Proved here is the sufficiency of certain conditions to ensure the Elliptic Curve Digital Signature Algorithm (ECDSA) existentially unforgeable by adaptive chosen-message attacks. The sufficient conditions include (i) a uniformity property and collision-resistance for the underlying hash function, (ii) pseudo-randomness in the private key space for the ephemeral private key generator, (iii) generic treatment of the underlying group, and (iv) a further condition on how the ephemeral public keys are mapped into the private key space. For completeness, a brief survey of necessary security conditions is also given. Some of the necessary conditions are weaker than the corresponding sufficient conditions used in the security proofs here, but others are identical.

In this paper we take a closer look at the security and efficiency of public-key encryption and signature schemes in public-key infrastructures (PKI). Unlike traditional analyses which assume an “ideal” implementation of the PKI, we focus on the security of joint constructions that consider the certification authority (CA) and the users, and include a key-registration protocol and the algorithms of an encryption or a signature scheme. We therefore consider significantly broader adversarial capabilities. Our analysis clarifies and validates several crucial aspects such as the amount of trust put in the CA, the necessity and specifics of proofs of possession of secret keys, and the security of the basic primitives in this more complex setting. We also provide constructions for encryption and signature schemes that provably satisfy our strong security definitions and are more efficient than the corresponding traditional constructions that assume a digital certificate issued by the CA must be verified whenever a public key is used. Our results address some important aspects for the design and standardization of PKIs, as targeted for example in the standards project ANSI X9.109. 1

Abstract. Digital signature schemes often use domain parameters such as prime numbers or elliptic curves. They can be subject to security threats when they are not treated like public keys. In this paper we formalize the notion of “signature scheme with domain parameter ” together with a new adversarial model: the “domain parameter shifting attack”. We take ECDSA as a case study. We make a domain parameter shifting attack against ECDSA: an attacker can impersonate a honest signer either by trying to modify the subgroup generator G or, when using point compression representation, by trying to modify the elliptic curve a and b domain parameters. We further propose to fix this ECDSA issue. 1

Verifiably encrypted signature is useful in handling the fair exchange problem especially, online contract signing. In this paper, we propose a verifiably encrypted signature scheme using bilinear pairings.

I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii Signcryption is a new cryptographic primitive which simultaneously provides both confidentiality and authenticity. Previously, these two goals had been considered separately, with encryption schemes providing confidentiality and signature schemes providing authenticity. In cases where both were required, the encryption and signature operations were simply sequentially composed. In 1997, Zheng demonstrated that by combining both goals into a single primitive, it is possible to achieve significant savings both in computational and communication overhead. Since then, a wide variety of signcryption

Abstract. We take a critical look at security models that are often used to give “provable security ” guarantees. We pay particular attention to digital signatures, symmetric-key encryption, and leakage resilience. We find that there has been a surprising amount of uncertainty about what the “right ” definitions might be. Even when definitions have an appealing logical elegance and nicely reflect certain notions of security, they fail to take into account many types of attacks and do not provide a comprehensive model of adversarial behavior. 1.

Abstract. We revisit the notion of the anonymous signature, first formalized by Yang, Wong, Deng and Wang [12], and then further developed by Fischlin [6] and Zhang and Imai [13]. We present a new formalism of anonymous signature, where instead of the message, a part of the signature is withheld to maintain anonymity. We introduce the notion unpretendability to guarantee infeasibility for someone other than the correct signer to pretend authorship of the message and signature. Our definition retains applicability for all previous applications of the anonymous signature, provides stronger security, and is conceptually simpler. We give a generic construction from any ordinary signature scheme, and also show that the short signature scheme by Boneh and Boyen [4] can be naturally regarded as such a secure anonymous signature scheme according to our formalism.