Practical Cryptanalysis of a Public-key Encryption Scheme Based on Non-linear Indeterminate Equations at SAC 2017

We investigate the security of a public-key encryption scheme, the Indeterminate Equation Cryptosystem (IEC), introduced by Akiyama, Goto, Okumura, Takagi, Nuida, and Hanaoka at SAC 2017 as postquantum cryptography. They gave two parameter sets PS1 (n,p,deg X,q) = (80,3,1,921601) and PS2 (n,p,deg X,q) = (80,3,2,58982400019). The paper gives practical key-recovery and message-recovery attacks against those parameter sets of IEC through lattice basis-reduction algorithms. We exploit the fact that n = 80 is composite and adopt the idea of Gentry\u27s attack against NTRU-Composite (EUROCRYPT2001) to this setting. The summary of our attacks follows: * On PS1, we recover 84 private keys from 100 public keys in 30–40 seconds per key. * On PS1, we recover partial information of all message from 100 ciphertexts in a second per ciphertext. * On PS2, we recover partial information of all message from 100 ciphertexts in 30 seconds per ciphertext. Moreover, we also give message-recovery and distinguishing attacks against the parameter sets with prime n, say, n = 83. We exploit another subring to reduce the dimension of lattices in our lattice-based attacks and our attack succeeds in the case of deg X = 2. * For PS2’ (n,p,deg X,q) = (83,3,2,68339982247), we recover 7 messages from 10 random ciphertexts within 61,000 seconds \approx 17 hours per ciphertext. * Even for larger n, we can fnd short vector from lattices to break the underlying assumption of IEC. In our experiment, we can found such vector within 330,000 seconds \approx 4 days for n = 113

Developments in multivariate post quantum cryptography.

Ever since Shor\u27s algorithm was introduced in 1994, cryptographers have been working to develop cryptosystems that can resist known quantum computer attacks. This push for quantum attack resistant schemes is known as post quantum cryptography. Specifically, my contributions to post quantum cryptography has been to the family of schemes known as Multivariate Public Key Cryptography (MPKC), which is a very attractive candidate for digital signature standardization in the post quantum collective for a wide variety of applications. In this document I will be providing all necessary background to fully understand MPKC and post quantum cryptography as a whole. Then, I will walk through the contributions I provided in my publications relating to differential security proofs for HFEv and HFEv−, key recovery attack for all parameters of HFEm, and my newly proposed multivariate encryption scheme, HFERP

A Public-key Encryption Scheme Based on Non-linear Indeterminate Equations (Giophantus)

In this paper, we propose a post-quantum public-key encryption scheme whose security depends on a problem arising from a multivariate non-linear indeterminate equation. The security of lattice cryptosystems, which are considered to be the most promising candidate for a post-quantum cryptosystem, is based on the shortest vector problem or the closest vector problem in the discrete linear solution spaces of simultaneous equations. However, several improved attacks for the underlying problems have recently been developed by using approximation methods, which result in requiring longer key sizes. As a scheme to avoid such attacks, we propose a public-key encryption scheme based on the smallest solution problem in the non-linear solution spaces of multivariate indeterminate equations that was developed from the algebraic surface cryptosystem. Since no efficient algorithm to find such a smallest solution is currently known, we introduce a new computational assumption under which proposed scheme is proven to be secure in the sense of IND-CPA. Then, we perform computational experiments based on known attack methods and evaluate that the key size of our scheme under the linear condition. This paper is a revised version of SAC2017

暗号ハードウェアの形式的設計に関する研究

Tohoku University青木孝文課

Improved Robustness and Versatility of Lattice-Based Cryptography

Current public key cryptosystems that are based on the hardness of integer factorization and discrete logarithm are insecure in the presence of large-scale quantum computers. Much effort has been devoted to replacing the quantum-insecure cryptosystems with newly developed "post-quantum" cryptosystem candidates, conjectured to be secure against quantum attack. Lattice-based cryptography has been widely recognized as a prominent candidate for practical post-quantum security.This dissertation improves the robustness and versatility of lattice-based cryptography through the following three contributions: 1. Chapter 3 introduces a constant-round protocol for unauthenticated group key exchange (i.e., with security against a passive eavesdropper). Group key exchange protocols allow a set of N parties to agree on a shared, secret key by communicating over a public network. Our protocol is based on the hardness of a lattice problem, which hence yields (plausible) post-quantum security. 2. In Chapter 4, we propose a framework for cryptanalysis of lattice-based schemes when certain types of information about the secret are leaked. Our framework generalizes the primal lattice reduction attack. The generalization allows for integrating the leaked information progressively before running a final lattice reduction step. Our framework can estimate the amount of security loss caused by the leaked information, and perform lattice reduction attacks with leaked information when computationally feasible. 3. Chapter 5 introduces an approach towards a ring analogue of the Leftover Hash Lemma (LHL). The LHL is a mathematical tool often used in the analysis of various lattice-based cryptosystems, as well as their leakage-resilient counterparts. However, it does not hold in the ring setting, which is typical for efficient cryptosystems. Lyubashevsky et al. (Eurocrypt '13) proved a "regularity lemma," which is used in the ring setting instead of the LHL; however, this applies only for centered, spherical Gaussian inputs, while the LHL applies when the input is drawn from any high min-entropy distribution. Our approach generalizes the "regularity lemma" of Lyubashevsky et al. to certain conditional distributions. A number of Ring-Learning with Errors based cryptosystems can achieve certain leakage resilience properties using our results

Proceedings of the 21st Conference on Formal Methods in Computer-Aided Design – FMCAD 2021

The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing

ICTERI 2020: ІКТ в освіті, дослідженнях та промислових застосуваннях. Інтеграція, гармонізація та передача знань 2020: Матеріали 16-ї Міжнародної конференції. Том II: Семінари. Харків, Україна, 06-10 жовтня 2020 р.

This volume represents the proceedings of the Workshops co-located with the 16th International Conference on ICT in Education, Research, and Industrial Applications, held in Kharkiv, Ukraine, in October 2020. It comprises 101 contributed papers that were carefully peer-reviewed and selected from 233 submissions for the five workshops: RMSEBT, TheRMIT, ITER, 3L-Person, CoSinE, MROL. The volume is structured in six parts, each presenting the contributions for a particular workshop. The topical scope of the volume is aligned with the thematic tracks of ICTERI 2020: (I) Advances in ICT Research; (II) Information Systems: Technology and Applications; (III) Academia/Industry ICT Cooperation; and (IV) ICT in Education.Цей збірник представляє матеріали семінарів, які були проведені в рамках 16-ї Міжнародної конференції з ІКТ в освіті, наукових дослідженнях та промислових застосуваннях, що відбулася в Харкові, Україна, у жовтні 2020 року. Він містить 101 доповідь, які були ретельно рецензовані та відібрані з 233 заявок на участь у п'яти воркшопах: RMSEBT, TheRMIT, ITER, 3L-Person, CoSinE, MROL. Збірник складається з шести частин, кожна з яких представляє матеріали для певного семінару. Тематична спрямованість збірника узгоджена з тематичними напрямками ICTERI 2020: (I) Досягнення в галузі досліджень ІКТ; (II) Інформаційні системи: Технології і застосування; (ІІІ) Співпраця в галузі ІКТ між академічними і промисловими колами; і (IV) ІКТ в освіті