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Groth16 BN128

The Groth16 Proving System over the BN128 prime field (also referred to as as BN254 and BabyJubJub by some applications).

Information​

  • P: 21888242871839275222246405745257275088548364400416034343698204186575808495617
  • Field Element Bits: 254
  • proof_type: Groth16BN128

Proof Verifier Data Pseudo Schema​

{
  "vk_alpha_1": [
      "<Field Element BigInt>",
      "<Field Element BigInt>",
      "<Field Element BigInt>"
    ],
    "vk_beta_2": [
      [
        "<Field Element BigInt>",
        "<Field Element BigInt>"
      ],
      [
        "<Field Element BigInt>",
        "<Field Element BigInt>"
      ],
      [
        "<Field Element BigInt>",
        "<Field Element BigInt>"
      ]
    ],
    "vk_gamma_2": [
      [
        "<Field Element BigInt>",
        "<Field Element BigInt>"
      ],
      [
        "<Field Element BigInt>",
        "<Field Element BigInt>"
      ],
      [
        "<Field Element BigInt>",
        "<Field Element BigInt>"
      ]
    ],
    "vk_delta_2": [
      [
        "<Field Element BigInt>",
        "<Field Element BigInt>"
      ],
      [
        "<Field Element BigInt>",
        "<Field Element BigInt>"
      ],
      [
        "<Field Element BigInt>",
        "<Field Element BigInt>0"
      ]
    ],
    "vk_alphabeta_12": [
      [
        [
          "<Field Element BigInt>",
          "<Field Element BigInt>"
        ],
        [
          "<Field Element BigInt>",
          "<Field Element BigInt>"
        ],
        [
          "<Field Element BigInt>",
          "<Field Element BigInt>"
        ]
      ],
      [
        [
          "<Field Element BigInt>",
          "<Field Element BigInt>"
        ],
        [
          "<Field Element BigInt>",
          "<Field Element BigInt>"
        ],
        [
          "<Field Element BigInt>",
          "<Field Element BigInt>"
        ]
      ]
    ],
    "ic": [
      [
        "<Field Element BigInt>",
        "<Field Element BigInt>",
        "<Field Element BigInt>"
      ],
      [
        "<Field Element BigInt>",
        "<Field Element BigInt>",
        "<Field Element BigInt>"
      ]
    ]
}

Proof Verifier Data Example​

{
  "vk_alpha_1": [
      "20491192805390485299153009773594534940189261866228447918068658471970481763042",
      "9383485363053290200918347156157836566562967994039712273449902621266178545958",
      "1"
    ],
    "vk_beta_2": [
      [
        "6375614351688725206403948262868962793625744043794305715222011528459656738731",
        "4252822878758300859123897981450591353533073413197771768651442665752259397132"
      ],
      [
        "10505242626370262277552901082094356697409835680220590971873171140371331206856",
        "21847035105528745403288232691147584728191162732299865338377159692350059136679"
      ],
      [
        "1",
        "0"
      ]
    ],
    "vk_gamma_2": [
      [
        "10857046999023057135944570762232829481370756359578518086990519993285655852781",
        "11559732032986387107991004021392285783925812861821192530917403151452391805634"
      ],
      [
        "8495653923123431417604973247489272438418190587263600148770280649306958101930",
        "4082367875863433681332203403145435568316851327593401208105741076214120093531"
      ],
      [
        "1",
        "0"
      ]
    ],
    "vk_delta_2": [
      [
        "9403222314096452130574953716594328346759513543371212880706987750458075639987",
        "2148746916934935276300808435247437823105104077198986802327713658047542876491"
      ],
      [
        "11859723293801627952443934346659957119534720371838878650651852603392480673919",
        "6573170423995455063841412786881534799438315741523306975664298942754208465855"
      ],
      [
        "1",
        "0"
      ]
    ],
    "vk_alphabeta_12": [
      [
        [
          "2029413683389138792403550203267699914886160938906632433982220835551125967885",
          "21072700047562757817161031222997517981543347628379360635925549008442030252106"
        ],
        [
          "5940354580057074848093997050200682056184807770593307860589430076672439820312",
          "12156638873931618554171829126792193045421052652279363021382169897324752428276"
        ],
        [
          "7898200236362823042373859371574133993780991612861777490112507062703164551277",
          "7074218545237549455313236346927434013100842096812539264420499035217050630853"
        ]
      ],
      [
        [
          "7077479683546002997211712695946002074877511277312570035766170199895071832130",
          "10093483419865920389913245021038182291233451549023025229112148274109565435465"
        ],
        [
          "4595479056700221319381530156280926371456704509942304414423590385166031118820",
          "19831328484489333784475432780421641293929726139240675179672856274388269393268"
        ],
        [
          "11934129596455521040620786944827826205713621633706285934057045369193958244500",
          "8037395052364110730298837004334506829870972346962140206007064471173334027475"
        ]
      ]
    ],
    "ic": [
      [
        "21283740458357553961334470970611838662846546242629649069480012272202633821993",
        "14849534530026848665315345123975828974311911309171353532045606811840803944790",
        "1"
      ],
      [
        "7694328154783572960215780118843820664662340976566792914500403448593687448747",
        "732615864654692326040517138836336014082626398109534097643426563708659766647",
        "1"
      ]
    ]
}

Proof Pseudo Schema​

{
  "public_inputs": [
    "<Field Element BigInt>"
  ],
  "pi_a": [
    "<Field Element BigInt>",
    "<Field Element BigInt>",
    "<Field Element BigInt>"
  ],
  "pi_b": [
    [
      "<Field Element BigInt>",
      "<Field Element BigInt>"
    ],
    [
      "<Field Element BigInt>",
      "<Field Element BigInt>"
    ],
    [
      "<Field Element BigInt>",
      "<Field Element BigInt>"
    ]
  ],
  "pi_c": [
    "<Field Element BigInt>",
    "<Field Element BigInt>",
    "<Field Element BigInt>"
  ]
}

Proof Example​

{
  "public_inputs": [
    "11280100872502127069480838594104185543273433001410495939274595021993185000375"
  ],
  "pi_a": [
    "9385890952955428126958656756976259457071170377421134904842515167603595843109",
    "16860232232140553002979745091821870408423002560573668803219437340736112763475",
    "1"
  ],
  "pi_b": [
    [
      "12943406347151935529489335492657814358772779287639937761947020237460725104053",
      "3624014360683444308010044793677141448718644643460743425021912808682363661020"
    ],
    [
      "8087583382578374869858425081685764117855489482806049018484408783454171866290",
      "12846146940115715343742778824340233399142084815024830037559944541243214854362"
    ],
    [
      "1",
      "0"
    ]
  ],
  "pi_c": [
    "10935549858652209106177829043339479341478554688927432977140359846861860016946",
    "16304845681526491710774548875843007825200131443254970519556259409300207772635",
    "1"
  ]
}