Questions tagged [algebraic-attack]

An algebraic attack is a method of cryptanalysis against a cipher 1)expressing the cipher operations as a system of equations. 2)substituting in known data for some of the variables. 3)solving for the key.

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Solving not so much overdetermined system of multivariate polynomial equations

I'm studying algorithms solving multivariate equations. I'm stuck in solving overdetermined set of quadratic equations. Concretely, with the number $n$ of variables, the number of equations is $m=\...
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What is the difference between the 23 bi-affine and the 39 fully quadratic equations of the rijndael sbox?

In Cryptanalysis of Block Ciphers with Overdefined Systems of Equations Nicolas Courtois and Josef Pieprzyk define 23 so called bi-affine equations (in Appendix A of the paper) between the input x and ...
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How can the Rijndael SBox be written as a linearized polynomial?

In Cryptanalysis of Block Ciphers with Overdefined Systems of Equations Nicolas Courtois and Josef Pieprzyk state (in Appendix A) that the Rijndael SBox can be written as a "linearized polynomial" $S(...
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238 views

Degree vs index of regularity

I'm studying the multivariate cryptography and specifically attacks using Groebner basis. On the complexity of such direct attacks, it is well-known that the most important parameter is the degree of ...
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Algebraic Attack on Mix Mode Modular Arithmetic

I have a toy cipher that comprises of Mix Mode Modular Arithmetic (bit similar to IDEA including, Addition Modulo $2^{n}$ , Multiplication Modulo $2^{n}$ , Subtraction Modulo $2^{n}$ and circular ...
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Using XL Algorithm to solve overdetermined systems, simple example required

Can someone give a small example of how the XL algorithm is used to solve an overdetermined system, with numbers and variables along with the steps if possible as apposed to just a general case? This ...
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Need an XL Algorithm example

could anyone give me a small example with actual numbers and variables over a finite field of how the XL algorithm is used to solve overdetermined systems? And the steps involved. I understand the ...
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Сryptanalysis of Hill's method

The brutal ciphertext is given. The text volume is more than 6000 characters. It is known that the text is encrypted with a 7x7 matrix. Unknown key and plaintext. Is it possible to crack this code? ...
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(Impossibility of?) Associative Pseudorandom Permutation

I'm not sure whether this had been a long-standing open problem in cryptography. Definition An associative pseudorandom permutation $f(k,m)$ is a permutation such that: $f(k_1, f(k_2, m)) = f(f(...
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Are low degree I/O relations in AES possible?

If I restrict the degree of each monomial to say 4 or 5 at maximum. Is it then actually possible to write down the I/O relations for an AES S-box?
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Can someone help me understand how to get the I/O relation equations in DES S- boxes

I am referring to the equations that have been discussed in Nicolas T. Courtois and Gregory V. Bard's Algebraic Cryptanalysis of the Data Encryption Standard (in proceedings of Cryptography and Coding ...
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Generate ANF from SBox

Given an SBox, how can I generate its component equations (in ANF)? For example, let's say I have this SBox: 6, 4, 7, 8, 0, 5, 2, 10, 14, 3, 13, 1, 12, 15, 9, 11 Then, the equations are: $y_0 =...
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Function to polynomial equation in GF(2)

Let F(a,b,c,d,e) be a function that returns the ith bit of 0x3A5C742E, where ...
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Algebraic Attacks against ARX

I have not seen much about algebraic attacks against ARX ciphers. How would ARX ciphers compare in algebraic security to AES or Present or Simon?
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Issue implementing Pollard's Rho for discrete logarithms

I've been trying to implement Pollard's Rho recently. The original idea was to implement the code in several languages and put it up for everyone to see for educational purposes. I first took to ...
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1answer
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Derive $x$ when given $g,g^x$ and $g^{(1/x)}$?

If an adversary has access to the generator g of a group G and is given access to $g^{x}$ and $g^{(1/x)}$, will it make it any easier to derive the value of $x$ compared to when he had access to only $...
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121 views

Difference of full codebook and non full codebook

While reading a paper about Dynamic cube attack, I saw two terms: full-codebook and non-full-codebook attacks. What do they mean? What is the difference? Regards
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Small subgroup confinement attack on Diffie-Hellman

I am trying to understand the small subgroup confinement attack on the Diffie-Hellman algorithm. I will present the attack and try to explain why it works. Small subgroup confinement attack on the ...
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1answer
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Algebraic cryptanalysis on public-key schemes

The book Algebraic Cryptanalysis (Bard, G.V.; Springer, 2009) speaks about transforming a symmetric scheme into a system of polynomial equations and solving these equations to break the scheme. But ...
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495 views

algebraic attacks for mixed operations (mod 2 and mod 256) [closed]

If a cipher has mixed operations, e.g $\oplus$ (addition mod $2$), and addition modulo $2^8$. How we we going to express them mathematically? Thanks in advance!
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Evaluating Algebraic Complexity of a S-box

While studying the design and the desirable properties of an AES S-box , I came to know that Algebraic Complexity is also an important property of an S-box which is usually considered while evaluating ...
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How Brittle Are LCG-Cracking Techniques?

There are published techniques for cracking LCGs, but to my eye those techniques seem very brittle — very minor changes can add nonlinearity that renders techniques like the LLL algorithm unusable. ...
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1answer
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What is the Geometric Generalised T' Method?

This page by Nicolas T. Courtois mentions Geometric Generalised T' Method. It is described as an advanced geometric algorithm, never published, for finding extra linearly independent equations at ...
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How do you find the inverse degree of a hash function?

I am trying to learn cryptanalysis on the Keccak hash function. One of the papers on zero sum distinguishers talks about Keccak having inverse degree of 3. I am unable to figure this out: how do you ...
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DSA signatures with related k and unknown payloads

Suppose that we are given DSA parameters $p$, $q$, $g$, a public key $y = g^x$, and two signatures $(r_1,s_1)$ and $(r_2,s_2)$. We are told that $(r_1,s_1)$ and $(r_2,s_2)$ were produced by related ...
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Attack on DSA with signatures made with k, k+1, k+2

For homework, I'm asked to find the private key, $x$, in a DSA digital signature scheme. In the particular instance, we are given the parameters $p$, $q$ and $g$, the public key $g^x$, 3 messages $(...
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232 views

Determine complexity of a SAT problem

Is there a standard way to determine a complexity of the specified SAT problem? I'm researching algebraic cryptanalysis and came to solving multivariate quadratic equation systems using CryptoMiniSat. ...
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1answer
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Is it possible to spoof an identity cert modulus?

I was looking at FOAF+SSL and wondering if its possible to spoof the modulus of the browser certificate so that the FOAF and browser certificate's modulus match?
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Background for modular arithmetic function

I'm investigating this function: $a := ((b\cdot c) \bmod k) - (b \cdot c)/k$ where $/$ indicates integer division. Two things I've noticed: It's equivalent to multiplying a·b, and then ...
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1answer
1k views

XSL on serpent and rijndael - which is most affected?

So I've often looked at serpent and thought it was a very strong contender in AES. Not so long ago I was looking for evidence as to why it didn't beat rijndael. So far, the closest I've got answering ...
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2answers
746 views

Why is there an enormous difference between SAT solvers?

SAT solvers are very important in algebraic attacks, for example walksat and minisat. However, when solving the benchmark problems available here there is an enormous performance difference between ...
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297 views

Are there any tools for expressing the cipher operations as a system of equations?

The first step In Algebraic-attack is expressing the cipher operations as a system of equations. Is there an automated tool to do this?