We put forward new techniques for designing signature schemes. As a result, we present practical signature schemes based on the CDH, the RSA, and the SIS assumptions. Our schemes compare favorably with existing schemes based on these assumptions. Our core idea is the use of tag-based signatures. Concretely, each signatures contains a tag which is uniformly chosen from a suitable tag set. Intuitively, the tag provides a way to embed instances of computational problems. Indeed, carefully choosing these tag spaces provides new ways to partition the set of possible message-tag pairs into "signable" and "unsignable" pairs. In our security proof, we will thus be able to sign all adversarially requested messages, and at the same time use an adversarially generated forgery with suitably large probability.

We put forward a new technique to construct very efficient and compact signature schemes. Our technique combines several instances of an only mildly secure signature scheme to obtain a fully secure scheme. Since the mild security notion we require is much easier to achieve than full security, we can combine our strategy with existing techniques to obtain a number of interesting new (stateless and fully secure) signature schemes. Concretely, we get:• A scheme based on the computational Diffie-Hellman (CDH) assumption in pairingfriendly groups. Signatures contain O(1) and verification keys O(log k) group elements, where k is the security parameter. Our scheme is the first fully secure CDH-based scheme with such compact verification keys.• A scheme based on the (non-strong) RSA assumption in which both signatures and verification keys contain O(1) group elements. Our scheme is significantly more efficient than existing RSA-based schemes.• A scheme based on the Short Integer Solutions (SIS) assumption. Signatures contain O(log(k) · m) and verification keys O(n · m) Z p -elements, where p may be polynomial in k, and n, m denote the usual SIS matrix dimensions. Compared to state-of-the-art SIS-based schemes, this gives very small verification keys, at the price of slightly larger signatures. In all cases, the involved constants are small, and the arising schemes provide significant improvements upon state-of-the-art schemes. The only price we pay is a rather large (polynomial) loss in the security reduction. However, this loss can be significantly reduced at the cost of an additive term in signature and verification key size.

Assume that an adversary observes many ciphertexts, and may then ask for openings, i.e. the plaintext and the randomness used for encryption, of some of them. Do the unopened ciphertexts remain secure? There are several ways to formalize this question, and the ensuing security notions are not known to be implied by standard notions of encryption security. In this work, we relate the two existing flavors of selective opening security. Our main result is that indistinguishability-based selective opening security and simulation-based selective opening security do not imply each other.We show our claims by counterexamples. Concretely, we construct two public-key encryption schemes. One scheme is secure under selective openings in a simulation-based sense, but not in an indistinguishability-based sense. The other scheme is secure in an indistinguishability-based sense, but not in a simulation-based sense.Our results settle an open question of Bellare et al. (Eurocrypt 2009). Also, taken together with known results about selective opening secure encryption, we get an almost complete picture how the two flavors of selective opening security relate to standard security notions.

We introduce a variant of the Universal Composability framework (UC; Canetti, FOCS 2001) that uses symbolic cryptography. Two salient properties of the UC framework are secure composition and the possibility of easily defining security by giving an ideal functionality as specification. These advantages are now also available in a symbolic modeling of cryptography, allowing for a modular analysis of complex protocols.We furthermore introduce a new technique for modular design of protocols that uses UC but avoids the need for powerful cryptographic primitives that often comes with UC protocols; this "virtual primitives" approach is unique to the symbolic setting and has no counterpart in the original computational UC framework.

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This paper presents MergeMAC, a MAC that is particularly suitable for environments with strict time requirements and extremely limited bandwidth. MergeMAC computes the MAC by splitting the message into two parts. We use a pseudorandom function (PRF) to map messages to random bit strings and then merge them with a very efficient keyless function. The advantage of this approach is that the outputs of the PRF can be cached for frequently needed message parts. We demonstrate the merits of MergeMAC for authenticating messages on the CAN bus where bandwidth is extremely limited and caching can be used to recover parts of the message counter instead of transmitting it. We recommend an instantiation of the merging function Merge and analyze the security of our construction. Requirements for a merging function are formally defined and the resulting EUF-CMA security of MergeMAC is proven.

Abstract. We construct secret-key encryption (SKE) schemes that are secure against related-key attacks and in the presence of key-dependent messages (RKA-KDM secure). We emphasize that RKA-KDM security is not merely the conjunction of individual security properties, but covers attacks in which ciphertexts of key-dependent messages under related keys are available. Besides being interesting in their own right, RKA-KDM secure schemes allow to garble circuits with XORs very efficiently (Applebaum, TCC 2013). Until now, the only known RKA-KDM secure SKE scheme (due to Applebaum) is based on the LPN assumption. Our schemes are based on various other computational assumptions, namely DDH, LWE, QR, and DCR.We abstract from Applebaum's construction and proof, and formalize three generic technical properties that imply RKA-KDM security: one property is IND-CPA security, and the other two are the existence of suitable oracles that produce ciphertexts under related keys, resp. of key-dependent messages. We then give simple SKE schemes that achieve these properties. Our constructions are variants of known KDM-secure public-key encryption schemes. To additionally achieve RKA security, we isolate suitable homomorphic properties of the underlying schemes in order to simulate ciphertexts under related keys in the security proof. RKA-KDM security for our schemes holds w.r.t. affine functions (over the respective mathematical domain).From a conceptual point of view, our work provides a generic and extensible way to construct encryption schemes with multiple special security properties.