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The Falcon signature verification algorithm relies heavily on modular arithmetic with respect to the prime $12289$. The current implementation `rpo_falcon512::mod_12289` is very inefficient since it u…
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> Beware! `Fin n` is endowed with modular arithmetic. Naively calling `2*i` would multiply `i` by two and perform modulo by `n/2`. We do not want that; we have to get the underlying natural number `i.…
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- https://www.geeksforgeeks.org/find-square-root-modulo-p-set-2-shanks-tonelli-algorithm/
- https://math.stackexchange.com/questions/633160/modular-arithmetic-find-the-square-root
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Implement the optimized squaring algorithm outlined in https://hackmd.io/@gnark/modular_multiplication#Montgomery-squaring.
An example implementation is available here: https://github.com/mratsim/c…
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The following code crashes in Sage v7.2 with a ZeroDivisionError:
```
V = FreeModule(Zmod(3^10), 1)
v = V.gen(0)
x = v * v
x.valuation(3)
```
The variable x is just 1 (mod 310), and if you just do …
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Cool project -- wanted to point you to some tools you may or may not be aware of.
NVLabs/CGBN
CUDA Accelerated Multiple Precision Arithmetic (Big Num) using Cooperative Groups
https://github.com/…
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Code generator for modular arithmetic using Montgomery reduction.
- [x] mont encode
- [x] mont decode
- [x] cmov
- [x] add
- [x] sub
- [x] neg
- [x] mul
- [ ] sqr
- [x] inv
- [ ] invsqrt
…
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I was wondering how much the modular exponentiation part of SRP's server-side verification (http://srp.stanford.edu/design.html)
That part could be run offline assuming database breach
`Host: S = (A…
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- GCD and LCM
- Prime Factorization and Divisors
- Fibonacci Numbers
- Catalan Numbers
- Modular Arithmetic
- Euler Totient Function
- nCr Computations
- Set Theory
- Chinese Remainder Theorem…