An important open problem in the area of Traitor Tracing is designing a scheme with constant expansion of the size of keys (users' keys and the encryption key) and of the size of ciphertexts with respect to the size of the plaintext. This problem is known from the introduction of Traitor Tracing by Chor, Fiat and Naor. We refer to such schemes as traitor tracing with constant transmission rate. Here we present a general methodology and two protocol constructions that result in the first two public-key traitor tracing schemes with constant transmission rate in settings where plaintexts can be calibrated to be sufficiently large. Our starting point is the notion of copyrighted function which was presented by Naccache, Shamir and Stern. We first solve the open problem of discrete-log-based and public-key-based copyrighted function. Then, we observe the simple yet crucial relation between (public-key) copyrighted encryption and (public-key) traitor tracing, which we exploit by introducing a generic design paradigm for designing constant transmission rate traitor tracing schemes based on copyrighted encryption functions. Our first scheme achieves the same expansion efficiency as regular ElGamal encryption. The second scheme introduces only a slightly larger (constant) overhead, however, it additionally achieves efficient black-box traitor tracing (against any pirate construction).

Traitor Tracing with constant transmission rate

The Internet of Things (IoT) is heavily affecting our daily lives in many domains, ranging from tiny wearable devices to large industrial systems. Consequently, a wide variety of IoT applications have been developed and deployed using different IoT frameworks. An IoT framework is a set of guiding rules, protocols, and standards which simplify the implementation of IoT applications. The success of these applications mainly depends on the ecosystem characteristics of the IoT framework, with the emphasis on the security mechanisms employed in it, where issues related to security and privacy are pivotal. In this paper, we survey the security of the main IoT frameworks, a total of 8 frameworks are considered. For each framework, we clarify the proposed architecture, the essentials of developing third-party smart apps, the compatible hardware, and the security features. Comparing security architectures shows that the same standards used for securing communications, whereas different methodologies followed for providing other security properties.

/pdf/internet-of-things-a-survey-on-the-security-of-iot-u07cbhrko5.pdf

Internet of Things: A survey on the security of IoT frameworks

Quantum computers will break today's most popular public-key cryptographic systems, including RSA, DSA, and ECDSA. This book introduces the reader to the next generation of cryptographic algorithms, the systems that resist quantum-computer attacks: in particular, post-quantum public-key encryption systems and post-quantum public-key signature systems. Leading experts have joined forces for the first time to explain the state of the art in quantum computing, hash-based cryptography, code-based cryptography, lattice-based cryptography, and multivariate cryptography. Mathematical foundations and implementation issues are included. This book is an essential resource for students and researchers who want to contribute to the field of post-quantum cryptography.

Post-quantum cryptography

While showing great promise, Bitcoin requires users to wait tens of minutes for transactions to commit, and even then, offering only probabilistic guarantees. This paper introduces ByzCoin, a novel Byzantine consensus protocol that leverages scalable collective signing to commit Bitcoin transactions irreversibly within seconds. ByzCoin achieves Byzantine consensus while preserving Bitcoin's open membership by dynamically forming hash power-proportionate consensus groups that represent recently-successful block miners. ByzCoin employs communication trees to optimize transaction commitment and verification under normal operation while guaranteeing safety and liveness under Byzantine faults, up to a near-optimal tolerance of f faulty group members among 3f + 2 total. ByzCoin mitigates double spending and selfish mining attacks by producing collectively signed transaction blocks within one minute of transaction submission. Tree-structured communication further reduces this latency to less than 30 seconds. Due to these optimizations, ByzCoin achieves a throughput higher than PayPal currently handles, with a confirmation latency of 15-20 seconds.

/pdf/enhancing-bitcoin-security-and-performance-with-strong-40ulnotow2.pdf

Enhancing Bitcoin Security and Performance with Strong Consistency via Collective Signing

This paper shows that a $390 mass-market quad-core 2.4GHz Intel Westmere (Xeon E5620) CPU can create 109000 signatures per second and verify 71000 signatures per second on an elliptic curve at a 2128 security level. Public keys are 32 bytes, and signatures are 64 bytes. These performance figures include strong defenses against software side-channel attacks: there is no data flow from secret keys to array indices, and there is no data flow from secret keys to branch conditions.

https://link.springer.com/content/pdf/10.1007%2Fs13389-012-0027-1.pdf

High-speed high-security signatures

This paper shows that a $390 mass-market quad-core 2.4GHz Intel Westmere (Xeon E5620) CPU can create 108000 signatures per second and verify 71000 signatures per second on an elliptic curve at a 2128 security level. Public keys are 32 bytes, and signatures are 64 bytes. These performance figures include strong defenses against software side channel attacks: there is no data flow from secret keys to array indices, and there is no data flow from secret keys to branch conditions. Keywords: Elliptic curves, Edwards curves, signatures, speed, software side channels, foolproof session keys

/pdf/high-speed-high-security-signatures-422our29ys.pdf

The Hidden Field Equations HFE Cryptosystem as proposed by Patarin is one of the best known and most studied multivariate schemes. While the security of the basic scheme appeared to be very weak, the HFEv- variant seems to be a good candidate for digital signature schemes on the basis of multivariate polynomials. However, the currently existing scheme of this type, the QUARTZ signature scheme, is hardly used in practice because of its poor efficiency. In this paper we analyze recent results from Ding and Yang about the degree of regularity of HFEv- systems and derive from them design principles for signature schemes of the HFEv- type. Based on these results we propose the new HFEv- based signature scheme Gui, which is more than 100 times faster than QUARTZ and therefore highly comparable with classical signature schemes such as RSA and ECDSA.

/pdf/design-principles-for-hfev-based-multivariate-signature-2ro4isiwvr.pdf

Design Principles for HFEv- Based Multivariate Signature Schemes

Multivariate public-key cryptosystems (sometimes polynomial-based PKC’s or just multivariates) handle polynomials of many variables over relatively small fields instead of elements of a large ring or group. The “tame-like” or “sparse” class of multivariates are distinguished by the relatively few terms that they have per central equation. We explain how they differ from the “big-field” type of multivariates, represented by derivatives of C∗ and HFE, how they are better, and give basic security criteria for them. The last is shown to be satisfied by efficient schemes called “Enhanced TTS” which is built on a combination of the Oil-and-Vinegar and Triangular ideas. Their security levels are estimated. In this process we summarize and in some cases, improve rank-based attacks, which seek linear combinations of certain matrices at given ranks. These attacks are responsible for breaking many prior multivariate designs.

/pdf/building-secure-tame-like-multivariate-public-key-2l6t3bcjwl.pdf

Building secure tame-like multivariate public-key cryptosystems: the new TTS

Multivariate Public Key Cryptosystems (MPKCs) are often touted as future-proofing against Quantum Computers It also has been known for efficiency compared to "traditional" alternatives However, this advantage seems to erode with the increase of arithmetic resources in modern CPUs and improved algorithms, especially with respect to Elliptic Curve Cryptography (ECC) In this paper, we show that hardware advances do not just favor ECC Modern commodity CPUs also have many small integer arithmetic/logic resources, embodied by SSE2 or other vector instruction sets, that are useful for MPKCs In particular, Intel's SSSE3 instructions can speed up both public and private maps over prior software implementations of Rainbow-type systems up to 4× Furthermore, MPKCs over fields of relatively small odd prime characteristics can exploit SSE2 instructions, supported by most modern 64-bit Intel and AMD CPUs For example, Rainbow over ${\mathbb F}_{31}$ can be up to 2× faster than prior implementations of similarly-sized systems over ${\mathbb F}_{16}$ Here a key advance is in using Wiedemann (as opposed to Gauss) solvers to invert the small linear systems in the central maps We explain the techniques and design choices in implementing our chosen MPKC instances over fields such as ${\mathbb F}_{31}$, ${\mathbb F}_{16}$ and ${\mathbb F}_{256}$ We believe that our results can easily carry over to modern FPGAs, which often contain a large number of small multipliers, usable by odd-field MPKCs

/pdf/sse-implementation-of-multivariate-pkcs-on-modern-x86-cpus-381r9enoa6.pdf

Bo-Yin Yang

Papers

High-speed high-security signatures

High-speed high-security signatures

Design Principles for HFEv- Based Multivariate Signature Schemes

Building secure tame-like multivariate public-key cryptosystems: the new TTS

SSE Implementation of Multivariate PKCs on Modern x86 CPUs