Abstract. Information theoretic cryptography is discussed based on conditional Rényi entropies. Our discussion focuses not only on cryptography but also on the definitions of conditional Rényi entropies and the related information theoretic inequalities. First, we revisit conditional Rényi entropies, and clarify what kind of properties are required and actually satisfied. Then, we propose security criteria based on Rényi entropies, which suggests us deep relations between (conditional) Rényi entropies and error probabilities by using several guessing strategies. Based on these results, unified proof of impossibility, namely, the lower bounds of key sizes is derived based on conditional Rényi entropies. Our model and lower bounds include the Shannon's perfect secrecy, and the min-entropy based encryption presented by Dodis, and Alimomeni and Safavi-Naini. Finally, a new optimal symmetric key encryption is proposed which achieve our lower bounds.

Abstract.A potentially serious problem with current digital signature schemes is that their underlying hard problems from number theory may be solved by an innovative technique or a new generation of computing devices such as quantum computers. Therefore while these signature schemes represent an efficient solution to the short term integrity (unforgeability and non-repudiation) of digital data, they provide no confidence on the long term (say of 20 years) integrity of data signed by these schemes. In this work, we focus on signature schemes whose security does not rely on any unproven assumption. More specifically, we establish a model for unconditionally secure digital signatures in a group, and demonstrate practical schemes in that model. An added advantage of the schemes is that they allow unlimited transfer of signatures without compromising the security of the schemes. Our scheme represents the first unconditionally secure signature that admits provably secure transfer of signatures.

In this paper, we discuss non-interactive updating of decryption keys in identity-based encryption (IBE). In practice, key revocation is a necessary and inevitable process and IBE is no exception when it comes to having to manage revocation of decryption keys without losing its merits in efficiency. Our main contribution of this paper is to propose novel constructions of IBE where a decryption key can be renewed without having to make changes to its public key, i.e. user's identity. We achieve this by extending the hierarchical IBE (HIBE). Regarding security, we address semantic security against adaptive chosen ciphertext attacks for a very strong attack environment that models all possible types of key exposures in the random oracle model. In addition to this, we show method of constructing a partially collusion resistant HIBE from arbitrary IBE in the random oracle model. By combining both results, we can construct an IBE with non-interactive key update from only an arbitrary IBE.

Abstract. This paper focuses on notions for the security of digital signature schemes whose resistance against forgery is not dependent on unproven computational assumptions. We establish successfully a sound and strong notion for such signature schemes. We arrive at the sound notion by examining carefully the more established security notions for digital signatures based on public-key cryptography, and taking into account desirable requirements of signature schemes in the unconditional security setting. We also reveal an interesting relation among relevant security notions which have appeared in the unconditionally setting, and significantly, prove that our new security notion is the strongest among all those for unconditionally secure authentication and signature schemes known to date. Furthermore, we show that our security notion encompasses that for public-key signature schemes, namely, existential unforgeability under adaptive chosen-message attack. Finally we propose a construction method for signature schemes that are provably secure in our strong security notion.

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