# Questions tagged [modular-arithmetic]

Modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value… the modulus.

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### How can LCG based stream ciphers be broken?

I'm watching Christoph Paar's Introduction to Cryptography lecture series on youtube. In it he describes an example of an insecure stream cipher which uses XOR as the encryption and decryption ...
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### Constraints needed to express a + b + c = d in zkp circuit

I am writing an ECC based zkp circuit and need to express the constraints: a + b + c = d a, b, c, d >= 0 a, b, c, d will be represented by points on the curve so addition can wrap around the ...
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### Are high-dimensional versions of NTRU cryptosystem more secure?

The basis for this question is a 1-dimensional NTRU cryptosystem. After some literature inspection I have found out it can be also generalised into higher algebras: quaternions (QTRU) and octonions (...
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### In RSA Encryption, Can I choose the public exponent e > m (modulus) ? or e > φ(n)? [duplicate]

In RSA ,the encryption, Can we choose the public exponent (e) greater than m (modulus) or e > φ(n) ? I wonder about choosing public key exponents (e) because the most information on the internet or ...
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### In RSA Encryption, Can the public exponent e > m (modulus) ? and can we choose any public key without paying attention to the conditions? [duplicate]

In RSA ,the encryption, Can we choose the public exponent (e) greater than m (modulus) or e > φ(n) ? I wonder about choosing public key exponents (e) because the most information on the internet or ...
• 11
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### Solving XOR modular system of equations

I have the following problem. Here's a rephrased version of your problem, keeping the LaTeX commands unchanged: We are given $n \in \mathbb{N}$, $p, q \in \mathbb{N}$, and $y \in \mathbb{N}^{n+2}$. ...
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### Determining the Parity of Exponent b in Modular Exponentiation Given Three Known Values

I have three numbers x, a, and c, where both a and c are odd numbers. The number x is the output of the following function: $$x = a^b\!\!\!\!\!\!\!\mod{c}$$ I am attempting to determine whether the ...
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### How does the Mongomery Algorithm work? [closed]

can someone please explain to me what's the role of montgomery reduction algorithm and how to implement it in python. I wrote the code below to calculate a*b mod m but it doesn't seem to work well. ...
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### Z superscript confusion

I was practicing some questions on cryptography (newbie) and came across this question: I know that Z26 means modulo-n arithmetic is used, but what does the superscript (3) denote? My guess is that ...
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