In brief, the public addresses are generated using a random number generator which is Crypto-Secure. Let me show you
an example of how addresses are generated.
0 - Having a private ECDSA key
18e14a7b6a307f426a94f8114701e7c8e774e7f9a47e2c2035db29a206321725
1 - Take the corresponding public key generated with it (33 bytes, 1 byte 0x02 (y-coord is even), and 32 bytes corresponding to X coordinate)
0250863ad64a87ae8a2fe83c1af1a8403cb53f53e486d8511dad8a04887e5b2352
2 - Perform SHA-256 hashing on the public key
0b7c28c9b7290c98d7438e70b3d3f7c848fbd7d1dc194ff83f4f7cc9b1378e98
3 - Perform RIPEMD-160 hashing on the result of SHA-256
f54a5851e9372b87810a8e60cdd2e7cfd80b6e31
4 - Add version byte in front of RIPEMD-160 hash (0x00 for Main Network)
00f54a5851e9372b87810a8e60cdd2e7cfd80b6e31
(note that below steps are the Base58Check encoding, which has multiple library options available implementing it)
5 - Perform SHA-256 hash on the extended RIPEMD-160 result
ad3c854da227c7e99c4abfad4ea41d71311160df2e415e713318c70d67c6b41c
6 - Perform SHA-256 hash on the result of the previous SHA-256 hash
c7f18fe8fcbed6396741e58ad259b5cb16b7fd7f041904147ba1dcffabf747fd
7 - Take the first 4 bytes of the second SHA-256 hash. This is the address checksum
c7f18fe8
8 - Add the 4 checksum bytes from stage 7 at the end of extended RIPEMD-160 hash from stage 4. This is the 25-byte binary Bitcoin Address.
00f54a5851e9372b87810a8e60cdd2e7cfd80b6e31c7f18fe8
9 - Convert the result from a byte string into a base58 string using Base58Check encoding. This is the most commonly used Bitcoin Address format
1PgELFwNQSvu1241GYtDc9YGpqjX3XUsyo
To know more, visit:
https://en.bitcoin.it/wiki/Technical_background_of_version_1_Bitcoin_addresses
