Information Theoretic Security for Shannon Cipher System under Side-Channel Attacks †

Abstract

In this paper, we propose a new theoretical security model for Shannon cipher systems under side-channel attacks, where the adversary is not only allowed to collect ciphertexts by eavesdropping the public communication channel but is also allowed to collect the physical information leaked by the devices where the cipher system is implemented on, such as running time, power consumption, electromagnetic radiation, etc. Our model is very robust as it does not depend on the kind of physical information leaked by the devices. We also prove that in the case of one-time pad encryption, we can strengthen the secrecy/security of the cipher system by using an appropriate affine encoder. More precisely, we prove that for any distribution of the secret keys and any measurement device used for collecting the physical information, we can derive an achievable rate region for reliability and security such that if we compress the ciphertext using an affine encoder with a rate within the achievable rate region, then: (1) anyone with a secret key will be able to decrypt and decode the ciphertext correctly, but (2) any adversary who obtains the ciphertext and also the side physical information will not be able to obtain any information about the hidden source as long as the leaked physical information is encoded with a rate within the rate region. We derive our result by adapting the framework of the one helper source coding problem posed and investigated by Ahlswede and Körner (1975) and Wyner (1975). For reliability and security, we obtain our result by combining the result of Csizár (1982) on universal coding for a single source using linear codes and the exponential strong converse theorem of Oohama (2015) for the one helper source coding problem.

Information Theoretic Security for Broadcasting of Two Encrypted Sources under Side-Channel Attacks †

“…We can prove Lemma 4 using a similar method shown in [ 4 ]. The detailed proof is given in Appendix C .…”

“…The adversarial/security model we use in this paper and its relation to a real-world example are shown in Figure 1 . Basically, we adapt the approach in [ 4 ] on modeling the side-channel, where the side-channel is modelled as a rate constraint noiseless channel.…”

“…Taking the advantage of the homomorphic property of one-time-pad and affine encoding, we separate the theoretical analysis of reliability and security such that we can deal with each issue independently. For reliability analysis, similar to the analysis in [ 4 , 5 , 6 , 7 ], we mainly obtain our result by adapting the result of Csizár [ 8 ] on the universal coding using linear codes. Our main theorem on security is based on the technique developed in [ 4 ] which is actually a combination of two other techniques.…”

“…For reliability analysis, similar to the analysis in [ 4 , 5 , 6 , 7 ], we mainly obtain our result by adapting the result of Csizár [ 8 ] on the universal coding using linear codes. Our main theorem on security is based on the technique developed in [ 4 ] which is actually a combination of two other techniques. One is a technique developed by Oohama in [ 9 ] for deriving approximation error exponents for the intrinsic randomness problem in some framework of distributed random number extraction.…”

Exponential Strong Converse for One Helper Source Coding Problem

“…Recently, Watanabe and Oohama [ 17 ] have found an interesting security problem, which has a close connection with the strong converse theorem for the AKW system. Furthermore, Oohama and Santoso [ 18 ] and Santoso and Oohama [ 19 ] clarify that the exponential strong converse theorem obtained by this paper plays an essential role in deriving a strong sufficient secure condition for the privacy amplification in their new theoritical model of side channel attacks to the Shannon chipher systems. From the above two cases, we expect that exponential strong converse theorems for multiterminal source networks will serve as a strong tool to several information theoretical security problems.…”