science

MULTI2

MULTI2 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 MULTI2 rather than just read about it. In short: MULTI2 is a block cipher, developed by Hitachi in 1988. Designed for general-purpose cryptography, its current use is encryption of high-definition television broadcasts in Japan.

Key takeaways

MULTI2 belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect MULTI2 to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of MULTI2 from memory before moving on to harder problems.

Reference excerpt

MULTI2 is a block cipher, developed by Hitachi in 1988. Designed for general-purpose cryptography, its current use is encryption of high-definition television broadcasts in Japan.

Cipher details MULTI2 is a symmetric key algorithm with variable number of rounds. It has a block size of 64 bits, and a key size of 64 bits. A 256-bit implementation-dependent substitution box constant is used during key schedule. Scramble and descramble is done by repeating four basic functions (involutions).

History 1988 MULTI2 patent applied by Hitachi, Ltd on April 28 1989 Algorithm announced to DPS-SIG Information Processing Society of Japan 1991 Patent number 4982429 granted for MULTI2 algorithm in United States 1994 Algorithm registered with ISO/IEC 9979 and assigned registration number 9 1995 MULTI2 adopted as standard cipher for CS-Digital broadcasting in Japan 1998 Japanese Patent number 2760799 granted for MULTI2 algorithm

Cryptanalysis There are a large class of equivalent keys in the Multi2 block cipher. The largest class (so far found) stems from the fact that the Pi3 round function in the key schedule is not bijective. For example, with the following 40-byte input key to the key schedule:

45 ec 86 d8 b6 5e 24 d5 38 fe 1d 90 ce fc a4 22 3e 39 1b e3 da 03 0f cb 9c 9e d7 c6 1c e4 73 61 d0 fa 39 86 58 5d 5b 90

You can perform the following single byte modifications (modification here means XOR against the original key byte):

Can mod byte 5 with CF Can mod byte 7 with 77 Can mod byte 20 with 9A Can mod byte 20 with A9 Can mod byte 20 with D7 Can mod byte 21 with 35 Can mod byte 21 with 6A Can mod byte 21 with 9F Can mod byte 21 with CC Can mod byte 22 with 4D Can mod byte 22 with 7A Can mod byte 22 with A7 Can mod byte 23 with 53 Can mod byte 23 with AE

In this case there are 15 different keys which will schedule to the same 8 32-bit round keys for the ciphers bulk encryption path. The keys are all different in the first keyword used in the Pi3 round function (keys k[1] and k[5]). The collision occurs because a single byte difference turns into a pattern like 0X0X0000 (rotated by 0, 8, 16, or 24 bits) which then expands to a variation of 0X000X00 and finally in the second last line (with the rotate by 16 and the XOR) the differences cancel out. Turning into a zero-delta. The problem stems from the fact that the function

x = ROL(x, y) ^ x

Where ROL means rotate left by y bits, is not bijective for any value of y. There are similar problems with the Pi2 and Pi4 functions but they are seemingly harder to exploit because the rotation value is smaller. There are other observations too, for example

x = ROL(x, 1) - x

Found in Pi3, is an identity function for 50% of the values of x (where the most significant byte is zero). This also means it is possible to have weak keys where instead of forcing single byte differences in the key, they are in the plaintext into Pi3 produces a zero-delta output and possibly leading to a 1R differential.

See also Integrated Services Digital Broadcasting

External links ALGORITHM REGISTER ENTRY, registered in 1994

Worked examples

Example 1 — a first encounter with MULTI2

Start with the simplest possible case. Write down what MULTI2 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 MULTI2 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 MULTI2 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 MULTI2

In research: MULTI2 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 MULTI2 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: MULTI2 is common in secondary-school and first-year university syllabi. It links to neighbouring topics Block ciphers, Feistel ciphers, ISDB, so understanding it makes those chapters shorter.
In everyday life: Look for MULTI2 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 MULTI2 in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what MULTI2 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 MULTI2 out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is MULTI2 in simple terms?

MULTI2 is a block cipher, developed by Hitachi in 1988. Designed for general-purpose cryptography, its current use is encryption of high-definition television broadcasts in Japan.

Why does MULTI2 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 MULTI2?

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 MULTI2.