Download PDF by Gregory Bard: Algebraic Cryptanalysis

By Gregory Bard

ISBN-10: 0387887563

ISBN-13: 9780387887562

ISBN-10: 0387887571

ISBN-13: 9780387887579

Algebraic Cryptanalysis bridges the distance among a path in cryptography, and having the ability to learn the cryptanalytic literature. This booklet is split into 3 components: half One covers the method of turning a cipher right into a method of equations; half covers finite box linear algebra; half 3 covers the answer of Polynomial structures of Equations, with a survey of the tools utilized in perform, together with SAT-solvers and the tools of Nicolas Courtois.

The cipher Keeloq, utilized in approximately all vehicles with distant key-less access, is defined as a operating instance, together with the manipulation of the equations to permit their resolution. The circulation cipher Trivium, besides its versions Bivium-A and Bivium-B, and the flow cipher relations QUAD also are analyzed as huge examples, together with summaries of a number of released attacks.

Additional themes include:

Analytic Combinatorics, and its program to cryptanalysis

The equicomplexity of linear algebra operations

Graph coloring

Factoring integers through the quadratic sieve, with its purposes to the cryptanalysis of RSA

Algebraic Cryptanalysis is designed for advanced-level scholars in machine technology and arithmetic as a secondary textual content or reference publication for self-guided learn. This e-book is very compatible for researchers in utilized summary Algebra or Algebraic Geometry who desire to locate extra utilized issues, practitioners operating for safeguard and communications businesses, or intelligence agencies.

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Additional info for Algebraic Cryptanalysis

Example text

92 , or “abort” in all other cases. 1: Guess the 16 bits of the key k0 , k1 , . . , k15 . (8) de f 2: Define the f (8) oracle to be fk 3: P ← {} 4: For x = 0 . . 232 − 1 do = g−1 k (Ek (x)). (8) a. If fk (x) = x then do i. For each y ∈ P do A. Write equations assuming fk (x) = x and fk (y) = y. B. Try to solve those equations. C. If the equations yield a key k′ , see if Ek (x) = gk′ (x) and Ek (y) = gk′ (y). • If YES: Halt and report k′ is the secret key. • If NO: do nothing. ii. Insert x into P.

Now we will make this idea more precise. Intuitively, we now know 64 bits of input and 64 bits of output (32 bits each (8) from each message) of the functions fk and fk as well. This forms a very rigid constraint, and it is highly likely that only one key could produce these outputs. This means that if we solve the system of equations for that key, we will get exactly one answer, which is the secret key. The only question is if the system of equations is rapidly solvable or not. The resulting system must have equations for the 64 rounds of f .

Of course, without the sorting explained in the previous paragraph, the expected number of Step 3 and Step 4 executions would be around 215 . For certain, the longest step is Step 1, iterating over the code-book. 1 Later Work on Keeloq The author’s attack was done in January of 2007, and between that time and the time of the writting of this book, several other attacks on Keeloq have been published, including some by the author of this book. They are found in the bibliography under the following entries, which we list in no particular order: Three things are noteworthy about this list.

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