A bird is recognized by its plumage… or professional protection against spam

Often, each of us has a desire to find people similar to ourselves (in a professional sense), but at the same time, posting our contact information on public networks can generate a lot of spam (oh, those ancient canned goods).

In this case, general knowledge comes to the rescue – educational qualifications in a professional field – which will not allow the “uninitiated” to use the data.

Please accept this simple privacy protection for mathematicians and programmers.


Let's remember one of the first asymmetric encryption systems, RSA – what is its basis?
Simple fact:
if for number m the value of the Euler function is known E(m),
then for anyone a != 0 performed a ^ E(m) % m = 1

Which means if p And E(m) are relatively simple, that is, they exist c And dsuch that c*p + d*E(m) = 1And s = c % m
then for anyone a from [0m)[0m) performed a ^ (s*p) % m = a

Let's take advantage of this.
Let's sketch out a program in js (I hope those reading this in a browser know how to log into the console)

function split(x) {
    for (let i = 2n; i * i <= x; i++) {
        let j = x / i;
        if (i * j == x) return [i, j];
    }
}

function toPrimes(x) {
    let arr = [x];
    let primes = [];
    while (arr.length > 0) {
        let x = arr.pop();
        let s = split(x);
        if (s) s.forEach(y => arr.push(y));
        else primes.push(x);
    }
    primes.sort((a, b) => a < b ? -1 : a > b ? 1 : 0);
    return primes;
}

function euler(p) {
    let z = 1n;
    let map = new Map();

    p.forEach(x => {
        let value = 0n;
        if (map.has(x)) { value = map.get(x); map.delete(x); }
        value++;
        map.set(x, value);
    });
    for (let [key, value] of map.entries()) {
        z *= pow(key, value) - 1n;
    }
    return z;
}

function xgcd(a, b) {
    if (!b) return [1n, 0n];
    let [c, d] = xgcd(b, a % b);
    let q = a / b;
    return [d, c - d * q];
}

function pow(x, y) {
    if (!y) return 1n;
    let h = y / 2n;
    let z = pow(x, h);
    let r = (z * z);
    if (y % 2n) r = (r * x);
    return r;
}

function powmod(x, y, m) {
    if (!y) return 1n;
    let h = y / 2n;
    let z = powmod(x, h, m);
    let r = (z * z) % m;
    if (y % 2n) r = (r * x) % m;
    return r;
}

let p = 3n;
let q = 13n;
let m = pow(10n, q) + 1n;

let primes = toPrimes(m);
let z = euler(primes);
let primes2 = toPrimes(z);
while (primes2.find(x => x == p)) p += 2n;
let [c, d] = xgcd(p, z);

let s = c >= 0n ? c : (m + c);

function get(x) {
    let t = powmod(x, s, m);
    console.log(`(${t} ^ ${p}) % (10 ^ ${q} + 1) =`, powmod(t, p, m));
}

get(81234567890n);

We launch, check, receive

(275491122648 ^ 7) % (10 ^ 13 + 1) = 81234567890n

Does the English typewriter work?