Poseidon377

https://docs.rs/poseidon377/1.2.0
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An instantiation of Poseidon for the BLS12-377 scalar field, providing cryptographic hashing...
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### Example Searches for Rate 5

Source: https://docs.rs/poseidon377/1.2.0/src/poseidon377/params/rate_5.rs.html?search=

Demonstrates common search patterns for rate 5 parameters. These examples show how to search for vector types, type conversions, and option transformations.

```rust
Example searches:
  * std::vec
  * u32 -> bool
  * Option<T>, (T -> U) -> Option<U>
```

--------------------------------

### Poseidon377 Rate 2 Initial State Example

Source: https://docs.rs/poseidon377/1.2.0/src/poseidon377/params/rate_2.rs.html?search=std%3A%3Avec

An example of initializing the state for Poseidon377 with a rate of 2. This involves setting up the initial matrix values.

```rust
Matrix::<1, 2, 2>::new_from_known([
                    Fq::from_montgomery_limbs([
                        18204910156218979669,
                        16293041589642941780,
                        9975069610392864084,
                        1088801882579738168,
                    ]),
                    Fq::from_montgomery_limbs([
                        3072474957567996411,
                        7632850653899625657,
                        6867324839353272651,
                        1129105644996777990,
                    ]),
                ]),
```

```rust
Matrix::<1, 2, 2>::new_from_known([
                    Fq::from_montgomery_limbs([
                        11749409346063797401,
                        13847779958722295463,
                        5230051856842938218,
                        809528761888529318,
                    ]),
                    Fq::from_montgomery_limbs([
                        16538317435082867476,
                        140673227072662684,
                        4917458456429054520,
                        951347002169384040,
                    ]),
                ]),
```

```rust
Matrix::<1, 2, 2>::new_from_known([
                    Fq::from_montgomery_limbs([
                        8049501819868988169,
                        4640840621228515661,
                        5281323386686467274,
                        1217317166531385469,
                    ]),
                    Fq::from_montgomery_limbs([
                        15861181624207003323,
                        10871450011713172103,
                        4492382029642778046,
                        495041570025076744,
                    ]),
                ]),
```

```rust
Matrix::<1, 2, 2>::new_from_known([
                    Fq::from_montgomery_limbs([
                        491531644685882947,
                        16236469504155238438,
                        13405996466460073108,
                        191442324574972544,
                    ]),
                    Fq::from_montgomery_limbs([
                        14234832595612208455,
                        16711171142020806901,
                        9818085755212544560,
                        433758843793119660,
                    ]),
                ]),
```

```rust
Matrix::<1, 2, 2>::new_from_known([
                    Fq::from_montgomery_limbs([
                        8692243294689566788,
                        17131754811489911037,
                        16082421295010554115,
                        245109642615998458,
                    ]),
                    Fq::from_montgomery_limbs([
                        12752747264486126419,
                        12936758402746978248,
                        7901753820298393242,
                        1086817638717069074,
                    ]),
                ]),
```

```rust
Matrix::<1, 2, 2>::new_from_known([
                    Fq::from_montgomery_limbs([
                        716899015486837574,
                        12929955716143301332,
                        6296181173922398814,
                        95630164573893864,
                    ]),
                    Fq::from_montgomery_limbs([
                        10771615223994036552,
                        12477611863199363886,
                        5019464732542008653,
                        260172239809303582,
                    ]),
                ]),
```

```rust
Matrix::<1, 2, 2>::new_from_known([
                    Fq::from_montgomery_limbs([
                        2083749357590716775,
                        7802489018239475310,
                        4719252491703553508,
                        331544147020630716,
                    ]),
                    Fq::from_montgomery_limbs([
                        11839081110669849836,
                        16458332811546812068,
                        4108523134706353886,
                        1014020374083768583,
                    ]),
                ]),
```

--------------------------------

### Rate 4 Matrix Initialization (Example 2)

Source: https://docs.rs/poseidon377/1.2.0/src/poseidon377/params/rate_4.rs.html?search=Option%3CT%3E%2C+%28T+-%3E+U%29+-%3E+Option%3CU%3E

Initializes another 4x1x4 matrix with different field elements for Poseidon377's rate 4 configuration. These matrices are crucial for the permutation.

```rust
Matrix::<4, 1, 4>::new_from_known([
                        Fq::from_montgomery_limbs([
                            5559270171112387908,
                            18090552370541844697,
                            4468532076227855438,
                            987685496358074261,
                        ]),
                        Fq::from_montgomery_limbs([
                            10757975082173786027,
                            17106276533668884653,
                            16008494306379137448,
                            1236424776827918502,
                        ]),
                        Fq::from_montgomery_limbs([
                            12651630831207509026,
                            9201507732813618723,
                            16271105479151831696,
                            1088028967768313039,
                        ]),
                        Fq::from_montgomery_limbs([
                            1230449153550648107,
                            265047928608104139,
                            14808043482234569955,
                            325688046287390058,
                        ]),
                    ]),
```

--------------------------------

### Initialize Rate 6 Constants

Source: https://docs.rs/poseidon377/1.2.0/src/poseidon377/params/rate_6.rs.html

Initializes the constants for the rate 6 configuration using `Fq::from_montgomery_limbs`. This is typically done once during setup.

```rust
Fq::from_montgomery_limbs([
                        9854620422114551002,
                        11862250176770700568,
                        874594626487585300,
                        932096667364472947,
                    ]),
                    Fq::from_montgomery_limbs([
                        2172530204291601442,
                        6393872278636522840,
                        684019909052108375,
                        180921268676761997,
                    ]),
                    Fq::from_montgomery_limbs([
                        747820584568953283,
                        11441694611866320992,
                        4524856196876367929,
                        874564518710804172,
                    ]),
                    Fq::from_montgomery_limbs([
                        7299335342253825037,
                        12867703813750147845,
                        7941311700245180087,
                        1108892033870182325,
                    ]),
                    Fq::from_montgomery_limbs([
                        17832410557204971163,
                        4075792975869963488,
                        7197135716780572438,
                        152677169125496593,
                    ])
```

--------------------------------

### Rate 4 Matrix Initialization (Example 1)

Source: https://docs.rs/poseidon377/1.2.0/src/poseidon377/params/rate_4.rs.html?search=Option%3CT%3E%2C+%28T+-%3E+U%29+-%3E+Option%3CU%3E

Initializes a 4x1x4 matrix with specific field elements for Poseidon377's rate 4 configuration. This matrix is part of the internal state.

```rust
Matrix::<4, 1, 4>::new_from_known([
                        Fq::from_montgomery_limbs([
                            9466887184987077213,
                            12707324624592417252,
                            5674722778664167831,
                            495915214907561344,
                        ]),
                    ]),
```

--------------------------------

### Poseidon377 Rate 6 Parameters (Example 2)

Source: https://docs.rs/poseidon377/1.2.0/src/poseidon377/params/rate_6.rs.html

Another instance of constructing a field element using `Fq::from_montgomery_limbs`. This demonstrates the repetition of parameter initialization for different elements within the rate 6 configuration.

```rust
Fq::from_montgomery_limbs([
                7802104352665277001,
                1712233803072817444,
                12180777293186749586,
                1125441666595228915,
            ])
```

--------------------------------

### Rate 4 Matrix Initialization (Example 5)

Source: https://docs.rs/poseidon377/1.2.0/src/poseidon377/params/rate_4.rs.html?search=Option%3CT%3E%2C+%28T+-%3E+U%29+-%3E+Option%3CU%3E

Initializes the final 4x1x4 matrix with specific field elements for Poseidon377's rate 4 configuration. This completes the set of matrices used in the permutation.

```rust
Matrix::<4, 1, 4>::new_from_known([
                        Fq::from_montgomery_limbs([
                            14899630606893874181,
                            6378344959523143322,
                            5326343488656073582,
                            678256632460809235,
                        ]),
                        Fq::from_montgomery_limbs([
                            8604354652434330145,
                            15276531567938090768,
                            4221676591098543719,
                            887292207042946940,
                        ]),
                        Fq::from_montgomery_limbs([
                            10167720299639556674,
                            4032113283136195884,
                            15412529848138749452,
                            21416729784789829,
                        ]),
                        Fq::from_montgomery_limbs([
                            1744850832220109759,
                        ]),
                    ]),
```

--------------------------------

### Rate 4 Matrix Initialization (Example 4)

Source: https://docs.rs/poseidon377/1.2.0/src/poseidon377/params/rate_4.rs.html?search=Option%3CT%3E%2C+%28T+-%3E+U%29+-%3E+Option%3CU%3E

Initializes a 4x1x4 matrix with another set of field elements for Poseidon377's rate 4 configuration. These parameters are essential for the cryptographic properties.

```rust
Matrix::<4, 1, 4>::new_from_known([
                        Fq::from_montgomery_limbs([
                            10156513900929988871,
                            10530356278918523762,
                            14822893961039084664,
                            161451167716228232,
                        ]),
                        Fq::from_montgomery_limbs([
                            5121741770267475287,
                            15513755736291034019,
                            15586246947451164544,
                            318686326614228424,
                        ]),
                        Fq::from_montgomery_limbs([
                            10544893749060569045,
                            16634377462455718128,
                            15424965125419130088,
                            421312194245698247,
                        ]),
                        Fq::from_montgomery_limbs([
                            11266056403263964991,
                            12568371609374858109,
                            3531321490936409191,
                            508836381468284493,
                        ]),
                    ]),
```

--------------------------------

### Rate 4 Matrix Initialization (Example 3)

Source: https://docs.rs/poseidon377/1.2.0/src/poseidon377/params/rate_4.rs.html?search=Option%3CT%3E%2C+%28T+-%3E+U%29+-%3E+Option%3CU%3E

Initializes a 4x1x4 matrix with a distinct set of field elements for Poseidon377's rate 4 configuration. These matrices are part of the permutation's linear layer.

```rust
Matrix::<4, 1, 4>::new_from_known([
                        Fq::from_montgomery_limbs([
                            13141399420347535214,
                            10323718706655672545,
                            5271972852381490754,
                            698174654390126163,
                        ]),
                        Fq::from_montgomery_limbs([
                            372444215127449162,
                            6596103022703759073,
                            1647706108480519163,
                            886941719362299906,
                        ]),
                        Fq::from_montgomery_limbs([
                            5032445406852833227,
                            3216505841560606858,
                            6517925226383774397,
                            1070169747543143371,
                        ]),
                        Fq::from_montgomery_limbs([
                            606117931900595268,
                            11653697130177906902,
                            16942600493441083920,
                            207641435432611378,
                        ]),
                    ]),
```

--------------------------------

### Poseidon377 Rate 5 Parameters Initialization

Source: https://docs.rs/poseidon377/1.2.0/src/poseidon377/params/rate_5.rs.html?search=

Initializes the Poseidon377 parameters for a rate of 5, including MDS matrices, alpha, and round numbers. This setup is used for cryptographic operations.

```rust
Fq::from_montgomery_limbs([
                7989155441247042094,
                18276457113184108543,
                17999817914616464103,
                943187440870955565,
            ]),
            Fq::from_montgomery_limbs([
                18204910156218979669,
                16293041589642941780,
                9975069610392864084,
                1088801882579738168,
            ]),
            Fq::from_montgomery_limbs([
                15441359965645378481,
                7022857083512140090,
                11162758362666494739,
                1108530997049617801,
            ]),
            Fq::from_montgomery_limbs([
                7802104352665277001,
                1712233803072817444,
                12180777293186749586,
                1125441666595228915,
            ]),
            Fq::from_montgomery_limbs([
                7330330845985706257,
                6947957132670498679,
                9373711551562393463,
                1140097580201425214,
            ]),
            Fq::from_montgomery_limbs([
                7330330845985706257,
                6947957132670498679,
                9373711551562393463,
                1140097580201425214,
            ]),
            Fq::from_montgomery_limbs([0, 0, 0, 1152921504606846976]),
        ]),
        alpha: Alpha::Exponent(17),
        rounds: RoundNumbers { r_P: 31, r_F: 8 },
        optimized_mds: OptimizedMdsMatrices {
            M_hat: SquareMatrix::<5, 25>::new_from_known([
                Fq::from_montgomery_limbs([
                    17721242321237835775,
                    11985636621509722110,
                    11478464757469040638,
                    960562638525520553,
                ]),
                Fq::from_montgomery_limbs([
                    17640631015407645126,
                    17416650484724036037,
                    14803487960933328666,
                    554882262980868625,
                ]),
                Fq::from_montgomery_limbs([
                    10632745392742701465,
                    7191381972905833266,
                    10576427669223334706,
                    1037506184958051122,
                ]),
                Fq::from_montgomery_limbs([
                    7989155441247042094,
                    18276457113184108543,
                    17999817914616464103,
                    943187440870955565,
                ]),
                Fq::from_montgomery_limbs([
                    18204910156218979669,
                    16293041589642941780,
                    9975069610392864084,
                    1088801882579738168,
                ]),
                Fq::from_montgomery_limbs([
                    17640631015407645126,
                    17416650484724036037,
                    14803487960933328666,
                    554882262980868625,
                ]),
                Fq::from_montgomery_limbs([
                    10632745392742701465,
                    7191381972905833266,
                    10576427669223334706,
                    1037506184958051122,
                ]),
                Fq::from_montgomery_limbs([
                    7989155441247042094,
                    18276457113184108543,
                    17999817914616464103,
                    943187440870955565,
                ]),
                Fq::from_montgomery_limbs([
                    18204910156218979669,
                    16293041589642941780,
                    9975069610392864084,
                    1088801882579738168,
                ]),
                Fq::from_montgomery_limbs([
                    15441359965645378481,
                    7022857083512140090,
                    11162758362666494739,
                    1108530997049617801,
                ]),
                Fq::from_montgomery_limbs([
                    10632745392742701465,
                    7191381972905833266,
                    10576427669223334706,
                    1037506184958051122,
                ]),
                Fq::from_montgomery_limbs([
                    7989155441247042094,
                    18276457113184108543,
                    17999817914616464103,
                    943187440870955565,
                ]),
                Fq::from_montgomery_limbs([
                    18204910156218979669,
                    16293041589642941780,
                    9975069610392864084,
                    1088801882579738168,
                ]),
            ])
        }
    }
```

--------------------------------

### Initialize Matrix with Montgomery Limbs

Source: https://docs.rs/poseidon377/1.2.0/src/poseidon377/params/rate_3.rs.html?search=std%3A%3Avec

Initializes a 1x3x3 matrix using `Fq::from_montgomery_limbs` for each element. This is used for setting up specific parameter matrices.

```rust
Matrix::<1, 3, 3>::new_from_known([
                    Fq::from_montgomery_limbs([
                        13532986407775683895,
                        9476195915097473266,
                        1008114724683017572,
                        545860035442724601,
                    ]),
                    Fq::from_montgomery_limbs([
                        16204216982352313226,
                        12925674836598514697,
                        6751896652466221822,
                        941483813900869065,
                    ]),
                    Fq::from_montgomery_limbs([
                        17313019480228630806,
                        566130559971125633,
                        11091260944862748358,
                        830377232140527827,
                    ]),
                ])
```

```rust
Matrix::<1, 3, 3>::new_from_known([
                    Fq::from_montgomery_limbs([
                        13653317352261633777,
                        10493929866956769626,
                        8396755137825041221,
                        1146048882209297127,
                    ]),
                    Fq::from_montgomery_limbs([
                        4132278932442914408,
                        14861671218963566328,
                        7959790402925606057,
                        1318243553399078199,
                    ]),
                    Fq::from_montgomery_limbs([
                        13456767915419596367,
                        17246911423899751971,
                        5711218416857391278,
                        35403035103928169,
                    ]),
                ])
```

```rust
Matrix::<1, 3, 3>::new_from_known([
                    Fq::from_montgomery_limbs([
                        12907160498704673184,
                        12152379198293294711,
                        9252679699965582400,
                        1224554265731421992,
                    ]),
                    Fq::from_montgomery_limbs([
                        13419199242664167498,
                        13891452473958728318,
                        13543072901518191311,
                        1037106053989502131,
                    ]),
                    Fq::from_montgomery_limbs([
                        16666897222883125359,
                        12131730689573449836,
                        13003710399516055414,
                        648272461984720515,
                    ]),
                ])
```

```rust
Matrix::<1, 3, 3>::new_from_known([
                    Fq::from_montgomery_limbs([
                        13991351580088989461,
                        17864339801785851041,
                        11695126599066872867,
                        921749339582652232,
                    ]),
                    Fq::from_montgomery_limbs([
                        11906579800297278037,
                        11470441940361903448,
                        15097374289742739909,
                        275174984759910272,
                    ]),
                    Fq::from_montgomery_limbs([
                        18232546040145726314,
                        14147307759659284922,
                        991776681097878315,
                        1065560959455072221,
                    ]),
                ])
```

```rust
Matrix::<1, 3, 3>::new_from_known([
                    Fq::from_montgomery_limbs([
                        3117800866767190184,
                        1873664776760606669,
                        13118797281780700540,
                        918694694774008673,
                    ]),
                    Fq::from_montgomery_limbs([
                        16198059297050513347,
                        8432506190058226772,
                        9370514214732897655,
                    ]),
                ])
```

--------------------------------

### Matrix Initialization with Fq::from_montgomery_limbs

Source: https://docs.rs/poseidon377/1.2.0/src/poseidon377/params/rate_5.rs.html?search=u32+-%3E+bool

Initializes a 5x1 matrix with 5 elements, where each element is an Fq (finite field element) constructed using Montgomery limbs. This is a common pattern for representing large numbers in finite field arithmetic.

```rust
Matrix::<5, 1, 5>::new_from_known([
                    Fq::from_montgomery_limbs([
                        26427962923262805,
                        13400472629512916744,
                        3808805306352074297,
                        128699596583089680,
                    ]),
                    Fq::from_montgomery_limbs([
                        18283636998376248321,
                        5779768391741799708,
                        8993926161412908836,
                        272788598277303242,
                    ]),
                    Fq::from_montgomery_limbs([
                        385260822800957491,
                        7888556288710245505,
                        12785711973091118063,
                        1290081227789032623,
                    ]),
                    Fq::from_montgomery_limbs([
                        7370461305656006315,
                        8097104282146432375,
                        3693139275053762963,
                        1200841519361465892,
                    ]),
                    Fq::from_montgomery_limbs([
                        12067130442173286908,
                        2170379854767453652,
                        13201336336736961495,
                        927175852053928205,
                    ]),
                ]),
```

```rust
Matrix::<5, 1, 5>::new_from_known([
                    Fq::from_montgomery_limbs([
                        11214687023235424600,
                        5560314158648804455,
                        17670625093449035024,
                        1242366510949799159,
                    ]),
                    Fq::from_montgomery_limbs([
                        8409895882379798325,
                        14471144258274119497,
                        5245528502428581668,
                        869805265859067382,
                    ]),
                    Fq::from_montgomery_limbs([
                        2802161834127193832,
                        181192611793840022,
                        1581405763136818654,
                        674326086636803499,
                    ]),
                    Fq::from_montgomery_limbs([
                        5748156006252401196,
                        9530968273316544473,
                        1373075747037319701,
                        478917773953068122,
                    ]),
                    Fq::from_montgomery_limbs([
                        10550634859635316442,
                        11115297058518078301,
                        15167740297739703393,
                        499663014055796942,
                    ]),
                ]),
```

```rust
Matrix::<5, 1, 5>::new_from_known([
                    Fq::from_montgomery_limbs([
                        8737679817842057617,
                        14335003891544767889,
                        5806471893265243804,
                        1199697546794663346,
                    ]),
                    Fq::from_montgomery_limbs([
                        18312746592170672376,
                        2468171777169034619,
                        11588707770047473860,
                        1167607620745843361,
                    ]),
                    Fq::from_montgomery_limbs([
                        8991056605371192176,
                        9683166706953599777,
                        3207279773035228554,
                        1036594322405142084,
                    ]),
                    Fq::from_montgomery_limbs([
                        10715958137830220707,
                        13790797151438523296,
                        3814352367403212083,
                        338399526865285980,
                    ]),
                    Fq::from_montgomery_limbs([
                        7602766395993095249,
                        15421116878917379598,
                        9842919232591540089,
                        811441858348229638,
                    ]),
                ]),
```

```rust
Matrix::<5, 1, 5>::new_from_known([
                    Fq::from_montgomery_limbs([
                        11240616276279859335,
                        18168970638218441074,
                        12681307963217316671,
                        529653072592394540,
                    ]),
                    
```

--------------------------------

### Get TypeId of Self

Source: https://docs.rs/poseidon377/1.2.0/poseidon377/struct.PoseidonParameters.html

Retrieves the `TypeId` of the current instance. This is a fundamental operation for type introspection.

```rust
fn type_id(&self) -> TypeId
```

--------------------------------

### Initialize Matrix with Montgomery Limbs (Rate 3)

Source: https://docs.rs/poseidon377/1.2.0/src/poseidon377/params/rate_3.rs.html?search=std%3A%3Avec

Demonstrates the initialization of a `Matrix<1, 3, 3>` using `Fq::from_montgomery_limbs` for each element. This is used for constructing the round constants or MDS matrices in Poseidon377.

```rust
Matrix::<1, 3, 3>::new_from_known([
                    Fq::from_montgomery_limbs([
                        5656989936467702279,
                        3451526239075705633,
                        12473714456419681817,
                        720076561380511801,
                    ]),
                    Fq::from_montgomery_limbs([
                        2752710254647861908,
                        11030634120397179297,
                        7520710074325720708,
                        849095153678924863,
                    ]),
                    Fq::from_montgomery_limbs([
                        15714192245785854425,
                        1934486269946887645,
                        249860026764225808,
                        1186606499687026685,
                    ]),
                ]),
                Matrix::<1, 3, 3>::new_from_known([
                    Fq::from_montgomery_limbs([
                        1065442882426850105,
                        18187640339393109068,
                        8850384031746892082,
                        317569289072515041,
                    ]),
                    Fq::from_montgomery_limbs([
                        1837681773828322091,
                        10850972211403707738,
                        336406577412961307,
                        885368386317519809,
                    ]),
                    Fq::from_montgomery_limbs([
                        15758214746904074141,
                        11583431684684102838,
                        7662385228843486433,
                        217065657978291661,
                    ]),
                ]),
                Matrix::<1, 3, 3>::new_from_known([
                    Fq::from_montgomery_limbs([
                        2532634061285367793,
                        4387885387692314654,
                        12158131981630891597,
                        230565483900354414,
                    ]),
                    Fq::from_montgomery_limbs([
                        13346419382798549501,
                        18280976687063744023,
                        5606331118089126185,
                        273578743992252446,
                    ]),
                    Fq::from_montgomery_limbs([
                        17577657789855982030,
                        9630457784692257422,
                        12902853055721181839,
                        36459624765202074,
                    ]),
                ]),
                Matrix::<1, 3, 3>::new_from_known([
                    Fq::from_montgomery_limbs([
                        9935908372408102992,
                        14641284087709280054,
                        17684292083487177951,
                        1155088959507788459,
                    ]),
                    Fq::from_montgomery_limbs([
                        541701721303367728,
                        3959174565794182274,
                        18151179085562458542,
                        340776254243440974,
                    ]),
                    Fq::from_montgomery_limbs([
                        17690336527687088662,
                        10937885152973991052,
                        3836836874424836886,
                        1090509013794447238,
                    ]),
                ]),
                Matrix::<1, 3, 3>::new_from_known([
                    Fq::from_montgomery_limbs([
                        12310573214022515884,
                        3043141462744167127,
                        7406092407251694082,
                        9160197655286166,
                    ]),
                    Fq::from_montgomery_limbs([
                        5101804845510497503,
                        7081024525590050191,
                        11990249650950760548,
                        264716438448155623,
                    ]),
                    Fq::from_montgomery_limbs([
                        14013782434072143361,
                        18031550597362521222,
                        4176916092795610844,
                        1008783913934215313,
                    ]),
                ]),
                Matrix::<1, 3, 3>::new_from_known([
                    Fq::from_montgomery_limbs([
                        5197923006462389769,
                        10850213912970425984,
                        6236288807254229677,
                        381647096775612803,
                    ]),
                    Fq::from_montgomery_limbs([
                        16904562081938006603,
                        1107639524721847015,
                        7662385228843486433,
                        217065657978291661,
                    ]),
                ])
```

--------------------------------

### Initialize Rate 2 Parameters

Source: https://docs.rs/poseidon377/1.2.0/src/poseidon377/params/rate_2.rs.html?search=

Initializes the Rate 2 parameters for Poseidon377 using Montgomery representation. This is typically done once during setup.

```rust
Fq::from_montgomery_limbs([
                        11143510974855252250,
                        1906425947937085984,
                        2407368748249553491,
                        504368299222388920,
                    ]),
                    Fq::from_montgomery_limbs([
                        8041950831366606113,
                        14611771049638947187,
                        11221299042990583579,
                        744635656555856530,
                    ]),
                ]),
                Matrix::<1, 2, 2>::new_from_known([
                    Fq::from_montgomery_limbs([
                        15987773674750471853,
                        7582780421302456968,
                        3513070142855093124,
                        449192997718482772,
                    ]),
                    Fq::from_montgomery_limbs([
                        1698389311466971615,
                        4208825745762883192,
                        17737380562723619127,
                        1023230515994865951,
                    ]),
                ]),
                Matrix::<1, 2, 2>::new_from_known([
                    Fq::from_montgomery_limbs([
                        15719775543772287808,
                        4711976878746234330,
                        9616083067266331949,
                        1291758636403773818,
                    ]),
                    Fq::from_montgomery_limbs([
                        11511319411419341690,
                        4611804125723845050,
                        17905923766281011346,
                        701498562864789906,
                    ]),
                ]),
                Matrix::<1, 2, 2>::new_from_known([
                    Fq::from_montgomery_limbs([
                        6775959117219461845,
                        7248217303083744152,
                        8323273847079805491,
                        1272121734883668680,
                    ]),
                    Fq::from_montgomery_limbs([
                        15960231410259949054,
                        831075562495169556,
                        666337526106305827,
                        827994946738712632,
                    ]),
                ]),
                Matrix::<1, 2, 2>::new_from_known([
                    Fq::from_montgomery_limbs([
                        3075648154561933440,
                        4787490504369527279,
                        2103456873768609578,
                        930535653041788534,
                    ]),
                    Fq::from_montgomery_limbs([
                        13632064958207562507,
                        2403612539570381736,
                        9671114344743639907,
                        554518676653218341,
                    ]),
                ]),
                Matrix::<1, 2, 2>::new_from_known([
                    Fq::from_montgomery_limbs([
                        16017511834618514656,
                        10675130055946071909,
                        4737919029540133580,
                        682111021257012783,
                    ]),
                    Fq::from_montgomery_limbs([
                        4054052073615595653,
                        15900491953977945207,
                        9657244812600116702,
                        746793989576728670,
                    ]),
                ]),
                Matrix::<1, 2, 2>::new_from_known([
                    Fq::from_montgomery_limbs([
                        11427159084253523216,
                        8137374149736453962,
                        493707633722255071,
                        574786622341431128,
                    ]),
                    Fq::from_montgomery_limbs([
                        3016813624761290833,
                        9410383431703917657,
                        207322790806709582,
                        604735846059941483,
                    ]),
                ]),
                Matrix::<1, 2, 2>::new_from_known([
                    Fq::from_montgomery_limbs([
                        13182715603850996122,
                        1385581621557644096,
                        15928797776098706943,
                        1247128249672542744,
                    ]),
                    Fq::from_montgomery_limbs([
                        12343557143080639521,
                        10608577464123341465,
                        8700628699767163855,
                        822798305869360351,
                    ]),
                ])
```

--------------------------------

### Poseidon377 Rate 6 Parameters (Example 5)

Source: https://docs.rs/poseidon377/1.2.0/src/poseidon377/params/rate_6.rs.html

Constructs a field element with another unique set of limb values, emphasizing the detailed parameterization for cryptographic operations.

```rust
Fq::from_montgomery_limbs([
                7989155441247042094,
                18276457113184108543,
                17999817914616464103,
                943187440870955565,
            ])
```

--------------------------------

### Initialize Poseidon377 Rate 3 Matrices

Source: https://docs.rs/poseidon377/1.2.0/src/poseidon377/params/rate_3.rs.html?search=Option%3CT%3E%2C+%28T+-%3E+U%29+-%3E+Option%3CU%3E

Demonstrates the initialization of multiple matrices for Poseidon377 with a rate of 3. Each matrix is constructed using `new_from_known` and populated with `Fq` elements derived from Montgomery limbs.

```rust
Matrix::<1, 3, 3>::new_from_known([
                    Fq::from_montgomery_limbs([
                        14896674334234435047,
                        6601140327636410720,
                        11594733032791631077,
                        947808208377648736,
                    ]),
                    Fq::from_montgomery_limbs([
                        93857753711709862,
                        17114219253807441153,
                        16571911382240086620,
                        644986335071170285,
                    ]),
                    Fq::from_montgomery_limbs([
                        11491045973623638105,
                        5832623718891215316,
                        4637897368334583442,
                        1270136782835782403,
                    ]),
                ]),
                Matrix::<1, 3, 3>::new_from_known([
                    Fq::from_montgomery_limbs([
                        12059760086965268413,
                        2104859632417338119,
                        3074047925029609319,
                        208685506241841351,
                    ]),
                    Fq::from_montgomery_limbs([
                        507458650320731749,
                        9076652763882528689,
                        10828995108044982790,
                        52861166057592230,
                    ]),
                    Fq::from_montgomery_limbs([
                        5221245564257429544,
                        602546441039285868,
                        15463515802777952068,
                        500262458682360187,
                    ]),
                ]),
                Matrix::<1, 3, 3>::new_from_known([
                    Fq::from_montgomery_limbs([
                        7894603091209534363,
                        5963299443776147743,
                        13622917766282071553,
                        713444535504669723,
                    ]),
                    Fq::from_montgomery_limbs([
                        4707822806056225947,
                        13008601324591260598,
                        6664196336989843628,
                        361594494120552721,
                    ]),
                    Fq::from_montgomery_limbs([
                        7234555332968855468,
                        13223173585719696534,
                        305242624856210053,
                        317409461914184558,
                    ]),
                ]),
                Matrix::<1, 3, 3>::new_from_known([
                    Fq::from_montgomery_limbs([
                        11052531972415731524,
                        6240249964832493008,
                        4690512975789608724,
                        274300931659090955,
                    ]),
                    Fq::from_montgomery_limbs([
                        12865203614941348009,
                        13629535421935003532,
                        14381802801123693296,
                        1108602536075241162,
                    ]),
                    Fq::from_montgomery_limbs([
                        5342089493189303187,
                        11299417329134660514,
                        10437815285599784456,
                        224625807758727328,
                    ]),
                ]),
                Matrix::<1, 3, 3>::new_from_known([
                    Fq::from_montgomery_limbs([
                        9419019633707904193,
                        17287104400249488354,
                        2449834218878066498,
                        880784160362712225,
                    ]),
                    Fq::from_montgomery_limbs([
                        1290387194510150606,
                        300217878573287348,
                        14712510331530271944,
                        675169241465258261,
                    ]),
                    Fq::from_montgomery_limbs([
                        4319449301091482228,
                        6604997191961440301,
                        3677473832318302588,
                        1226257433999087430,
                    ]),
                ]),
                Matrix::<1, 3, 3>::new_from_known([
                    Fq::from_montgomery_limbs([
                        9534885027294214845,
                        4233504142154122132,
                        671184154419538440,
                        588715198189399632,
                    ]),
                    Fq::from_montgomery_limbs([
                        7834331777517711657,
                    ]),
                ]),
            ])
```

--------------------------------

### Initialize Poseidon377 Rate 6 with Round Constants

Source: https://docs.rs/poseidon377/1.2.0/src/poseidon377/params/rate_6.rs.html

Initializes the Poseidon377 permutation with a rate of 6 using predefined round constants. This is a common setup for hashing operations.

```rust
Fq::from_montgomery_limbs([
                        6518969013844050226,
                        10104698889580418215,
                        12831301188037688559,
                        783109772397025172,
                    ]),
                    Fq::from_montgomery_limbs([
                        6181962216281397012,
                        8791420351320694807,
                        5845391987758232061,
                        691946495243473347,
                    ]),
                    Fq::from_montgomery_limbs([
                        555663508144587651,
                        2813166513808555896,
                        9604748549845359549,
                        1115460934710212864,
                    ]),
                    Fq::from_montgomery_limbs([
                        638373104524889548,
                        6961133691969109992,
                        16899272275885442322,
                        107354495377389126,
                    ]),
```

--------------------------------

### Poseidon377 Rate 6 Parameters (Example 21)

Source: https://docs.rs/poseidon377/1.2.0/src/poseidon377/params/rate_6.rs.html

Constructs a field element with a distinct set of limb values, contributing to the unique parameterization required for the rate 6 configuration.

```rust
Fq::from_montgomery_limbs([
                829043150522309210,
                7485532467658058089,
                17072453966431109601,
                610297755857677130,
            ])
```

--------------------------------

### Initialize Matrix for Poseidon377 Rate 5

Source: https://docs.rs/poseidon377/1.2.0/src/poseidon377/params/rate_5.rs.html?search=

Initializes a `Matrix::<1, 5, 5>` using `Fq::from_montgomery_limbs` with predefined values. This is used for setting up the Poseidon377 permutation with a rate of 5.

```rust
Matrix::<1, 5, 5>::new_from_known([
                    Fq::from_montgomery_limbs([
                        4222768071479979923,
                        6221868890067618237,
                        6706788302094795072,
                        470857396285528184,
                    ]),
                    Fq::from_montgomery_limbs([
                        837480829798517493,
                        2139750872442256742,
                        5213024737969853757,
                        586284678362031355,
                    ]),
                    Fq::from_montgomery_limbs([
                        18413923626929455705,
                        12351565965899756217,
                        17706788027426014962,
                        396824563157594134,
                    ]),
                    Fq::from_montgomery_limbs([
                        11865172518676463006,
                        15009302994533156097,
                        16026973397263722566,
                        1243693536982901909,
                    ]),
                    Fq::from_montgomery_limbs([
                        7252462303444002809,
                        9549080656602382200,
                        6400682688095758738,
                        206059245034621582,
                    ]),
                ])
```

```rust
Matrix::<1, 5, 5>::new_from_known([
                    Fq::from_montgomery_limbs([
                        8375555895564253468,
                        7925422648691473256,
                        16821885625729885556,
                        985921094928817309,
                    ]),
                    Fq::from_montgomery_limbs([
                        2046299323863281369,
                        13882781361146929705,
                        15448488877161513887,
                        490830679341871217,
                    ]),
                    Fq::from_montgomery_limbs([
                        7429671875567937801,
                        10229990955659579326,
                        17998819479213658262,
                        468703275856634003,
                    ]),
                    Fq::from_montgomery_limbs([
                        935091299463462187,
                        8817490257427535584,
                        4201099561438792936,
                        308509415209580254,
                    ]),
                    Fq::from_montgomery_limbs([
                        15175273292104113428,
                        15547411926550064745,
                        18326735472470278187,
                        46288025765161350,
                    ]),
                ])
```

```rust
Matrix::<1, 5, 5>::new_from_known([
                    Fq::from_montgomery_limbs([
                        2376775726955536549,
                        7198072882321834778,
                        5820986721223000167,
                        1305597767879405697,
                    ]),
                    Fq::from_montgomery_limbs([
                        11562318758115257029,
                        422264710018175990,
                        4674708296176782956,
                        321605471576378125,
                    ]),
                    Fq::from_montgomery_limbs([
                        14422446717346283559,
                        4522943560525804925,
                        12524200552641302343,
                        992174839589322314,
                    ]),
                    Fq::from_montgomery_limbs([
                        2660063348396745477,
                        3046452749899310106,
                        12556614243413712855,
                        292167348848223777,
                    ]),
                    Fq::from_montgomery_limbs([
                        6669133378666467376,
                        16135058416591179983,
                        5627772722389914612,
                        379140231019033687,
                    ]),
                ])
```
Tokens:
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