Abstract
Ciphertext indistinguishability under chosen plaintext attacks is a standard security notion for public key encryption. It crucially relies on the usage of good randomness and is trivially unachievable if the randomness is known by the adversary. Yilek (CT-RSA’10) defined security against resetting attacks, where randomness might be reused but remains unknown to the adversary. Furthermore, Yilek claimed that security against adversaries making a single query to the challenge oracle implies security against adversaries making multiple queries to the challenge oracle. This is a typical simplification for indistinguishability security notions proven via a standard hybrid argument. The given proof, however, was pointed out to be flawed by Paterson, Schuldt, and Sibborn (PKC’14). Prior to this work, it has been unclear whether this simplification of the security notion also holds in case of resetting attacks.
We remedy this state of affairs as follows. First, we show the strength of resetting attacks by showing that many public key encryption schemes are susceptible to these attacks. As our main contribution, we show that the simplification to adversaries making only one query to the challenge oracle also holds in the light of resetting attacks. More precisely, we show that the existing proof can not be fixed and give a different proof for the claim. Finally, we define real-or-random security against resetting attacks and prove it equivalent to the notion by Yilek which is of the form left-or-right.
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Change history
09 April 2021
In the original version of this book there are several formatting mistakes. This has been corrected.
Notes
- 1.
We will often omit this input.
- 2.
In [29] the notion is also extended to the \(\mathrm {IND{\hbox {-}}CCA}\) case, which is not relevant for this work.
- 3.
Note that this definition is tailored to the single randomness setting. The equivalent, more complicated definition for multiple randomnesses (see, e.g., [29, Appendix A]) is irrelevant for this work and therefore omitted.
- 4.
In [29] the scheme also consists of a MAC to achieve CCA security which we omit here for simplicity.
- 5.
RQC is very much akin to HQC, hence we provide the description and the formal proofs only for HQC.
- 6.
The issue described in [21] corresponds to the issue for flipping queries we show here.
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Acknowledgements
This work was funded by the Deutsche Forschungsgemeinschaft (DFG) – SFB 1119 – 236615297.
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Krämer, J., Struck, P. (2020). Security of Public Key Encryption Against Resetting Attacks. In: Bhargavan, K., Oswald, E., Prabhakaran, M. (eds) Progress in Cryptology – INDOCRYPT 2020. INDOCRYPT 2020. Lecture Notes in Computer Science(), vol 12578. Springer, Cham. https://doi.org/10.1007/978-3-030-65277-7_23
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