International Association
for Cryptologic Research

Incompressibility is one of the most fundamental security goals in white-box cryptography. Given recent advances in the design of efficient and incompressible block ciphers such as SPACE, SPNbox and WhiteBlock, we demonstrate the feasibility of reducing incompressible AEAD modes to incompressible block ciphers. We first observe that several existing AEAD modes of operation, including CCM, GCM(-SIV), and OCB, would be all insecure against white-box adversaries even when used with an incompressble block cipher. This motivates us to revisit and formalize incompressibility-based security definitions for AEAD schemes and for block ciphers, so that we become able to design modes and reduce their security to that of the underlying ciphers. Our new security notion for AEAD, which we name whPRI, is an extension of the pseudo-random injection security in the black-box setting. Similar security notions are also defined for other cryptosystems such as privacy-only encryption schemes. We emphasize that whPRI ensures quite strong authenticity against white-box adversaries: existential unforgeability beyond leakage. This contrasts sharply with previous notions which have ensured either no authenticity or only universal unforgeability. For the underlying ciphers we introduce a new notion of whPRP, which extends that of PRP in the black-box setting. Interestingly, our incompressibility reductions follow from a variant of public indifferentiability. In particular, we show that a practical whPRI-secure AEAD mode can be built from a whPRP-secure block cipher: We present a SIV-like composition of the sponge construction (utilizing a block cipher as its underlying primitive) with the counter mode and prove that such a construction is (in the variant sense) public indifferentiable from a random injection. To instantiate such an AEAD scheme, we propose a 256-bit variant of SPACE, based on our conjecture that SPACE should be a whPRP-secure cipher.

Observing the growing popularity of random permutation (RP)-based designs (e.g, Sponge), Bart Mennink in CRYPTO 2019 has initiated an interesting research in the direction of RP-based pseudorandom functions (PRFs). Both are claimed to achieve beyond-the-birthday-bound (BBB) security of 2n/3 bits (n being the input block size in bits) but require two instances of RPs and can handle only oneblock inputs. In this work, we extend research in this direction by providing two new BBB-secure constructions by composing the tweakable Even-Mansour appropriately. Our first construction requires only one instance of an RP and requires only one key. Our second construction extends the first to a nonce-based Message Authentication Code (MAC) using a universal hash to deal with multi-block inputs. We show that the hash key can be derived from the original key when the underlying hash is the Poly hash. We provide matching attacks for both constructions to demonstrate the tightness of the proven security bounds.

The Sponge function is known to achieve $$2^{c/2}$$ 2 c / 2 security, where c is its capacity. This bound was carried over to its keyed variants, such as SpongeWrap, to achieve a $$\min \{2^{c/2},2^\kappa \}$$ min { 2 c / 2 , 2 κ } security bound, with $$\kappa $$ κ the key length. Similarly, many CAESAR competition submissions were designed to comply with the classical $$2^{c/2}$$ 2 c / 2 security bound. We show that Sponge-based constructions for authenticated encryption can achieve the significantly higher bound of $$\min \{2^{b/2},2^c,2^\kappa \}$$ min { 2 b / 2 , 2 c , 2 κ } , with $$b>c$$ b > c the permutation size, by proving that the CAESAR submission NORX achieves this bound. The proof relies on rigorous computation of multi-collision probabilities, which may be of independent interest. We additionally derive a generic attack based on multi-collisions that matches the bound. We show how to apply the proof to five other Sponge-based CAESAR submissions: Ascon, CBEAM/STRIBOB, ICEPOLE, Keyak, and two out of the three PRIMATEs. A direct application of the result shows that the parameter choices of some of these submissions are overly conservative. Simple tweaks render the schemes considerably more efficient without sacrificing security. We finally consider the remaining one of the three PRIMATEs, APE, and derive a blockwise adaptive attack in the nonce-respecting setting with complexity $$2^{c/2}$$ 2 c / 2 , therewith demonstrating that the techniques cannot be applied to APE.

At CRYPTO 2016, Cogliati and Seurin have proposed a highly secure nonce-based MAC called Encrypted Wegman-Carter with Davies-Meyer ($$\textsf {EWCDM}$$EWCDM) construction, as $$\textsf {E}_{K_2}\bigl (\textsf {E}_{K_1}(N)\oplus N\oplus \textsf {H}_{K_h}(M)\bigr )$$EK2(EK1(N)⊕N⊕HKh(M)) for a nonce N and a message M. This construction achieves roughly $$2^{2n/3}$$22n/3 bit MAC security with the assumption that $$\textsf {E}$$E is a PRP secure n-bit block cipher and $$\textsf {H}$$H is an almost xor universal n-bit hash function. In this paper we propose Decrypted Wegman-Carter with Davies-Meyer ($$\textsf {DWCDM}$$DWCDM) construction, which is structurally very similar to its predecessor $$\textsf {EWCDM}$$EWCDM except that the outer encryption call is replaced by decryption. The biggest advantage of $$\textsf {DWCDM}$$DWCDM is that we can make a truly single key MAC: the two block cipher calls can use the same block cipher key $$K=K_1=K_2$$K=K1=K2. Moreover, we can derive the hash key as $$K_h=\textsf {E}_K(1)$$Kh=EK(1), as long as $$|K_h|=n$$|Kh|=n. Whether we use encryption or decryption in the outer layer makes a huge difference; using the decryption instead enables us to apply an extended version of the mirror theory by Patarin to the security analysis of the construction. $$\textsf {DWCDM}$$DWCDM is secure beyond the birthday bound, roughly up to $$2^{2n/3}$$22n/3 MAC queries and $$2^n$$2n verification queries against nonce-respecting adversaries. $$\textsf {DWCDM}$$DWCDM remains secure up to $$2^{n/2}$$2n/2 MAC queries and $$2^n$$2n verification queries against nonce-misusing adversaries.

This paper presents a lightweight, sponge-based authenticated encryption (AE) family called Beetle. When instantiated with the PHOTON permutation from CRYPTO 2011, Beetle achieves the smallest footprint—consuming only a few more than 600 LUTs on FPGA while maintaining 64-bit security. This figure is significantly smaller than all known lightweight AE candidates which consume more than 1,000 LUTs, including the latest COFB-AES from CHES 2017. In order to realize such small hardware implementation, we equip Beetle with an “extremely tight” bound of security. The trick is to use combined feedback to create a difference between the cipher text block and the rate part of the next feedback (in traditional sponge these two values are the same). Then we are able to show that Beetle is provably secure up to min{c − log r, b/2, r} bits, where b is the permutation size and r and c are parameters called rate and capacity, respectively. The tight security bound allows us to select the smallest security parameters, which in turn result in the smallest footprint.

We present hash functions that are almost optimally one-way in the quantum setting. Our hash functions are based on the Merkle-Damgård construction iterating a Davies-Meyer compression function, which is built from a block cipher. The quantum setting that we use is a natural extention of the classical ideal cipher model. Recent work has revealed that symmetric-key schemes using a block cipher or a public permutation, such as CBC-MAC or the Even-Mansour cipher, can get completely broken with quantum superposition attacks, in polynomial time of the block size. Since many of the popular schemes are built from a block cipher or a permutation, the recent findings motivate us to study such schemes that are provably secure in the quantum setting. Unfortunately, no such schemes are known, unless one relies on certain algebraic assumptions. In this paper we present hash constructions that are provably one-way in the quantum setting without algebraic assumptions, solely based on the assumption that the underlying block cipher is ideal. To do this, we reduce one-wayness to a problem of finding a fixed point and then bound its success probability with a distinguishing advantage. We develop a generic tool that helps us prove indistinguishability of two quantum oracle distributions.