Salvaging Weak Security Bounds for Blockcipher-Based Constructions

The concrete security bounds for some blockcipher-based constructions sometimes become worrisome or even vacuous; for example, when a light-weight blockcipher is used, when large amounts of data are processed, or when a large number of connections need to be kept secure. Rotating keys helps, but introduces a ``hybrid factor\u27\u27 $m$ equal to the number of keys used. In such instances, analysis in the ideal-cipher model (ICM) can give a sharper picture of security, but this heuristic is called into question when cryptanalysis of the real-world blockcipher reveals weak keys, related-key attacks, etc. To address both concerns, we introduce a new analysis model, the ideal-cipher model under key-oblivious access (ICM-KOA). Like the ICM, the ICM-KOA can give sharp security bounds when standard-model bounds do not. Unlike the ICM, results in the ICM-KOA are less brittle to current and future cryptanalytic results on the blockcipher used to instantiate the ideal cipher. Also, results in the ICM-KOA immediately imply results in the ICM _and_ the standard model, giving multiple viewpoints on a construction with a single effort. The ICM-KOA provides a conceptual bridge between ideal ciphers and tweakable blockciphers (TBC): blockcipher-based constructions secure in the ICM-KOA have TBC-based analogs that are secure under standard-model TBC security assumptions. Finally, the ICM-KOA provides a natural framework for analyzing blockcipher key-update strategies that use the blockcipher to derive the new key. This is done, for example, in the NIST CTR-DRBG and in the hardware RNG that ships on Intel chips

An Analysis of the Blockcipher-Based Hash Functions from PGV

Preneel, Govaerts, and Vandewalle (1993) considered the 64 most basic ways to construct a hash function H: {0, 1}*->{0, 1}(n) from a blockcipher E: {0, 1}(n) x {0, 1}(n)->{0,1}(n). They regarded 12 of these 64 schemes as secure, though no proofs or formal claims were given. Here we provide a proof-based treatment of the PGV schemes. We show that, in the ideal-cipher model, the 12 schemes considered secure by PGV really are secure: we give tight upper and lower bounds on their collision resistance. Furthermore, by stepping outside of the Merkle-Damgard approach to analysis, we show that an additional 8 of the PGV schemes are just as collision resistant (up to a constant). Nonetheless, we are able to differentiate among the 20 collision-resistant schemes by considering their preimage resistance: only the 12 initial schemes enjoy optimal preimage resistance. Our work demonstrates that proving ideal-cipher-model bounds is a feasible and useful step for understanding the security of blockcipher-based hash-function constructions

Tweakable Blockciphers for Efficient Authenticated Encryptions with Beyond the Birthday-Bound Security

Modular design via a tweakable blockcipher (TBC) offers efficient authenticated encryption (AE) schemes (with associated data) that call a blockcipher once for each data block (of associated data or a plaintext). However, the existing efficient blockcipher-based TBCs are secure up to the birthday bound, where the underlying keyed blockcipher is a secure strong pseudorandom permutation. Existing blockcipher-based AE schemes with beyond-birthday-bound (BBB) security are not efficient, that is, a blockcipher is called twice or more for each data block. In this paper, we present a TBC, XKX, that offers efficient blockcipher-based AE schemes with BBB security, by combining with efficient TBC-based AE schemes such as ΘCB3 an

Blockcipher-based Double-length Hash Functions for Pseudorandom Oracles

The notion of PRO (pseudorandom oracle) is an important security notion of hash functions because a PRO hash function inherits all properties of a random oracle up to the PRO bound (e.g., security against generic attacks, collision resistant security, preimage resistant security and so on). In this paper, we propose a new block cipher-based double-length hash function for PROs. Our hash function uses a single block cipher, which encrypts an $n$-bit string using a $2n$-bit key, and maps an input of arbitrary length to a $2n$-bit output. Since many block ciphers supports a $2n$-bit key (e.g. AES supports a $256$-bit key), the assumption to use the $2n$-bit key length block cipher is acceptable. We prove that our hash function is PRO up to \order(2^n) query complexity as long as the block cipher is an ideal cipher. To our knowledge, this is the first time double-length hash function based on a single (practical size) block cipher with the birthday type PRO security

The Symbiosis between Collision and Preimage Resistance

We revisit the definitions of preimage resistance, focussing on the question of finding a definition that is simple enough to prove security against, yet flexible enough to be of use for most applications. We give an in-depth analysis of existing preimage resistance notions, introduce several new notions, and establish relations and separations between the known and new preimage notions. This establishes a clear separation between domain-oriented and range-oriented preimage resistance notions. For the former an element is chosen from the domain and hashed to form the target digest; for the latter the target digest is chosen directly from the range. In particular, we show that Rogaway and Shrimpton’s notion of everywhere preimage resistance on its own is less powerful than previously thought. However, we prove that in conjunction with collision resistance, everywhere preimage resistance implies ‘ordinary’ (domain-based) preimage resistance. We show the implications of our result for iterated hash functions and hash chains, where the latter is related to the Winternitz one-time signature scheme.status: publishe

Salvaging Merkle-Damgard for Practical Applications

Many cryptographic applications of hash functions are analyzed in the random oracle model. Unfortunately, most concrete hash functions, including the SHA family, use the iterative (strengthened) Merkle-Damgard transform applied to a corresponding compression function. Moreover, it is well known that the resulting ``structured\u27\u27 hash function cannot be generically used as a random oracle, even if the compression function is assumed to be ideal. This leaves a large disconnect between theory and practice: although no attack is known for many concrete applications utilizing existing (Merkle-Damgard-based) hash functions, there is no security guarantee either, even by idealizing the compression function. Motivated by this question, we initiate a rigorous and modular study of finding kinds of (still idealized) hash functions which would be (a) elegant and interesting in their own right; (b) still enough to argue security of important applications; and (c) provably instantiable by the (strengthened) Merkle-Damgard transform, applied to a strong enough compression function. We develop two such notions which we believe are natural and interesting in their own right: preimage awareness and being indifferentiable from a public-use random oracle

Analyzing Multi-key Security Degradation

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Security Analysis of NIST CTR-DRBG

We study the security of CTR-DRBG, one of NIST\u27s recommended Pseudorandom Number Generator (PRNG) designs. Recently, Woodage and Shumow (Eurocrypt\u27 19), and then Cohney et al. (S&P\u27 20) point out some potential vulnerabilities in both NIST specification and common implementations of CTR-DRBG. While these researchers do suggest counter-measures, the security of the patched CTR-DRBG is still questionable. Our work fills this gap, proving that CTR-DRBG satisfies the robustness notion of Dodis et al. (CCS\u2713), the standard security goal for PRNGs

Identity-Based Format-Preserving Encryption

We introduce identity-based format-preserving encryption (IB-FPE) as a way to localize and limit the damage to format-preserving encryption (FPE) from key exposure. We give definitions, relations between them, generic attacks and two transforms of FPE schemes to IB-FPE schemes. As a special case, we introduce and cover identity-based tweakable blockciphers. We apply all this to analyze DFF, an FPE scheme proposed to NIST for standardization

Design and Analysis of Multi-Block-Length Hash Functions

Cryptographic hash functions are used in many cryptographic applications, and the design of provably secure hash functions (relative to various security notions) is an active area of research. Most of the currently existing hash functions use the Merkle-Damgård paradigm, where by appropriate iteration the hash function inherits its collision and preimage resistance from the underlying compression function. Compression functions can either be constructed from scratch or be built using well-known cryptographic primitives such as a blockcipher. One classic type of primitive-based compression functions is single-block-length : It contains designs that have an output size matching the output length n of the underlying primitive. The single-block-length setting is well-understood. Yet even for the optimally secure constructions, the (time) complexity of collision- and preimage-finding attacks is at most 2n/2, respectively 2n ; when n = 128 (e.g., Advanced Encryption Standard) the resulting bounds have been deemed unacceptable for current practice. As a remedy, multi-block-length primitive-based compression functions, which output more than n bits, have been proposed. This output expansion is typically achieved by calling the primitive multiple times and then combining the resulting primitive outputs in some clever way. In this thesis, we study the collision and preimage resistance of certain types of multi-call multi-block-length primitive-based compression (and the corresponding Merkle-Damgård iterated hash) functions : Our contribution is three-fold. First, we provide a novel framework for blockcipher-based compression functions that compress 3n bits to 2n bits and that use two calls to a 2n-bit key blockcipher with block-length n. We restrict ourselves to two parallel calls and analyze the sufficient conditions to obtain close-to-optimal collision resistance, either in the compression function or in the Merkle-Damgård iteration. Second, we present a new compression function h: {0,1}3n → {0,1}2n ; it uses two parallel calls to an ideal primitive (public random function) from 2n to n bits. This is similar to MDC-2 or the recently proposed MJH by Lee and Stam (CT-RSA'11). However, unlike these constructions, already in the compression function we achieve that an adversary limited (asymptotically in n) to O (22n(1-δ)/3) queries (for any δ > 0) has a disappearing advantage to find collisions. This is the first construction of this type offering collision resistance beyond 2n/2 queries. Our final contribution is the (re)analysis of the preimage and collision resistance of the Knudsen-Preneel compression functions in the setting of public random functions. Knudsen-Preneel compression functions utilize an [r,k,d] linear error-correcting code over 𝔽2e (for e > 1) to build a compression function from underlying blockciphers operating in the Davies-Meyer mode. Knudsen and Preneel show, in the complexity-theoretic setting, that finding collisions takes time at least 2(d-1)n2. Preimage resistance, however, is conjectured to be the square of the collision resistance. Our results show that both the collision resistance proof and the preimage resistance conjecture of Knudsen and Preneel are incorrect : With the exception of two of the proposed parameters, the Knudsen-Preneel compression functions do not achieve the security level they were designed for