method of [<code>FP2</code>](#FP2)
	this: <code>{FP2}</code>

	\| Param \| Description \|
	\| --- \| --- \|
	\| y \| FP2 instance, the multiplier \|

	<a name="FP2+sqrt"></a>

	### fP2.sqrt() ⇒
	sqrt(a+ib) = sqrt(a+sqrt(aa-nbb)/2)+ib/(2sqrt(a+sqrt(aa-nb*b)/2))

	Kind: instance method of [<code>FP2</code>](#FP2)
	Returns: true if this is QR
	this: <code>{FP2}</code>
	<a name="FP2+toString"></a>

	### fP2.toString()
	convert this to hex string

	Kind: instance method of [<code>FP2</code>](#FP2)
	this: <code>{FP2}</code>
	<a name="FP2+inverse"></a>

	### fP2.inverse()
	Inverting an FP2

	Kind: instance method of [<code>FP2</code>](#FP2)
	this: <code>{FP2}</code>
	<a name="FP2+div2"></a>

	### fP2.div2()
	Divide an FP2 by 2

	Kind: instance method of [<code>FP2</code>](#FP2)
	this: <code>{FP2}</code>
	<a name="FP2+times_i"></a>

	### fP2.times\_i()
	Multiply an FP2 by sqrt(-1)

	Kind: instance method of [<code>FP2</code>](#FP2)
	this: <code>{FP2}</code>
	<a name="FP2+mul_ip"></a>

	### fP2.mul\_ip()
	Multiply an FP2 by (1+sqrt(-1))

	Kind: instance method of [<code>FP2</code>](#FP2)
	this: <code>{FP2}</code>
	<a name="FP2+div_ip2"></a>

	### fP2.div\_ip2()
	Divide an FP2 by (1+sqrt(-1))/2

	Kind: instance method of [<code>FP2</code>](#FP2)
	this: <code>{FP2}</code>
	<a name="FP2+div_ip"></a>

	### fP2.div\_ip()
	Divide an FP2 by (1+sqrt(-1))

	Kind: instance method of [<code>FP2</code>](#FP2)
	this: <code>{FP2}</code>
	<a name="FP2+pow"></a>

	### fP2.pow(e)
	Raises an FP2 to the power of a BIG

	Kind: instance method of [<code>FP2</code>](#FP2)
	this: <code>{FP2}</code>

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