science

Khufu and Khafre

Khufu and Khafre is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Khufu and Khafre rather than just read about it. In short: In cryptography, Khufu and Khafre are two block ciphers designed by Ralph Merkle in 1989 while working at Xerox's Palo Alto Research Center. Along with Snefru, a cryptographic hash function, the ciphers were named after the Egyptian Pharaohs Khufu, Khafre and Sneferu.

Key takeaways

Khufu and Khafre belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Khufu and Khafre to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Khufu and Khafre from memory before moving on to harder problems.

Reference excerpt

In cryptography, Khufu and Khafre are two block ciphers designed by Ralph Merkle in 1989 while working at Xerox's Palo Alto Research Center. Along with Snefru, a cryptographic hash function, the ciphers were named after the Egyptian Pharaohs Khufu, Khafre and Sneferu. Under a voluntary scheme, Xerox submitted Khufu and Khafre to the US National Security Agency (NSA) prior to publication. NSA requested that Xerox not publish the algorithms, citing concerns about national security. Xerox, a large contractor to the US government, complied. However, a reviewer of the paper passed a copy to John Gilmore, who made it available via the sci.crypt newsgroup. It would appear this was against Merkle's wishes. The scheme was subsequently published at the 1990 CRYPTO conference (Merkle, 1990). Khufu and Khafre were patented by Xerox; the patent was issued on March 26, 1991.

Khufu

Khufu is a 64-bit block cipher which, unusually, uses keys of size 512 bits; block ciphers typically have much smaller keys, rarely exceeding 256 bits. Most of the key material is used to construct the cipher's S-boxes. Because the key-setup time is quite time consuming, Khufu is not well suited to situations in which many small messages are handled. It is better suited to bulk encryption of large amounts of data. Khufu is a Feistel cipher with 16 rounds by default (other multiples of eight between 8 and 64 are allowed). Each set of eight rounds is termed an octet; a different S-box is used in each octet. In a round, the least significant byte of half of the block is passed into the 8×32-bit S-box. The S-box output is then combined (using XOR) with the other 32-bit half. The left half is rotated to bring a new byte into position, and the halves are swapped. At the start and end of the algorithm, extra key material is XORed with the block (key whitening). Other than this, all the key is contained in the S-boxes. There is a differential attack on 16 rounds of Khufu which can recover the secret key. It requires 243 chosen plaintexts and has a 243 time complexity (Gilbert and Chauvaud, 1994). 232 plaintexts and complexity are required merely to distinguish the cipher from random. A boomerang attack (Wagner, 1999) can be used in an adaptive chosen plaintext / chosen ciphertext scenario with 218 queries and a similar time complexity. Khufu is also susceptible to an impossible differential attack, which can break up to 18 rounds of the cipher (Biham et al., 1999). Schneier and Kelsey (1996) categorise Khafre and Khufu as "even incomplete heterogeneous target-heavy Unbalanced Feistel Networks".

Khafre

Khafre is similar to Khufu, but uses a standard set of S-boxes, and does not compute them from the key. (Rather, they are generated from the RAND tables, used as a source of "nothing up my sleeve numbers".) An advantage is that Khafre can encrypt a small amount of data very rapidly — it has good key agility. However, Khafre probably requires a greater number of rounds to achieve a similar level of security as Khufu, making it slower at bulk encryption. Khafre uses a key whose size is a multiple of 64 bits. Because the S-boxes are not key-dependent, Khafre XORs subkeys every eight rounds. Differential cryptanalysis is effective against Khafre: 16 rounds can be broken using either 1500 chosen plaintexts or 238 known plaintexts. Similarly, 24 rounds can be attacked using 253 chosen plaintexts or 259 known plaintexts.

References

General

R.C. Merkle (August 1990). Fast Software Encryption Functions (PDF/PostScript). Advances in Cryptology—CRYPTO '90. Santa Barbara, California: Springer-Verlag. pp. 476–501. Retrieved August 23, 2007.{{cite conference}}: CS1 maint: miscellaneous url (link) Eli Biham; Adi Shamir (August 1991). Differential Cryptanalysis of Snefru, Khafre, REDOC-II, LOKI and Lucifer (PDF/PostScript). Advances in Cryptology—CRYPTO '91. Santa Barbara, California: Springer-Verlag. pp. 156–171. Retrieved August 23, 2007.{{cite conference}}: CS1 maint: miscellaneous url (link) Henri Gilbert; Pascal Chauvaud (August 1994). A Chosen Plaintext Attack of the 16-round Khufu Cryptosystem. Advances in Cryptology—CRYPTO '94. Santa Barbara, California: Springer-Verlag. pp. 359–368. Bruce Schneier; John Kelsey (February 1996). Unbalanced Feistel Networks and Block Cipher Design (PDF/PostScript). 3rd International Workshop on Fast Software Encryption (FSE '96). Cambridge: Springer-Verlag. pp. 121–144. Retrieved August 23, 2007. Eli Biham; Alex Biryukov; Adi Shamir (March 1999). Miss in the Middle Attacks on IDEA, Khufu and Khafre. 6th International Workshop on Fast Software Encryption (FSE '99). Rome: Springer-Verlag. pp. 124–138. Archived from the original (gzipped PostScript) on May 15, 2011. Retrieved February 14, 2007. David Wagner (March 1999). The Boomerang Attack (PDF/PostScript). 6th International Workshop on Fast Software Encryption (FSE '99). Rome: Springer-Verlag. pp. 156–170. Retrieved February 5, 2007.{{cite conference}}: CS1 maint: miscellaneous url (link)

Worked examples

Example 1 — a first encounter with Khufu and Khafre

Start with the simplest possible case. Write down what Khufu and Khafre claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Khufu and Khafre before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Khufu and Khafre ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Khufu and Khafre

In research: Khufu and Khafre appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Khufu and Khafre in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Khufu and Khafre is common in secondary-school and first-year university syllabi. It links to neighbouring topics Block ciphers, Broken block ciphers, Feistel ciphers, so understanding it makes those chapters shorter.
In everyday life: Look for Khufu and Khafre outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Khufu and Khafre in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Khufu and Khafre means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Khufu and Khafre out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Khufu and Khafre in simple terms?

Why does Khufu and Khafre matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Khufu and Khafre?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Khufu and Khafre.