Merkle–Hellman knapsack cryptosystem
one of the earliest public key cryptosystems invented by Ralph Merkle and Martin Hellman in 1978. The ideas behind it are simpler than those involving RSA, and it has been broken
The Merkle–Hellman knapsack cryptosystem was one of the earliest public key cryptosystems. It was published by Ralph Merkle and Martin Hellman in 1978. A polynomial time attack was published by Adi Shamir in 1984. As a result, the cryptosystem is now considered insecure.
History
The concept of public key cryptography was introduced by Whitfield Diffie and Martin Hellman in 1976. At that time they proposed the general concept of a "trap-door one-way function", a function whose inverse is computationally infeasible to calculate without some secret "trap-door information"; but they had not yet found a practical example of such a function. Several specific public-key cryptosystems were then proposed by other researchers over the next few years, such as RSA in 1977 and Merkle-Hellman in 1978.
Description
Merkle–Hellman is a public key cryptosystem, meaning that two keys are used, a public key for encryption and a private key for decryption. It is based on the subset sum problem (a special case of the knapsack problem). The problem is as follows: given a set of integers
A
{\displaystyle A}
and an integer
c
{\displaystyle c}
, find a subset of
A
{\displaystyle A}
which sums to
c
{\displaystyle c}
.
This brief starts where responsible research should: with the source description of “Merkle–Hellman knapsack cryptosystem” as one of the earliest public key cryptosystems invented by Ralph Merkle and Martin Hellman in 1978. The ideas behind it are simpler than those involving RSA, and it has been broken. Everything that follows is an evidence route, not borrowed authority.
Why this record matters
The subject matters to the general reference register because the source frames it as one of the earliest public key cryptosystems invented by Ralph Merkle and Martin Hellman in 1978. The ideas behind it are simpler than those involving RSA, and it has been broken. Its deeper value depends on whether names, dates, institutions and citations support that framing.
Vocabulary and entity names are the principal evidence signals here, because they determine the precision of every later search. The source revision retrieved here is dated Mar 30, 2026. The linked authority identifier is Q1760368. None of the 0 selected statements returned an explicit reference. The first chronological checks are 1978, 1984, 1976 and 1977.
The absence of detail may reflect summary conventions rather than a lack of surviving documentation. The lead is largely declarative, so disagreement and counter-evidence require a deliberate search beyond the opening account. Authority statements aid reconciliation but still require their own references, qualifiers and ranks to be checked.
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This entry incorporates text from “Merkle–Hellman knapsack cryptosystem” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.