Examples

Examples of POD2 use cases

EthDos

Check also the custom statement example section.

Original in prolog https://gist.github.com/ludns/f84b379ec8c53c97b7f95630e16cc39c#file-eth_dos-pl

An EthDos Pod exposes a single custom statement with two custom deduction rules, the inductive case and the base case.

// src, dst: PubKey, attetation_pod: Pod
eth_dos_friend(src, dst, private: attestation_pod) = AND(
    ValueOf(?attestation_pod[KEY_TYPE], SIGNATURE)
    Equal(?attestation_pod[KEY_SIGNER], src)
    Equal(?attestation_pod["attestation"], dst) 
)

// src, intermed, dst: PubKey, distance, shorter_distance: Int
eth_dos_distance(src, dst, distance, private: shorter_distance, intermed) = OR(
    AND(
        eth_dos_distance(?src, ?intermed, ?shorter)
        SumOf(?distance, ?shorter_distance, 1)
        eth_friend(?intermed, ?dst)
    )
    AND(
        Equal(?src, ?dst)
        Equal(?distance, 0)
    )
)

ZuKYC (classic)

Original using GPC https://github.com/proofcarryingdata/zukyc

Authority public keys:

• ZOO_GOV: PubKey, issues IDs
• ZOO_DEEL: PubKey, issues bank statements Authority lists:
• SANCTION_LIST: Set, Merkle Tree Root of set of sanctioned public keys
  • values: ["G2345678", "G1987654", "G1657678"] Date values:
• NOW_MINUS_18Y: Int, 18 years ago
• NOW_MINUS_1Y: Int, 1 year ago
• NOW_MINUS_7D: Int, 7 days ago

A ZuKYC Pod exposes a single custom statement with one custom deduction rule.

// receiver: PubKey, gov_id, paystub, sk_pok: Pod, nullifier, sk: Raw
loan_check(receiver, private: gov_id, paystub, nullifier, sk, sk_pok) = AND(
    Equal(?gov_id["pk"], receiver)
    // Not in the sanction list
    SetNotContains(SANCTION_LIST, receiver)
    // Valid government-issued ID
    Equal(?gov_id[KEY_SIGNER], ZOO_GOV)
    Equal(?gov_id[KEY_TYPE], SIGNATURE)
    // At least 18 years old
    Lt(?gov_id["date_of_birth"], NOW_MINUS_18Y) # date_of_birdth is more than 18y old
    Equal(?paystub[KEY_SIGNER], ZOO_DEEL)
    Equal(?paystub[KEY_TYPE], SIGNATURE)
    Equal(?paystub[ssn], ?gov_id["ssn"])
    // At least one year of consistent employment with your current employer
    Lt(?paystub["start_date"], NOW_MINUS_1Y) # start_date is more than 1y old
    Gt(?paystub["issue_date"], NOW_MINUS_7D) # issue_date is less than 7d old
    // Annual salary is at least $20,000
    Gt(?paystub["annual_salary"], 20000)
    // Private key knowledge
    Equal(?sk_pok[KEY_SIGNER], receiver)
    Equal(?sk_pok[KEY_TYPE], SIGNATURE)
    Equal(?sk_pok["auth"], "ZUKYC_V1_AUTH")
    HashOf(, 0, ?sk)
    // Nullifier
    HashOf(nullifier, "ZUKYC_V1_NULLIFIER", ?sk)
)

ZuKYC (simplified for P1)

This simplified version uses less statements but requires a very similar set of features.

Authority lists:

• SANCTION_LIST: Set, Merkle Tree Root of set of sanctioned public keys
  • values: ["G2345678", "G1987654", "G1657678"] Date values:
• NOW_MINUS_18Y: Int, 18 years ago
• NOW_MINUS_1Y: Int, 1 year ago

A ZuKYC Pod exposes a single custom statement with one custom deduction rule.

// receiver: String, gov_pk, paystub_pk: PubKey, gov_id, paystub: Pod
loan_check(receiver, gov_pk, paystub_pk, private: gov_id, paystub) = AND(
    Equal(?gov_id["id_number"], ?receiver)
    // Not in the sanction list
    SetNotContains(SANCTION_LIST, ?gov_id["id_number"])
    // Valid government-issued ID
    ValueOf(?gov_id[KEY_SIGNER], ?gov_pk)
    Equal(?gov_id[KEY_TYPE], SIGNATURE)
    // At least 18 years old
    Lt(?gov_id["date_of_birth"], NOW_MINUS_18Y) # date_of_birdth is more than 18y old
    ValueOf(?paystub[KEY_SIGNER], ?paystub_pk)
    Equal(?paystub[KEY_TYPE], SIGNATURE)
    Equal(?paystub["ssn"], ?gov_id["ssn"])
    // At least one year of consistent employment with your current employer
    Lt(?paystub["start_date"], NOW_MINUS_1Y) # start_date is more than 1y old
)

GreatBoy

A Good Boy Pod exposes one custom statement with one custom deduction rule.

// user: PubKey, good_boy_issuers: Set, pod: Pod, age: Int
is_good_boy(user, good_boy_issuers, private: pod, age) = AND(
    Equal(?pod[KEY_TYPE], SIGNATURE)
    SetContains(?good_boy_issuers, ?pod[KEY_SIGNER])
    // A good boy issuer says this user is a good boy
    Equal(?pod["user"], ?user)
    Equal(?pod["age"], ?age)
)

A Friend Pod exposes one custom statement with one custom deduction rule.

// good_boy, friend: PubKey, good_boy_issuers: Set, friend_pod: Pod
is_friend(good_boy, friend, good_boy_issuers, friend_pod) = AND(
    Equal(?pod[KEY_TYPE], SIGNATURE)
    // The issuer is a good boy
    is_good_boy(?good_boy, ?good_boy_issuers)
    // A good boy says this is their friend
    Equal(?pod[KEY_SIGNER], ?good_boy)
    Equal(?pod["friend"], ?friend)
)

A Great Boy Pod exposes (in addition to the above) one new custom statement with one custom deduction rule.

great_boy: PubKey, good_boy_issuers: Set, friend_pod_0, friend_pod_1: Pod
is_great_boy(great_boy, good_boy_issuers, private: friend_pod_0, friend_pod_1) = AND
    // Two good boys consider this user their friend
    is_friend(?friend_pod_0[KEY_SIGNER], ?great_boy)
    is_friend(?friend_pod_1[KEY_SIGNER], ?great_boy)
    // good boy 0 != good boy 1
    NotEqual(?friend_pod_0[KEY_SIGNER], ?friend_pod_1[KEY_SIGNER])

Attested GreatBoy

An Attested Great Boy Pod is like a Great Boy Pod, but the names of the signers are revealed.

// great_boy: PubKey, friend0, friend1: String, good_boy_issuers: Set, friend_pod_0, friend_pod_1: Pod
is_great_boy(great_boy, friend0, friend1, good_boy_issuers, private: friend_pod_0, friend_pod_1) = AND
    // Two good boys consider this user their friend
    is_friend(?friend_pod_0[KEY_SIGNER], ?great_boy)
    is_friend(?friend_pod_1[KEY_SIGNER], ?great_boy)
    // good boy 0 != good boy 1
    NotEqual(?friend_pod_0[KEY_SIGNER], ?friend_pod_1[KEY_SIGNER])
    // publicize signer names
    ValueOf(?friend_pod_0["name"], ?friend0)
    ValueOf(?friend_pod_1["name"], ?friend1)

To produce a Great Boy Pod, you need two Friend Pods, friend_pod0 and friend_pod1, each of which reveals its signer.

Tracking PodIDs: Posts and comments

The goal of this example is to model a social network, where posts and comments are pods.

A Post is a signature pod with the following fields:

content: String
poster: String
signer: PubKey
timestamp: Int

A Comment is a signature pod with the following fields:

content: String
referenced_post: PodID
signer: PubKey
timestamp: Int

A post is popular if it has at least two comments from different signers.

// post, comment1, comment2: Pod
statement is_popular(post, private: comment1, comment2) = AND(
    IsEqual(?comment1["referenced_post"], ?post)
    IsEqual(?comment2["referenced_post"], ?post)
    NotEqual(?comment1[KEY_SIGNER], ?comment2[KEY_SIGNER])
)

Multiple people over 18

Suppose I want to prove that two different people are over 18, and a third person is under 18, using the custom predicates over_18 and under_18.

// age: Int
over_18(age) = AND(
    GtEq(?age, 18)
)

// age: Int
under_18(age) = AND(
    Lt(age, 18)
)

With wildcards:

over_18(?1) = AND(
    GtEq(?1, 18)
)

Maybe I have two input pods gov_id1 and gov_id2, and I want to prove that these pods refer to two different people, both of whom are over 18; and a third pods gov_id3 refers to someone under 18. So in my public output statements, I want to have:

NotEqual(?gov_id1["name"], ?gov_id2["name"])
over_18(?gov_id1["age"])
over_18(?gov_id2["age"])
under_18(?gov_id3["age"]).

I would prove this with the following sequence of deductions: