問題の説明

root@blueboz:~/Downloads# ./qt-opensource-linux-x64-5.5.0-2.run 
qt.network.ssl: QSslSocket: cannot resolve CRYPTO_num_locks
qt.network.ssl: QSslSocket: cannot resolve CRYPTO_set_id_callback
qt.network.ssl: QSslSocket: cannot resolve CRYPTO_set_locking_callback
qt.network.ssl: QSslSocket: cannot resolve ERR_free_strings
qt.network.ssl: QSslSocket: cannot resolve sk_new_null
qt.network.ssl: QSslSocket: cannot resolve sk_push
qt.network.ssl: QSslSocket: cannot resolve sk_free
qt.network.ssl: QSslSocket: cannot resolve sk_num
qt.network.ssl: QSslSocket: cannot resolve sk_pop_free
qt.network.ssl: QSslSocket: cannot resolve sk_value
qt.network.ssl: QSslSocket: cannot resolve SSL_library_init
qt.network.ssl: QSslSocket: cannot resolve SSL_load_error_strings
qt.network.ssl: QSslSocket: cannot resolve SSLv2_client_method
qt.network.ssl: QSslSocket: cannot resolve SSLv3_client_method
qt.network.ssl: QSslSocket: cannot resolve SSLv23_client_method
qt.network.ssl: QSslSocket: cannot resolve SSLv2_server_method
qt.network.ssl: QSslSocket: cannot resolve SSLv3_server_method
qt.network.ssl: QSslSocket: cannot resolve SSLv23_server_method
qt.network.ssl: QSslSocket: cannot resolve X509_STORE_CTX_get_chain
qt.network.ssl: QSslSocket: cannot resolve OPENSSL_add_all_algorithms_noconf
qt.network.ssl: QSslSocket: cannot resolve OPENSSL_add_all_algorithms_conf
qt.network.ssl: QSslSocket: cannot resolve SSLeay
qt.network.ssl: QSslSocket: cannot resolve SSLeay_version
qt.network.ssl: QSslSocket: cannot call unresolved function CRYPTO_num_locks
qt.network.ssl: QSslSocket: cannot call unresolved function CRYPTO_set_id_callback
qt.network.ssl: QSslSocket: cannot call unresolved function CRYPTO_set_locking_callback
qt.network.ssl: QSslSocket: cannot call unresolved function SSL_library_init
Could not register file downloader for https protocol: QSslSocket::supportsSsl() returns false
[0] Warning: QSslSocket: cannot call unresolved function SSLv23_client_method
[1] Warning: QSslSocket: cannot call unresolved function sk_num
Segmentation fault

解決策

apt install libssl1.0-dev