Profiling Attack against RSA Key Generation Based on a Euclidean Algorithm

A profiling attack is a powerful variant among the noninvasive side channel attacks. In this work, we target RSA key generation relying on the binary version of the extended Euclidean algorithm for modular inverse and GCD computations. To date, this algorithm has only been exploited by simple power analysis; therefore, the countermeasures described in the literature are focused on mitigating only this kind of attack. We demonstrate that one of those countermeasures is not effective in preventing profiling attacks. The feasibility of our approach relies on the extraction of several leakage vectors from a single power trace. Moreover, because there are known relationships between the secrets and the public modulo in RSA, the uncertainty in some of the guessed secrets can be reduced by simple tests. This increases the effectiveness of the proposed attack.

GCD of Aunu Binary Polynomials of Cardinality Seven Using Extended Euclidean Algorithm

Finite fields is considered to be the most widely used algebraic structures today due to its applications in cryptography, coding theory, error correcting codes among others. This paper reports the use of extended Euclidean algorithm in computing the greatest common divisor (gcd) of Aunu binary polynomials of cardinality seven. Each class of the polynomial is permuted into pairs until all the succeeding classes are exhausted. The findings of this research reveals that the gcd of most of the pairs of the permuted classes are relatively prime. This results can be used further in constructing some cryptographic architectures that could be used in design of strong encryption schemes.

A Note on the Computation of the Modular Inverse for Cryptography

In literature, there are a number of cryptographic algorithms (RSA, ElGamal, NTRU, etc.) that require multiple computations of modulo multiplicative inverses. In this paper, we describe the modulo operation and we recollect the main approaches to computing the modulus. Then, given a and n positive integers, we present the sequence (zj)j≥0, where zj=zj−1+aβj−n, a<n and GCD(a,n)=1. Regarding the above sequence, we show that it is bounded and admits a simple explicit, periodic solution. The main result is that the inverse of a modulo n is given by a−1=⌊im⌋+1 with m=n/a. The computational cost of such an index i is O(a), which is less than O(nlnn) of the Euler’s phi function. Furthermore, we suggest an algorithm for the computation of a−1 using plain multiplications instead of modular multiplications. The latter, still, has complexity O(a) versus complexity O(n) (naive algorithm) or complexity O(lnn) (extended Euclidean algorithm). Therefore, the above procedure is more convenient when a<<n (e.g., a<lnn).

Privacy Preserving Using Extended Euclidean Algorithm Applied To RSA-Homomorphic Encryption Technique

Communication of confidential information over Internet is the key aspect of security applications. Providing protection to sensitive information is of major concern. Many cryptographic algorithms have been in use for providing security of confidential information. Providing security for data has become major challenge in this era. Classical cryptography is playing a major role in providing security for applications. In modern days securing confidential information in the cloud is considered as an important challenge. Homomorphic Encryption technique is one of the best solutions that provide security in the cloud[1]. In this paper, Extended Euclidean Algorithm is used for generating keys. This technique follows RSA Homomorphic encryption technique. .RSA Homomorphic encryption using Extended Euclidean algorithm (RSA-HEEEA) is secure when compared to RSA as it based on the generation of private key which makes the algorithm complex .This technique of using Extended Euclidean Algorithm(EEA) is fast and secure when compared to RSA homomorphic encryption technique. The encryption process utilizes modulo operator which gives security as well.The beauty of this algorithm is in generation of private key which uses Extended Euclidean Algorithm (EEA) that helps in avoiding brute force attacks. Also, this technique uses Homomorphic operations which gives enhance security to confidential information in the cloud

Computing multiplicative inverses in finite fields by long division

We study a method of computing multiplicative inverses in finite fields using long division. In the case of fields of a prime order p, we construct one fixed integer d(p) with the property that for any nonzero field element a, we can compute its inverse by dividing d(p) by a and by reducing the result modulo p. We show how to construct the smallest d(p) with this property. We demonstrate that a similar approach works in finite fields of a non-prime order, as well. However, we demonstrate that the studied method (in both cases) has worse asymptotic complexity than the extended Euclidean algorithm.