The right is explicitly acknowledged in the 4th Amend. The initial phrase in the 4th refers specifically to the right: "The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated,..."
"Smith: The “right to privacy,” when originally formulated, referred to the right to have such things as one’s journal or conversations kept private."
This is ridiculous, since they explicitly included persons, houses and effects. The right extended to everything, not just one's journal, or conversations.
"In 1965, in Griswold v. Connecticut, the Supreme Court found constitutional protection for the sale, distribution and use of contraceptives"
Here's a summary from Wiki:
"Although the Bill of Rights does not explicitly mention "privacy", Justice William O. Douglas wrote for the majority that the right was to be found in the "penumbras" and "emanations" of other constitutional protections. Justice Arthur Goldberg wrote a concurring opinion in which he used the Ninth Amendment to defend the Supreme Court's ruling. Justice John Marshall Harlan II wrote a concurring opinion in which he argued that privacy is protected by the due process clause of the Fourteenth Amendment. Justice Byron White also wrote a concurrence based on the due process clause."
The only Justice to get it right was Potter Stewart. "Justice Stewart famously called the Connecticut statute "an uncommonly silly law", but argued that it was nevertheless constitutional."
It depends what is meant by “privacy”: it is an elastic law.
Surely, the 4th amendment establishes due process. Let us say a law against contraception is enacted. The 4th amendment will still not allow the cops to search for condoms in bedside drawers; but the prescribing, sale and advertising of contraception will be restricted or completely banned.
It is no different from the current laws against some recreational drugs, or against some pornography. The 4th amendment does not invalidate these laws. If the right to privacy as enshrined in the constitutional penumbras meant what Griswald decided, we would not have laws against cocaine, child pornography, or prostitution, all activities similarly private.