Digital Signatures from Symmetric-Key Primitives

We propose practically efficient signature schemes which feature several attractive properties: (a) they only rely on the security of symmetric-key primitives (block ciphers, hash functions), and are therefore a viable candidate for post-quantum security, (b) they have extremely small signing keys, essentially the smallest possible, and, (c) they are highly parametrizable. For this result we take advantage of advances in two very distinct areas of cryptography. The first is the area of primitives in symmetric cryptography, where recent developments led to designs which exhibit an especially low number of multiplications. The second is the area of zero-knowledge proof systems, where significant progress for efficiently proving statements over general circuits was recently made. We follow two different directions, one of them yielding the first practical instantiation of a design paradigm due to Bellare and Goldwasser without relying on structured hardness assumptions. For both our schemes we explore the whole design spectrum to obtain optimal parameter choices for different settings. Within limits, in all cases our schemes allow to trade-off computational effort with signature sizes. We also demonstrate that our schemes are parallelizable to the extent that they can practically take advantage of several cores on a CPU

Algebraic Frameworks for Cryptographic Primitives

A fundamental goal in theoretical cryptography is to identify the conceptually simplest abstractions that generically imply a collection of other cryptographic primitives. For symmetric-key primitives, this goal has been accomplished by showing that one-way functions are necessary and sufficient to realize primitives ranging from symmetric-key encryption to digital signatures. By contrast, for asymmetric primitives, we have no (known) unifying simple abstraction even for a few of its most basic objects. Moreover, even for public-key encryption (PKE) alone, we have no unifying abstraction that all known constructions follow. The fact that almost all known PKE constructions exploit some algebraic structure suggests considering abstractions that have some basic algebraic properties, irrespective of their concrete instantiation. We make progress on the aforementioned fundamental goal by identifying simple and useful cryptographic abstractions and showing that they imply a variety of asymmetric primitives. Our general approach is to augment symmetric abstractions with algebraic structure that turns out to be sufficient for PKE and much more, thus yielding a “bridge” between symmetric and asymmetric primitives. We introduce two algebraic frameworks that capture almost all concrete instantiations of (asymmetric) cryptographic primitives, and we also demonstrate their applicability by showing their cryptographic implications. Therefore, rather than manually building different cryptosystems from a new assumption, one only needs to build one (or more) of our simple structured primitives, and a whole host of cryptosystems immediately follows.PHDComputer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/166137/1/alamati_1.pd

Lengths May Break Privacy – Or How to Check for Equivalences with Length

Security protocols have been successfully analyzed using symbolic models, where messages are represented by terms and protocols by processes. Privacy properties like anonymity or untraceability are typically expressed as equivalence between processes. While some decision procedures have been proposed for automatically deciding process equivalence, all existing approaches abstract away the information an attacker may get when observing the length of messages. In this paper, we study process equivalence with length tests. We first show that, in the static case, almost all existing decidability results (for static equivalence) can be extended to cope with length tests. In the active case, we prove decidability of trace equivalence with length tests, for a bounded number of sessions and for standard primitives. Our result relies on a previous decidability result from Cheval et al (without length tests). Our procedure has been implemented and we have discovered a new flaw against privacy in the biometric passport protocol

Post-Quantum ID-based Ring Signatures from Symmetric-key Primitives

Ring signatures and ID-based cryptography are considered promising in terms of application. A ring signature authenticates messages while the author of the message remains anonymous. ID-based cryptographic primitives suppress the need for certificates in public key infrastructures (PKI). In this work, we propose a generic construction for post-quantum ID-based ring signatures (IDRS) based on symmetric-key primitives from which we derive the first two constructions of IDRS. The first construction named PicRS utilizes the Picnic digital signature to ensure its security while the second construction XRS is motivated by the stateful digital signature XMSS instead of Picnic, allowing a signature size reduction. Both constructions have a competitive signature size when compared with state-of-the-art lattice-based IDRS. XRS can achieve a competitive signature size of 889KB for a ring of 4096 users while the fully stateless PicRS achieves a signature size of 1.900MB for a ring of 4096 users. In contrast, the shortest lattice-based IDRS achieves a signature size of 335MB for the same ring size

Still Wrong Use of Pairings in Cryptography

Several pairing-based cryptographic protocols are recently proposed with a wide variety of new novel applications including the ones in emerging technologies like cloud computing, internet of things (IoT), e-health systems and wearable technologies. There have been however a wide range of incorrect use of these primitives. The paper of Galbraith, Paterson, and Smart (2006) pointed out most of the issues related to the incorrect use of pairing-based cryptography. However, we noticed that some recently proposed applications still do not use these primitives correctly. This leads to unrealizable, insecure or too inefficient designs of pairing-based protocols. We observed that one reason is not being aware of the recent advancements on solving the discrete logarithm problems in some groups. The main purpose of this article is to give an understandable, informative, and the most up-to-date criteria for the correct use of pairing-based cryptography. We thereby deliberately avoid most of the technical details and rather give special emphasis on the importance of the correct use of bilinear maps by realizing secure cryptographic protocols. We list a collection of some recent papers having wrong security assumptions or realizability/efficiency issues. Finally, we give a compact and an up-to-date recipe of the correct use of pairings.Comment: 25 page