[pg314]

> There is just no way to securely create a secret key.

That is wrong. You can generate one relatively easily with dice (google for it).

> Because the algorithm is so complex, you have to trust somebody else's software to create the key.

You're conflating generating the key, which is just generating a random number in a certain range, with calculating the public address, which involves some operations on elliptic curves.

The algorithm is not that complex. Using a library like openssl/ec it is not that hard to generate the public address. It takes about 30 lines of C code using that library.

> How do you know that software is neither malicious nor buggy?

You can read the source code.

[TekMol]

    You can read the source code.

Which code? Any link to that 30 lines of C code?

[pg314]

The source code of whatever software you're using.

Here's some C code I used when I played around with it 5 years ago. No guarantees that it is bug-free or does anything useful (you still need a double sha256 and base58 encoding to get a string representation), but it gives you an idea of the complexity/simplicity.

  void sha256_ripe160(uint8_t *bytes, size_t len, uint8_t result[RIPEMD160_DIGEST_LENGTH])
  {
    uint8_t buf[32];
    CC_SHA256(bytes, len, buf);
    RIPEMD160(buf, 32, result);
  }

  void privkey_to_pubsig_hash(uint8_t privkey[32], uint8_t pubsig[20])
  {
    static EC_GROUP *curve = 0;
    if (!curve) {
      curve = EC_GROUP_new_by_curve_name(NID_secp256k1);
    }
    assert(curve);

    BIGNUM *priv_bn = BN_new();
    priv_bn = BN_bin2bn(privkey, 32, priv_bn);
    assert(priv_bn);

    EC_POINT *pub_pt = EC_POINT_new(curve);
    BN_CTX *ctx = BN_CTX_new();
    int result = EC_POINT_mul(curve, pub_pt, priv_bn, NULL, NULL, ctx);
    assert(result);
    BN_free(priv_bn);

    BIGNUM *pub_bn = BN_new();
    EC_POINT_point2bn(curve, pub_pt, POINT_CONVERSION_UNCOMPRESSED, pub_bn, ctx);
    EC_POINT_free(pub_pt);
    BN_CTX_free(ctx);
    assert(BN_num_bytes(pub_bn) == 65);

    uint8_t pub_bytes[65];
    BN_bn2bin(pub_bn, pub_bytes);
    BN_free(pub_bn);

    sha256_ripe160(pub_bytes, 65, pubsig);
  }

One of the myriad Python libraries to deal with bitcoin is probably a better starting point if you want to explore more.