# 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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### Is modular exponentiation always cyclical?

In RSA clock arithmetics is used, and as Fermat's little theorem says, $a^p \bmod p = a$. The exponentiation is cyclical, $a^x = a^{x \bmod p-1} \bmod p$, the same sequence of numbers is repeated in ...
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### Question about using Montgomery form for elliptic curve operations on bls12-381

Since the prime for bls12-381 is not of a form to allow easy modular reduction , is the best approach to use the Montgomery multiplication + reduction algorithm? ...
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### What makes the Discrete Logarithm Problem hard?

I am missing a crucial piece of the maths behind the DLP, and I'm hoping someone can give me a really dumbed down answer.. If $h=g^x \bmod p$ and we're working in the group $Z^*_p$, why can I not ...
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### How does the squeeze function in the NaCl Poly1305 implementation work?

The NaCl ref implementation of the Poly1305 algorithm uses the following reduction function (which is called squeeze()): ...
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### One Time Pad OTP: with modular math, ciphertext reveals modulus always, yes or no?

Assuming that in the OTP scheme, the key has more values than the alphabet, then: using modular math predetermines that the highest possible value in the ciphertext will reveal the modulus used in ...
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### One-Time Pad : How does modulus size greater than alphabet size eliminate perfect secrecy?

If my plaintext alphabet is {0,1,2} has three characters, I understand why I cannot use a modulus less than 3 (decryption won't work). My key has 100 different values, {0,1,2 .....99} . So key ...
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### One Time Pad OTP : Optimal modular base per given plaintext space?

Background: my question at : My pencil and paper One Time Pad works fine without modular math ...... or does it? I am trying to understand, from a layman's point of view, how to make the best one ...
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### choices for k in binary finite field modular reduction algorithm

In the Guide to Elliptic Curve Cryptography there's this algorithm: My question is... what is $k$? Is it just some random value we pick? If so are some numbers better than others?
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