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

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What happens if no final subtraction is done in Montgomery multiplication?

I'm doing Montgomery arithmetic modulo $N = 2^{255}-19$ for the Curve25519, picking $R = 2^{256}$ for Montgomery. After multiplying two numbers $0 <= A,B < N$ in the Montgomery representation ...
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Recover secret $x$ when $c\equiv m^x \pmod p$ with public $p$ (modified)

Given an encryption system where $c\equiv m^x \pmod p$, $p$ is a known prime, 1. Is it possible to recover $x$ with a known plaintext attack? Given $(p,\text{factorization of }\varphi(p),m,c)$ 2. Is ...
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Discrete logarithms: large prime modulus vs. large semi prime modulus

I have a cryptography homework question, in the question it says a cryptographic hash function in the form of $f(x) = g^x \bmod n$ , where $n$ is a very large prime (1024bits and more), $g$ is a ...
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Proxy re-encryption mod operations

I managed to implement the proxy re-encryption scheme from http://eprint.iacr.org/2009/189.pdf in Python 2.7, however I am having performance issues. As it is, I can run the algorithm for key sizes up ...
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Gallant-Lambert-Vanstone method

I am experimenting with the GLV method but cannot manage to get the right results according to the literature. I managed to find lambda, beta, split $K$ into $k_1$ and $k_2$ etc. for the curve I'm ...
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Does the RSA algorithm use repeated squaring?

Simple question: in order to reduce such huge exponents in modular arithmetic, is repeated squaring used in RSA or is there a better way to implement it?
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Reducing key shares in Damgård-Dupont threshold RSA

I'm working on understanding and implementing Damgård, I., & Dupont, K. (2005). Efficient Threshold RSA Signatures with General Moduli and No Extra Assumptions. Public Key Cryptography-PKC ...
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Modulo settings for successful encryption?

I saw this awesome video which shows how encryption works using "discrete logarithm". The example says: $3^x\mod17$. I understood that $3$ is called “generator”, because it has no "straight" root and ...
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RSA : Double-Encryption and order of Encryption

I'm studying cryptography and we're looking at RSA. We're required to do a double encryption from Alice to Bob and then Bob back to Alice. We've been told the order of encryption is important and it ...
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what is the fastest and efficient method to perform modular multiplication?

I'm working on a code that needs to perform modular multiplication of big numbers several times. Since the operation takes place several times, using division to find the remainder is very expensive. ...
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Bilinear pairing arithmetic - cryptographic accumulators

For calculating accumulated values for set of elements chosen randomly from say $ { e_1 ,e_2,...e_n}\varepsilon X $ we use the formula $acc= g^{f(e,s)}$ where $ f(e,s)= (e_1+s)(e_2+s).....(e_n+s)$ ...
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Factorization of a number obtained by a modular multiplication operation can reveal factors of the used operands?

Consider a number $r$ obtained by: $r=a \cdot b \mod n$ Can knowing the factorization of $r$ reveal some information (bits) of $a$ and $b$ ?
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Deriving a decryption equation

Consider a very simple symmetric block encryption algorithm, in which 32-bits blocks of plaintext are encrypted using a 64-bit key. Encryption is defined as C = (P⊕KL)⊗KR where C = ciphertext; K = ...
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Polynomial Inversion over Galois Field

Hello guys I am looking to calculate the Inverse of a given polynomial in Galois field I have found the little Fermat's algorithm and the Itoh-Tsujii I am getting a bit confused with both algorithm ...