Initial attempt. I think we can do this with less impact on compilation flow and thus less risk for stability.

lexer/smarty_internal_templateparser.y

@@ -759,6 +759,19 @@ value(res)    ::= varindexed(vi) DOUBLECOLON static_class_access(r). {
     res = $prefixVar .'::'.r[0].r[1];
 }
 
+value(res)    ::= varindexed(vi) DOUBLECOLON static_class_constant(r). {
+    if ($this->security && $this->security->static_classes !== array()) {
+        $this->compiler->trigger_template_error('dynamic static class not allowed by security setting');
+    }
+    $prefixVar = $this->compiler->getNewPrefixVariable();
+    if (vi['var'] === '\'smarty\'') {
+        $this->compiler->appendPrefixCode("<?php {$prefixVar} = ". $this->compiler->compileTag('private_special_variable',array(),vi['smarty_internal_index']).';?>');
+     } else {
+        $this->compiler->appendPrefixCode("<?php  {$prefixVar} = ". $this->compiler->compileVariable(vi['var']).vi['smarty_internal_index'].';?>');
+    }
+    res = $prefixVar .'::'.r[0];
+}
+
                   // Smarty tag
 value(res)       ::= smartytag(st). {
     $prefixVar = $this->compiler->getNewPrefixVariable();
@@ -779,7 +792,21 @@ value(res)       ::= NAMESPACE(c). {
 value(res)       ::= arraydef(a). {
     res = a;
 }
-                  // static class access
+
+                  // static class constant access
+value(res)       ::= ns1(c)DOUBLECOLON static_class_constant(s). {
+    if (!in_array(strtolower(c), array('self', 'parent')) && (!$this->security || $this->security->isTrustedStaticClassAccess(c, s, $this->compiler))) {
+         if (isset($this->smarty->registered_classes[c])) {
+            res = $this->smarty->registered_classes[c].'::'.s[0];
+        } else {
+            res = c.'::'.s[0];
+        }
+    } else {
+        $this->compiler->trigger_template_error ('static class \''.c.'\' is undefined or not allowed by security setting');
+    }
+}
+
+                  // other static class access
 value(res)       ::= ns1(c)DOUBLECOLON static_class_access(s). {
     if (!in_array(strtolower(c), array('self', 'parent')) && (!$this->security || $this->security->isTrustedStaticClassAccess(c, s, $this->compiler))) {
         if (isset($this->smarty->registered_classes[c])) {
@@ -1111,6 +1138,11 @@ modparameter(res) ::= COLON array(mp). {
     res = array(mp);
 }
 
+                  // static class constant
+static_class_constant(res)       ::= ID(v). {
+    res = array(v);
+}
+
                   // static class methode call
 static_class_access(res)       ::= method(m). {
     res = array(m, '', 'method');
@@ -1121,11 +1153,6 @@ static_class_access(res)       ::= method(m) objectchain(oc). {
     res = array(m, oc, 'method');
 }
 
-                  // static class constant
-static_class_access(res)       ::= ID(v). {
-    res = array(v, '');
-}
-
                   // static class variables
 static_class_access(res)       ::=  DOLLARID(v) arrayindex(a). {
     res = array(v, a, 'property');

tests/UnitTests/TemplateSource/ValueTests/PHPfunctions/PhpFunctionTest.php

@@ -255,8 +255,9 @@ class PhpFunctionTest extends PHPUnit_Smarty
 		}
 
 		if ($shouldTriggerDeprecationNotice) {
-			$this->assertStringContainsString('Using unregistered function', $errorMessage);
+			$this->assertStringContainsString('Using unregistered ', $errorMessage);
 		} else {
+			$this->assertEquals('', $errorMessage);
 			$this->assertEquals($expected, $output);
 			$this->assertEquals('', $errorMessage);
 		}
@@ -295,6 +296,9 @@ class PhpFunctionTest extends PHPUnit_Smarty
 			['{$a|addslashes}', '', true],
 			['{$a|sha1}', '', true],
 			['{$a|get_parent_class}', '', true],
+
+			['{StaticMethodsTesterClass::giveMeEmptyString($a)}', '', true],
+			['{StaticMethodsTesterClass::EMPTY_STRING}', '', false],
 		];
 	}
 
@@ -326,3 +330,12 @@ class TestIsset {
         return $v;
     }
 }
+
+class StaticMethodsTesterClass {
+
+	const EMPTY_STRING = '';
+
+	public static function giveMeEmptyString($data) {
+		return '';
+	}
+}