diff --git a/src/wp-admin/includes/file.php b/src/wp-admin/includes/file.php
index cd3551bfad..538ec2e1ca 100644
--- a/src/wp-admin/includes/file.php
+++ b/src/wp-admin/includes/file.php
@@ -1199,6 +1199,39 @@ function verify_file_signature( $filename, $signatures, $filename_for_errors = f
 
 	}
 
+	// Verify runtime speed of Sodium_Compat is acceptable.
+	if ( ! extension_loaded( 'sodium' ) && ! ParagonIE_Sodium_Compat::polyfill_is_fast() ) {
+		$sodium_compat_is_fast = false;
+
+		// Allow for an old version of Sodium_Compat being loaded before the bundled WordPress one.
+		if ( method_exists( 'ParagonIE_Sodium_Compat', 'runtime_speed_test' ) ) {
+			// Run `ParagonIE_Sodium_Compat::runtime_speed_test()` in optimized integer mode, as that's what WordPress utilises during signing verifications.
+			$old_fastMult                      = ParagonIE_Sodium_Compat::$fastMult;
+			ParagonIE_Sodium_Compat::$fastMult = true;
+			$sodium_compat_is_fast             = ParagonIE_Sodium_Compat::runtime_speed_test( 100, 10 );
+			ParagonIE_Sodium_Compat::$fastMult = $old_fastMult;
+		}
+
+		// This cannot be performed in a reasonable amount of time
+		// https://github.com/paragonie/sodium_compat#help-sodium_compat-is-slow-how-can-i-make-it-fast
+		if ( ! $sodium_compat_is_fast ) {
+			return new WP_Error(
+				'signature_verification_unsupported',
+				sprintf(
+					/* translators: 1: The filename of the package. */
+					__( 'The authenticity of %1$s could not be verified as signature verification is unavailable on this system.' ),
+					'<span class="code">' . esc_html( $filename_for_errors ) . '</span>'
+				),
+				array(
+					'php'                => phpversion(),
+					'sodium'             => defined( 'SODIUM_LIBRARY_VERSION' ) ? SODIUM_LIBRARY_VERSION : ( defined( 'ParagonIE_Sodium_Compat::VERSION_STRING' ) ? ParagonIE_Sodium_Compat::VERSION_STRING : false ),
+					'polyfill_is_fast'   => false,
+					'max_execution_time' => ini_get( 'max_execution_time' ),
+				)
+			);
+		}
+	}
+
 	if ( ! $signatures ) {
 		return new WP_Error(
 			'signature_verification_no_signature',