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IEICE ESS FUNDAMENTALS REVIEW

Information Theoretically Secure Key Agreement and Related Topics

Shun Watanabe

Published Jan 1, 2013• 0 citations
Publisher

Abstract

本稿では，情報理論的に安全な秘密鍵共有とそれに関連するトピックについて概説する．まず，秘密鍵共有のモデルについて説明した後，鍵共有プロトコルが情報整合と秘匿増強と呼ばれる二つのステップから成ることを説明し，幾つかの安全性基準を紹介する．その後，情報整合の手段としてSlepian-Wolf 符号化と呼ばれるデータ圧縮法について説明する．次に，従来広く使われていた秘匿増強の方法について述べる．特に，その方法によって生成された秘密鍵は弱い安全性を満たすものの，その他の安全性基準は満たさないことを説明する．そして弱い安全性基準以外の基準を満足するにはどのように秘匿増強を行えばよいか説明する．更に，Slepian-Wolf 符号化と秘匿増強の一般化として，多端子情報源符号化問題と多端子乱数生成問題について説明する．これらの応用として，3者以上の正規ユーザ間での秘密鍵共有と秘匿関数計算について紹介する．

DOI
10.1587/essfr.7.38

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本稿では，情報理論的に安全な秘密鍵共有とそれに関連するトピックについて概説する．まず，秘密鍵共有のモデルについて説明した後，鍵共有プロトコルが情報整合と秘匿増強と呼ばれる二つのステップから成ることを説明し，幾つかの安全性基準を紹介する．その後，情報整合の手段としてSlepian-Wolf 符号化と呼ばれるデータ圧縮法について説明する．次に，従来広く使われていた秘匿増強の方法について述べる．特に，その方法によって生成された秘密鍵は弱い安全性を満たすものの，その他の安全性基準は満たさないことを説明する．そして弱い安全性基準以外の基準を満足するにはどのように秘匿増強を行えばよいか説明する．更に，Slepian-Wolf 符号化と秘匿増強の一般化として，多端子情報源符号化問題と多端子乱数生成問題について説明する．これらの応用として，3者以上の正規ユーザ間での秘密鍵共有と秘匿関数計算について紹介する．
We analyze the error performance of coding scheme that is found in the protocol for secret key agreement based on the Gaussian channel. The approach is regarded as the Slepian-Wolf coding or the source coding with side information at the decoder. One remarkable feature of the coding in the key agreement is that two parties may extract the set of reliable signals before Slepian-Wolf coding is performed. We derive a tight upper bound on the error probability of this coding scheme, which allows us to quantify the effect of signal extraction.
이 논문에서 우리는 여러 사용자들이 동시에 세션키를 교환하는 키 교환 스킴에 대해서 연구한다. 이런 상황은 사용자들을 그래프 노드들로 표현하고 두 사용자간에 키를 만들어야 하는 상황을 에지로 표현하는 키 그래프에 의해서 묘사될 수 있다. 우리는 키 그래프에 있는 모든 에지들을 위한 세션키들을 하나의 세션에서 동시에 만드는 키 교환 스킴을 설계한다. 키 그래프를 위한 키 교환은 양자간 키 교환의 확장판이라고 할 수 있다. 우리는 양자간 키 교환 안전성 모델을 확장해서 키 그래프를 위한 키 교환 안전성 모델을 제안한다. 우리는 란수 직 산용 테크닉을 사용해서 두개의 키 그래프를 위한 키 교환 스킴을 설계하며 안전성을 증명한다. 우리가 제안하는 스킴들의 안전성은 decisional Diffie-Hellman 가정에 의존한다. 첫 번째 스킴은 일 라운드 키 교환 프로토콜이며 키 독립성을 보장한다. 두 번째 스킴은 일 라운드이며 전방위 안전성을 보장한다. 제안하는 두 가지 스킴들의 안전성은 모두 표준 모델에서 증명된다. 제안되는 프로토콜들은 최초의 다중 키 교환 프로토콜이며, 단순히 양자간 키 교환 프로토콜들을 반복 사용해서 키들을 만드는 것보다 훨씬 효율적이다. 예로서 한 사용자가 n명의 다른 사용자와 키를 만든다고 가정하자. 가장 단순한 프로토콜은 각각의 사용자들과의 키 교환을 위해서 양자간 키 교환을 사용하는 것으로서, 이 때는 계산량과 메시지 전송량이 n에 비례하게 된다. 제안되는 프로토콜들은 n개의 키를 만드는데 있어서 계산량은 n에 비례하나 전송되는 메시지의 양은 교환되는 키들의 수에 상관없이 일정하다. In the paper we study key agreement schemes when a party needs to establish a session key with each of several parties, thus having multiple session keys. This situation can be represented by a graph, tailed a key graph, where a vertex represents a party and an edge represents a relation between two parties sharing a session key. graphs to establish all session keys corresponding to all edges in a key graph simultaneously in a single session. A key agreement protocol of a key graph is a natural extension of a two-party key agreement protocol. We propose a new key exchange model for key graphs which is an extension of a two-party key exchange model. using the so-called randomness re-use technique which re-uses random values to make session keys for different sessions, we suggest two efficient key agreement protocols for key graphs based on the decisional Diffie-Hellman assumption, and prove their securities in the key exchange model of key graphs. Our first scheme requires only a single round and provides key independence. Our second scheme requires two rounds and provides forward secrecy. Both are proven secure In the standard model. The suggested protocols are the first pairwise key agreement protocols and more efficient than a simple scheme which uses a two-party key exchange for each necessary key. Suppose that a user makes a session key with n other users, respectively. The simple scheme's computational cost and the length of the transmitted messages are increased by a factor of n. The suggested protocols's computational cost also depends on n, but the length of the transmitted messages are constant.
The privacy amplification is a technique to distill a secret key from a random variable by a hash function so that the distilled key and an eavesdropper's random variable is statistically independent. There are two kinds of security criteria for the key distilled by the privacy amplification: the weak security criterion and the strong security criterion. As a technique to distill a secret key, it is known that the encoder of a Slepian-Wolf (the source coding with full side-information at the decoder) code can be used as a hash function for the privacy amplification if we employ the weak security criterion. In this paper, we show that the encoder of a Slepian-Wolf code cannot be used as a hash function for the privacy amplification if we employ the strong security criterion.
Privacy amplification is a technique to distill a secret key from a random variable by a function so that the distilled key and eavesdropper's random variable are statistically independent. There are three kinds of security criteria for the key distilled by privacy amplification: the normalized divergence criterion, which is also known as the weak security criterion, the variational distance criterion, and the divergence criterion, which is also known as the strong security criterion. As a technique to distill a secret key, it is known that the encoder of a Slepian-Wolf (the source coding with full side-information at the decoder) code can be used as a function for privacy amplification if we employ the weak security criterion. In this paper, we show that the encoder of a Slepian-Wolf code cannot be used as a function for privacy amplification if we employ the criteria other than the weak one.