Lattice-based weak curve fault attack on ECDSA

ECDSA algorithm is usually used in ICT system to achieve communication authenticity. But weakness in various implementations of the algorithm may make its security deviate from theoretical guarantee. This paper proposes a new lattice-based weak curve fault attack on ECDSA. An elliptic curve is weak if the problem of ECDLP in a \emph{subgroup} of the point group $\langle G \rangle$ is computationally solvable in practice, where $G$ is the specified basis point of ECDSA algorithm. Since ECDLP is not required to be computationally practical in the whole group of $\langle G \rangle$, our approach extends the known existing attacks along this line. In detail, the proposed attack assumes a fault injection process can perturb a segment of consecutive bits of the curve parameter $a$ in the Weierstrass equation of ECDSA. An analysis on the density of smooth numbers indicates the faulty value $a\u27$ parameterized elliptic curve is weak in high probability. Then we show the faulty value $a\u27$ can be recovered by a dedicated quadratic residue distinguisher, which makes it possible to collect enough side channel information about the nonce used in the ECDSA signature generation process. With the help of these information, we can construct a lattice to recover the private key with lattice basis reduction techniques. Further, we show the same strategy can defeat the nonce masking countermeasure if the random mask is not too long, and makes the commonly employed countermeasures ineffective. To our knowledge, the problem remains untractable to the existing weak curve fault attacks. Thus the proposed approach can find more applications than the existing ones. This is demonstrated by the experimental analysis

Side-Channel Analysis and Cryptography Engineering : Getting OpenSSL Closer to Constant-Time

As side-channel attacks reached general purpose PCs and started to be more practical for attackers to exploit, OpenSSL adopted in 2005 a flagging mechanism to protect against SCA. The opt-in mechanism allows to flag secret values, such as keys, with the BN_FLG_CONSTTIME flag. Whenever a flag is checked and detected, the library changes its execution flow to SCA-secure functions that are slower but safer, protecting these secret values from being leaked. This mechanism favors performance over security, it is error-prone, and is obscure for most library developers, increasing the potential for side-channel vulnerabilities. This dissertation presents an extensive side-channel analysis of OpenSSL and criticizes its fragile flagging mechanism. This analysis reveals several flaws affecting the library resulting in multiple side-channel attacks, improved cache-timing attack techniques, and a new side channel vector. The first part of this dissertation introduces the main topic and the necessary related work, including the microarchitecture, the cache hierarchy, and attack techniques; then it presents a brief troubled history of side-channel attacks and defenses in OpenSSL, setting the stage for the related publications. This dissertation includes seven original publications contributing to the area of side-channel analysis, microarchitecture timing attacks, and applied cryptography. From an SCA perspective, the results identify several vulnerabilities and flaws enabling protocol-level attacks on RSA, DSA, and ECDSA, in addition to full SCA of the SM2 cryptosystem. With respect to microarchitecture timing attacks, the dissertation presents a new side-channel vector due to port contention in the CPU execution units. And finally, on the applied cryptography front, OpenSSL now enjoys a revamped code base securing several cryptosystems against SCA, favoring a secure-by-default protection against side-channel attacks, instead of the insecure opt-in flagging mechanism provided by the fragile BN_FLG_CONSTTIME flag

Systematic Literature Review of EM-SCA Attacks on Encryption

Cryptography is vital for data security, but cryptographic algorithms can still be vulnerable to side-channel attacks (SCAs), physical assaults exploiting power consumption and EM radiation. SCAs pose a significant threat to cryptographic integrity, compromising device keys. While literature on SCAs focuses on real-world devices, the rise of sophisticated devices necessitates fresh approaches. Electromagnetic side-channel analysis (EM-SCA) gathers information by monitoring EM radiation, capable of retrieving encryption keys and detecting malicious activity. This study evaluates EM-SCA's impact on encryption across scenarios and explores its role in digital forensics and law enforcement. Addressing encryption susceptibility to EM-SCA can empower forensic investigators in overcoming encryption challenges, maintaining their crucial role in law enforcement. Additionally, the paper defines EM-SCA's current state in attacking encryption, highlighting vulnerable and resistant encryption algorithms and devices, and promising EM-SCA approaches. This study offers a comprehensive analysis of EM-SCA in law enforcement and digital forensics, suggesting avenues for further research

Cryptanalysis and Secure Implementation of Modern Cryptographic Algorithms

Cryptanalytic attacks can be divided into two classes: pure mathematical attacks and Side Channel Attacks (SCAs). Pure mathematical attacks are traditional cryptanalytic techniques that rely on known or chosen input-output pairs of the cryptographic function and exploit the inner structure of the cipher to reveal the secret key information. On the other hand, in SCAs, it is assumed that attackers have some access to the cryptographic device and can gain some information from its physical implementation. Cold-boot attack is a SCA which exploits the data remanence property of Random Access Memory (RAM) to retrieve its content which remains readable shortly after its power has been removed. Fault analysis is another example of SCAs in which the attacker is assumed to be able to induce faults in the cryptographic device and observe the faulty output. Then, by careful inspection of faulty outputs, the attacker recovers the secret information, such as secret inner state or secret key. Scan-based Design-For-Test (DFT) is a widely deployed technique for testing hardware chips. Scan-based SCAs exploit the information obtained by analyzing the scanned data in order to retrieve secret information from cryptographic hardware devices that are designed with this testability feature. In the first part of this work, we investigate the use of an off-the-shelf SAT solver, CryptoMinSat, to improve the key recovery of the Advance Encryption Standard (AES-128) key schedules from its corresponding decayed memory images which can be obtained using cold-boot attacks. We also present a fault analysis on both NTRUEncrypt and NTRUSign cryptosystems. For this specific original instantiation of the NTRU encryption system with parameters $(N,p,q)$, our attack succeeds with probability $\approx 1-\frac{1}{p}$ and when the number of faulted coefficients is upper bounded by $t$, it requires $O((pN)^t)$ polynomial inversions in $\mathbb Z/p\mathbb Z[x]/(x^{N}-1)$. We also investigate several techniques to strengthen hardware implementations of NTRUEncrypt against this class of attacks. For NTRUSign with parameters ($N$, $q=p^l$, $\mathcal{B}$, \emph{standard}, $\mathcal{N}$), when the attacker is able to skip the norm-bound signature checking step, our attack needs one fault to succeed with probability $\approx 1-\frac{1}{p}$ and requires $O((qN)^t)$ steps when the number of faulted polynomial coefficients is upper bounded by $t$. The attack is also applicable to NTRUSign utilizing the \emph{transpose} NTRU lattice but it requires double the number of fault injections. Different countermeasures against the proposed attack are also investigated. Furthermore, we present a scan-based SCA on NTRUEncrypt hardware implementations that employ scan-based DFT techniques. Our attack determines the scan chain structure of the polynomial multiplication circuits used in the decryption algorithm which allows the cryptanalyst to efficiently retrieve the secret key. Several key agreement schemes based on matrices were recently proposed. For example, \'{A}lvarez \emph{et al.} proposed a scheme in which the secret key is obtained by multiplying powers of block upper triangular matrices whose elements are defined over $\mathbb{Z}_p$. Climent \emph{et al.} identified the elements of the endomorphisms ring $End(\mathbb{Z}_p \times \mathbb{Z}_{p^2})$ with elements in a set, $E_p$, of matrices of size $2\times 2$, whose elements in the first row belong to $\mathbb{Z}_{p}$ and the elements in the second row belong to $\mathbb{Z}_{p^2}$. Keith Salvin presented a key exchange protocol using matrices in the general linear group, $GL(r,\mathbb{Z}_n)$, where $n$ is the product of two distinct large primes. The system is fully specified in the US patent number 7346162 issued in 2008. In the second part of this work, we present mathematical cryptanalytic attacks against these three schemes and show that they can be easily broken for all practical choices of their security parameters

Port Contention for Fun and Profit

Simultaneous Multithreading (SMT) architectures are attractive targets for side-channel enabled attackers, with their inherently broader attack surface that exposes more per physical core microarchitecture components than cross-core attacks. In this work, we explore SMT execution engine sharing as a side-channel leakage source. We target ports to stacks of execution units to create a high-resolution timing side-channel due to port contention, inherently stealthy since it does not depend on the memory subsystem like other cache or TLB based attacks. Implementing said channel on Intel Skylake and Kaby Lake architectures featuring Hyper-Threading, we mount and end-to-end attack that recovers a P-384 private key from an OpenSSL-powered TLS server using a small number of repeated TLS handshake attempts. Furthermore, we show that traces targeting shared libraries, static builds, and SGX enclaves are essentially identical, hence our channel has wide target application

A Formula for Disaster : A Unified Approach to Elliptic Curve Special-Point-Based Attacks

The Refined Power Analysis, Zero-Value Point, and Exceptional Procedure attacks introduced side-channel techniques against specific cases of elliptic curve cryptography. The three attacks recover bits of a static ECDH key adaptively, collecting information on whether a certain multiple of the input point was computed. We unify and generalize these attacks in a common framework, and solve the corresponding problem for a broader class of inputs. We also introduce a version of the attack against windowed scalar multiplication methods, recovering the full scalar instead of just a part of it. Finally, we systematically analyze elliptic curve point addition formulas from the Explicit-Formulas Database, classify all non-trivial exceptional points, and find them in new formulas. These results indicate the usefulness of our tooling, which we released publicly, for unrolling formulas and finding special points, and potentially for independent future work.acceptedVersionPeer reviewe

On Security and Privacy for Networked Information Society : Observations and Solutions for Security Engineering and Trust Building in Advanced Societal Processes

Our society has developed into a networked information society, in which all aspects of human life are interconnected via the Internet — the backbone through which a significant part of communications traffic is routed. This makes the Internet arguably the most important piece of critical infrastructure in the world. Securing Internet communications for everyone using it is extremely important, as the continuing growth of the networked information society relies upon fast, reliable and secure communications. A prominent threat to the security and privacy of Internet users is mass surveillance of Internet communications. The methods and tools used to implement mass surveillance capabilities on the Internet pose a danger to the security of all communications, not just the intended targets. When we continue to further build the networked information upon the unreliable foundation of the Internet we encounter increasingly complex problems,which are the main focus of this dissertation. As the reliance on communication technology grows in a society, so does the importance of information security. At this stage, information security issues become separated from the purely technological domain and begin to affect everyone in society. The approach taken in this thesis is therefore both technical and socio-technical. The research presented in this PhD thesis builds security in to the networked information society and provides parameters for further development of a safe and secure networked information society. This is achieved by proposing improvements on a multitude of layers. In the technical domain we present an efficient design flow for secure embedded devices that use cryptographic primitives in a resource-constrained environment, examine and analyze threats to biometric passport and electronic voting systems, observe techniques used to conduct mass Internet surveillance, and analyze the security of Finnish web user passwords. In the socio-technical domain we examine surveillance and how it affects the citizens of a networked information society, study methods for delivering efficient security education, examine what is essential security knowledge for citizens, advocate mastery over surveillance data by the targeted citizens in the networked information society, and examine the concept of forced trust that permeates all topics examined in this work.Yhteiskunta, jossa elämme, on muovautunut teknologian kehityksen myötä todelliseksi tietoyhteiskunnaksi. Monet verkottuneen tietoyhteiskunnan osa-alueet ovat kokeneet muutoksen tämän kehityksen seurauksena. Tämän muutoksen keskiössä on Internet: maailmanlaajuinen tietoverkko, joka mahdollistaa verkottuneiden laitteiden keskenäisen viestinnän ennennäkemättömässä mittakaavassa. Internet on muovautunut ehkä keskeisimmäksi osaksi globaalia viestintäinfrastruktuuria, ja siksi myös globaalin viestinnän turvaaminen korostuu tulevaisuudessa yhä enemmän. Verkottuneen tietoyhteiskunnan kasvu ja kehitys edellyttävät vakaan, turvallisen ja nopean viestintäjärjestelmän olemassaoloa. Laajamittainen tietoverkkojen joukkovalvonta muodostaa merkittävän uhan tämän järjestelmän vakaudelle ja turvallisuudelle. Verkkovalvonnan toteuttamiseen käytetyt menetelmät ja työkalut eivät vain anna mahdollisuutta tarkastella valvonnan kohteena olevaa viestiliikennettä, vaan myös vaarantavat kaiken Internet-liikenteen ja siitä riippuvaisen toiminnan turvallisuuden. Kun verkottunutta tietoyhteiskuntaa rakennetaan tämän kaltaisia valuvikoja ja haavoittuvuuksia sisältävän järjestelmän varaan, keskeinen uhkatekijä on, että yhteiskunnan ydintoiminnot ovat alttiina ulkopuoliselle vaikuttamiselle. Näiden uhkatekijöiden ja niiden taustalla vaikuttavien mekanismien tarkastelu on tämän väitöskirjatyön keskiössä. Koska työssä on teknisen sisällön lisäksi vahva yhteiskunnallinen elementti, tarkastellaan tiukan teknisen tarkastelun sijaan aihepiirä laajemmin myös yhteiskunnallisesta näkökulmasta. Tässä väitöskirjassa pyritään rakentamaan kokonaiskuvaa verkottuneen tietoyhteiskunnan turvallisuuteen, toimintaan ja vakauteen vaikuttavista tekijöistä, sekä tuomaan esiin uusia ratkaisuja ja avauksia eri näkökulmista. Työn tavoitteena on osaltaan mahdollistaa entistä turvallisemman verkottuneen tietoyhteiskunnan rakentaminen tulevaisuudessa. Teknisestä näkökulmasta työssä esitetään suunnitteluvuo kryptografisia primitiivejä tehokkaasti hyödyntäville rajallisen laskentatehon sulautetuviiille järjestelmille, analysoidaan biometrisiin passeihin, kansainväliseen passijärjestelmään, sekä sähköiseen äänestykseen kohdistuvia uhkia, tarkastellaan joukkovalvontaan käytettyjen tekniikoiden toimintaperiaatteita ja niiden aiheuttamia uhkia, sekä tutkitaan suomalaisten Internet-käyttäjien salasanatottumuksia verkkosovelluksissa. Teknis-yhteiskunnallisesta näkökulmasta työssä tarkastellaan valvonnan teoriaa ja perehdytään siihen, miten valvonta vaikuttaa verkottuneen tietoyhteiskunnan kansalaisiin. Lisäksi kehitetään menetelmiä parempaan tietoturvaopetukseen kaikilla koulutusasteilla, määritellään keskeiset tietoturvatietouden käsitteet, tarkastellaan mahdollisuutta soveltaa tiedon herruuden periaatetta verkottuneen tietoyhteiskunnan kansalaisistaan keräämän tiedon hallintaan ja käyttöön, sekä tutkitaan luottamuksen merkitystä yhteiskunnan ydintoimintojen turvallisuudelle ja toiminnalle, keskittyen erityisesti pakotetun luottamuksen vaikutuksiin