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

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Calculating $\mathbb F_{p^2}$-rational points of an elliptic curve defined over $\mathbb F_p$

How can I calculate points on an elliptic curve defined over $\mathbb F_p$, for example $y^2 \equiv x^3 + 1 \pmod p$, with coordinates in $\mathbb F_{p^2}$? (points might have complex number format in ...
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Using same modulus for RSA

I know that there exist some attack when using same modulus. Can two different pairs of RSA key have the same modulus? RSA cracking: The same message is sent to two different people problem But ...
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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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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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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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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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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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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 ...