diff --git a/std/js/src/main/scala/cats/effect/std/SecureRandomCompanionPlatform.scala b/std/js/src/main/scala/cats/effect/std/SecureRandomCompanionPlatform.scala
index 95aaca72d3..4ffe111546 100644
--- a/std/js/src/main/scala/cats/effect/std/SecureRandomCompanionPlatform.scala
+++ b/std/js/src/main/scala/cats/effect/std/SecureRandomCompanionPlatform.scala
@@ -114,9 +114,15 @@ private[std] trait SecureRandomCompanionPlatform {
     }
   }
 
+  @deprecated("Use 'of' instead", "3.7.0")
   def javaSecuritySecureRandom[F[_]: Sync]: F[SecureRandom[F]] =
     Sync[F].delay(unsafeJavaSecuritySecureRandom())
 
+  def of[F[_]: Sync]: F[SecureRandom[F]] = in[F, F]
+
+  def in[F[_]: Sync, G[_]: Sync]: F[SecureRandom[G]] =
+    Sync[F].delay(unsafeJavaSecuritySecureRandom[G]())
+
   private[effect] def unsafeJavaSecuritySecureRandom[F[_]: Sync](): SecureRandom[F] =
     new ScalaRandom[F](Applicative[F].pure(new JavaSecureRandom())) with SecureRandom[F] {}
 
diff --git a/std/jvm/src/main/scala/cats/effect/std/SecureRandomCompanionPlatform.scala b/std/jvm/src/main/scala/cats/effect/std/SecureRandomCompanionPlatform.scala
index 6d55c388f6..04a499597c 100644
--- a/std/jvm/src/main/scala/cats/effect/std/SecureRandomCompanionPlatform.scala
+++ b/std/jvm/src/main/scala/cats/effect/std/SecureRandomCompanionPlatform.scala
@@ -43,9 +43,15 @@ private[std] trait SecureRandomCompanionPlatform {
   private def javaUtilRandomBlocking[F[_]: Sync](random: JavaSecureRandom): SecureRandom[F] =
     new ScalaRandom[F](Applicative[F].pure(random), Sync.Type.Blocking) with SecureRandom[F] {}
 
+  @deprecated("Use 'of' instead", "3.7.0")
   def javaSecuritySecureRandom[F[_]: Sync]: F[SecureRandom[F]] =
     Sync[F].delay(unsafeJavaSecuritySecureRandom())
 
+  def of[F[_]: Sync]: F[SecureRandom[F]] = in[F, F]
+
+  def in[F[_]: Sync, G[_]: Sync]: F[SecureRandom[G]] =
+    Sync[F].delay(unsafeJavaSecuritySecureRandom[G]())
+
   /**
    * Ported from https://github.com/http4s/http4s/.
    */
diff --git a/std/native/src/main/scala/cats/effect/std/SecureRandomCompanionPlatform.scala b/std/native/src/main/scala/cats/effect/std/SecureRandomCompanionPlatform.scala
index 2aa8ca8d89..f455845729 100644
--- a/std/native/src/main/scala/cats/effect/std/SecureRandomCompanionPlatform.scala
+++ b/std/native/src/main/scala/cats/effect/std/SecureRandomCompanionPlatform.scala
@@ -57,9 +57,15 @@ private[std] trait SecureRandomCompanionPlatform {
 
   }
 
+  @deprecated("Use 'of' instead", "3.7.0")
   def javaSecuritySecureRandom[F[_]: Sync]: F[SecureRandom[F]] =
     Sync[F].delay(unsafeJavaSecuritySecureRandom())
 
+  def of[F[_]: Sync]: F[SecureRandom[F]] = in[F, F]
+
+  def in[F[_]: Sync, G[_]: Sync]: F[SecureRandom[G]] =
+    Sync[F].delay(unsafeJavaSecuritySecureRandom())
+
   private[effect] def unsafeJavaSecuritySecureRandom[F[_]: Sync](): SecureRandom[F] =
     new ScalaRandom[F](Applicative[F].pure(new JavaSecureRandom())) with SecureRandom[F] {}
 
diff --git a/std/shared/src/main/scala/cats/effect/std/SecureRandom.scala b/std/shared/src/main/scala/cats/effect/std/SecureRandom.scala
index 991e266690..e25046dfb6 100644
--- a/std/shared/src/main/scala/cats/effect/std/SecureRandom.scala
+++ b/std/shared/src/main/scala/cats/effect/std/SecureRandom.scala
@@ -124,6 +124,9 @@ object SecureRandom extends SecureRandomCompanionPlatform {
     }
 
   /**
+   * Builds a `SecureRandom[F]` value for effect types that are [[cats.effect.kernel.Sync]] and
+   * initializes random state using the same effect type
+   *
    * On the JVM, delegates to [[java.security.SecureRandom]].
    *
    * In browsers, delegates to the
@@ -136,7 +139,31 @@ object SecureRandom extends SecureRandomCompanionPlatform {
    * on Linux, macOS, and BSD. Unsupported platforms such as Windows will encounter link-time
    * errors.
    */
-  override def javaSecuritySecureRandom[F[_]: Sync]: F[SecureRandom[F]] =
-    super.javaSecuritySecureRandom[F]
+  override def javaSecuritySecureRandom[F[_]: Sync]: F[SecureRandom[F]] = of
+
+  /**
+   * Builds a `SecureRandom[F]` value for effect types that are [[cats.effect.kernel.Sync]] and
+   * initializes random state using the same effect type
+   *
+   * On the JVM, delegates to [[java.security.SecureRandom]].
+   *
+   * In browsers, delegates to the
+   * [[https://developer.mozilla.org/en-US/docs/Web/API/Web_Crypto_API Web Crypto API]].
+   *
+   * In Node.js, delegates to the [[https://nodejs.org/api/crypto.html crypto module]].
+   *
+   * On Native, delegates to
+   * [[https://man7.org/linux/man-pages/man3/getentropy.3.html getentropy]] which is supported
+   * on Linux, macOS, and BSD. Unsupported platforms such as Windows will encounter link-time
+   * errors.
+   */
+  override def of[F[_]: Sync]: F[SecureRandom[F]] = in[F, F]
+
+  /**
+   * Builds a `SecureRandom[G]` value for effect types that are [[cats.effect.kernel.Sync]] but
+   * initializes random state using another effect constructor
+   */
+  override def in[F[_]: Sync, G[_]: Sync]: F[SecureRandom[G]] =
+    Sync[F].delay(unsafeJavaSecuritySecureRandom[G]())
 
 }