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

learn more… | top users | synonyms

2
votes
2answers
102 views

How do I create a secure encryption scheme using addition?

You have a 4 number long PIN code with each number ranging from 0 to 9 which you wish to encrypt. You are then given a random 4 digit number ranging from 0 to 9999, which when added to the original ...
5
votes
0answers
67 views

What is the fastest modular reduction algorithm available?

I have been browsing for the fastest and most efficient modular reduction algorithms and came across quite a few. But the one in A Fast Modular Reduction Method (2014) by Zhengjun Cao, Ruizhong Wei ...
3
votes
0answers
101 views

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 $0 \leq A,B < N$ in the Montgomery representation ...
2
votes
0answers
41 views

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 ...
2
votes
0answers
55 views

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 ...
2
votes
0answers
147 views

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 ...
2
votes
0answers
136 views

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 ...
1
vote
0answers
79 views

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?
1
vote
0answers
34 views

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 ...
1
vote
0answers
98 views

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 ...
0
votes
0answers
58 views

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 ...
0
votes
0answers
48 views

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. ...
0
votes
0answers
66 views

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)$ ...
0
votes
0answers
45 views

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 $b$ ?
0
votes
0answers
163 views

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 = ...
0
votes
0answers
118 views

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 ...
-2
votes
0answers
41 views

How can I find a key matrix to decode a Hill Cipher?

For an assignment, I've been given a 2x2 cipher and a 3x3 cipher and I have to decode both of them. I have no key, so I really don't know where to start. Also, this is all modulo 27, because my prof ...