Santanu Sarkar

Bio: Santanu Sarkar is an academic researcher from Indian Institutes of Technology. The author has contributed to research in topic(s): Greatest common divisor & Fault (power engineering). The author has an hindex of 1, co-authored 3 publication(s) receiving 3 citation(s).

Revisiting Approximate Polynomial Common Divisor Problem and Noisy Multipolynomial Reconstruction

Abstract: In this paper, we present a polynomial lattice method to solve the approximate polynomial common divisor problem. This problem is the polynomial version of the well known approximate integer common divisor problem introduced by Howgrave-Graham (Calc 2001). Our idea can be applied directly to solve the noisy multipolynomial reconstruction problem in the field of error-correcting codes. Compared to the method proposed by Devet, Goldberg and Heninger in USENIX 2012, our approach is faster.

Cryptanalysis of Multi-Prime \varPhi -Hiding Assumption

Abstract: In Crypto 2010, Kiltz, O’Neill and Smith used m-prime RSA modulus N with \(m\ge 3\) for constructing lossy RSA. The security of the proposal is based on the Multi-Prime \(\varPhi \)-Hiding Assumption. In this paper, we propose a heuristic algorithm based on the Herrmann-May lattice method (Asiacrypt 2008) to solve the Multi-Prime \(\varPhi \)-Hiding Problem when prime \(e>N^{\frac{2}{3m}}\). Further, by combining with mixed lattice techniques, we give an improved heuristic algorithm to solve this problem when prime \(e>N^{\frac{2}{3m}-\frac{1}{4m^2}}\). These two results are verified by our experiments. Our bounds are better than the existing works.

Public Key Compression and Modulus Switching for Fully Homomorphic Encryption over the Integers

Abstract: We describe a compression technique that reduces the public key size of van Dijk, Gentry, Halevi and Vaikuntanathan's (DGHV) fully homomorphic scheme over the integers from O(λ7) to O(λ5). Our variant remains semantically secure, but in the random oracle model. We obtain an implementation of the full scheme with a 10.1 MB public key instead of 802 MB using similar parameters as in [7]. Additionally we show how to extend the quadratic encryption technique of [7] to higher degrees, to obtain a shorter public-key for the basic scheme. This paper also describes a new modulus switching technique for the DGHV scheme that enables to use the new FHE framework without bootstrapping from Brakerski, Gentry and Vaikuntanathan with the DGHV scheme. Finally we describe an improved attack against the Approximate GCD Problem on which the DGHV scheme is based, with complexity O(2ρ) instead of O(23ρ/2).

Improved Factoring Attacks on Multi-prime RSA with Small Prime Difference

Abstract: In this paper, we study the security of multi-prime RSA with small prime difference and propose two improved factoring attacks The modulus involved in this variant is the product of r distinct prime factors of same bit-size Zhang and Takagi (ACISP 2013) showed a Fermat-like factoring attack on multi-prime RSA In order to improve the previous result, we gather more information about the prime factors to derive r simultaneous modular equations The first attack is based on combining r equations to solve one multivariate modular equation by a generic lattice approach Since the equation form is similar to multi-prime \(\varPhi \)-hiding problem, we propose the second attack by applying the optimal linearization technique We also show that our attacks can achieve better bounds in the experiments

Investigating Deep Learning Approaches on the Security Analysis of Cryptographic Algorithms

Abstract: This paper studies the use of deep learning (DL) models under a known-plaintext scenario. The goal of the models is to predict the secret key of a cipher using DL techniques. We investigate the DL techniques against different ciphers, namely, Simplified Data Encryption Standard (S-DES), Speck, Simeck and Katan. For S-DES, we examine the classification of the full key set, and the results are better than a random guess. However, we found that it is difficult to apply the same classification model beyond 2-round Speck. We also demonstrate that DL models trained under a known-plaintext scenario can successfully recover the random key of S-DES. However, the same method has been less successful when applied to modern ciphers Speck, Simeck, and Katan. The ciphers Simeck and Katan are further investigated using the DL models but with a text-based key. This application found the linear approximations between the plaintext–ciphertext pairs and the text-based key.