Slack does not have a Head of Diversity. He wants these efforts to be something “everyone is engaged in” and not “shunted off to a designated specialist,” a statement that raises the bar for all of us

Figure 1. What Does Implicit Bias Look Like in STEM?

henever the encryption scheme used for the computa-tional interpretation provides indistinguishability under chosen-ciphertext attacks(IND-CCA2 security)

hide all infor-mation about the encryption key

However, while (Q)ROM is often needed for the analysis of primitives, it is less often needed for protocols.

we use theCoSP framework (Backes, Hofheinz, and Unruh, CCS 2009)

return ()

nd

NBPES

Section ?? and ??

out(A) = out(A)

in(G) = ∅

output interface out(P)

in(P) ∩ out(P′) = ∅

provides these package

Before we prove this lemma, we explain why such a lemma is useful for proofs in the quantumrandom oracle model.

unencrypted acknowledg-ment to the group indicating that it has applied the update

all group members converge to the same view of the groupstate as they receive the same set of control messages.

alternatively, a consensus protocol could be used

WhatsApp’s group messaging protocol doesnot provide PCS [35,42].

has been adapted to thecomputational model in [14]; it uses type annotations to help the proo

We also show how our construction im-proves the efficiency of all existing tightly-secure AKE protocols.

non-interactive complexity assumption

Alice and Bob can then use a key-derivation function that includes K, K_A, and K_B to derive a symmetric key.

Q_plain

proxy and target indistinguishability

of unique per-client keys

an

Q_encrypted

key_id

context

Expand(Extract("", config), "odoh key id", Nh)

Intuitively, in order to prove that a processQ0satisfiesa non-injective correspondenceψ⇒φ, we collect all factsthat hold at events inψand show that these facts implyφusing the equational prover.

6.3. Injective CorrespondencesInjective correspondences are more difficult to checkthan non-injective ones, because they require distinguishingbetween several executions of the same event. We achievethat as follows

Actually, the modifications of games can beseen as “rewriting rules” of the probability distributions of the variables involved in the games. Theymay consist of a simple renaming of some variables, and thus to perfectly identical distributions. Theymay introduce unlikely differences, and then the distributions are “statistically” indistinguishable.Finally, the rewriting rule may be true under a computational assumption only: then appears thecomputational indistinguishability

GetKey

IsOuter

opadis 0

ParseUasX‖Ywith|X|=d

Another example is exactly the set of widestconsequence: the set of all keys of a fixed length that is less thand−1.

some applications may even have a secret salt value available for use; in such a case, HKDF provides an even stronger security guarantee.

Experimental schemes like caching pre-generated temporary keys from the clients on the servers increase the server and protocol complexity, leading to lower reliability and more potential for mistakes that impact security.

4.A.2 Security Definition for Encryption/Key-Establishment

and that is independent of the implementation of the encryptionscheme

compressed public keypk2={bi t,(t1,t2,t3)∈(Z2e2)3,A∈Fp2,ent_bi t,r∈Z256}

Does a non- negligible failure rate affect the security of TLS?

RealMOS

6.6 Conjecture: TextSecure Iron Triangle

In contrast, theorems in Abstract Cryptography can be provedat a (high) level of abstraction without the instantiation ofthe lower levels. The lower levels inherit these theorems ifthey satisfy the postulated axioms of the higher level. Eachabstraction level can thus focus on specific aspects, such ascomposability or efficiency.

To implement the X25519(k, u) and X448(k, u) functions (where k is the scalar and u is the u-coordinate), first decode k and u and then perform the following procedure

For X25519, in order to decode 32 random bytes as an integer scalar, set the three least significant bits of the first byte and the most significant bit of the last to zero, set the second most significant bit of the last byte to 1 and, finally, decode as little-endian.

The necessity ofskRbeing secure for sender authentication is due to HPKEbeing vulnerable to key-compromise impersonation.

his level is not required if one considersonly information-theoretic security

re in some cases evenwrong in technical details, thus missing the promise ofthe bottom-up approach

As a result, the algorithm enjoys a "tight" security proof in the random oracle model.

(Thus, for these curves, the cofactor is always h = 1.)

Note that by definition of the corruptionqueryCi⊆Ci+1.

findu′≤nsuchthat defined(y[u′],u1[u′],...,um[u′])∧u1[u′] =u1∧...∧um[u′] =umthenc〈y[u′]

Q|Rx≈Q|R′x

Enfin, il faut que les quatre opérateurs principaux soient obligatoirement im-pliqués dans le processus de traçage.

pourraient alors être prévenus par sms

des applications d’intelligence artificielle (IA),

The probability that the authenticated encryption function ever will be invoked with the same IV and the same key on two (or more) distinct sets of input data shall be no greater than 2-32.

learn

s

Thehealthauthorityneedstoknowwhoisatrisksothattheycannotifythem.

PRG( PRF(SK​t​, “broadcast key”) )

Itsufficeswithaddingthetarget​EphID​stothelistofobservedeventspriortouploadingittothe backend.

Inthedecentralizedsystem

Thesmartphonethenrelaysthisat-riskstatustothehealthauthoritysothatthehealthauthoritycancontactthephone’suser.

as if it was not roaming

Afterreportingtheircurrent​SK​t​,thesmartphoneoftheinfectedpatientpicksanewcompletely random key.

beablelearn the

HMAC is used with all hash functions instead of allowing hashes to use a more specialized function (e.g. keyed BLAKE2), because: HKDF requires the use of HMAC

SHA3 candidates such as Keccak and BLAKE were required to be suitable with HMAC

HKDF-Expand-Label(Secret, Label, Context, Length) = HKDF-Expand(Secret, HkdfLabel, Length)

Figure 2: Simulator forH

4 Indifferentiability of Hash Chains

WireGuard excludes zero Diffie-Hellman shared secrets to avoid points of small order, while Noiserecommends not to perform this check

In the case of password-based KDFs, a main goal is to slow down dictionary attacks using two ingredients: a salt value, and the intentional slowing of the key derivation computation. HKDF naturally accommodates the use of salt; however, a slowing down mechanism is not part of this specification.

Ideally, the salt value is a random (or pseudorandom) string of the length HashLen. Yet, even a salt value of less quality (shorter in size or with limited entropy) may still make a significant contribution to the security of the output keying material;

(and adding 'info' as an input to the extract step is not advisable -- see [HKDF-paper]).

Definition 2.1(GenericPRF-ODHassumption)

The strong DH assumption (StDH) demands that the adversary solves the computational problemof computingguvfromgu,gv, but having access to a decisional oracleDDH(gu,·,·)checking for DHtuples.

the strong Diffie–Hellman (StDH), or the even more general Gap-Diffie–Hellman (GapDH) problem

While we show that even the strongest variantis achievable in the random oracle model under the strong Diffie–Hellman assumption, we provide anegative result showing that it is implausible to instantiate even the weaker variants in the standardmodel via algebraic black-box reductions to common cryptographic problems.

D Some Practical Notes onHKDF

This is acceptable because the standard security levels are primarily driven by much simpler, symmetric primitives where the security level naturally falls on a power of two. For asymmetric primitives, rigidly adhering to a power-of-two security level would require compromises in other parts of the design, which we reject.

Designers using these curves should be aware that for each public key, there are several publicly computable public keys that are equivalent to it, i.e., they produce the same shared secrets. Thus using a public key as an identifier and knowledge of a shared secret as proof of ownership (without including the public keys in the key derivation) might lead to subtle vulnerabilities.

Protocol designers using Diffie-Hellman over the curves defined in this document must not assume "contributory behaviour". Specially, contributory behaviour means that both parties' private keys contribute to the resulting shared key. Since curve25519 and curve448 have cofactors of 8 and 4 (respectively), an input point of small order will eliminate any contribution from the other party's private key. This situation can be detected by checking for the all- zero output, which implementations MAY do, as specified in Section 6. However, a large number of existing implementations do not do this.

The check for the all-zero value results from the fact that the X25519 function produces that value if it operates on an input corresponding to a point with small order, where the order divides the cofactor of the curve (see Section 7).

Both MAY check, without leaking extra information about the value of K, whether K is the all-zero value and abort if so (see below).

n

an ECC key-establishment scheme requires the use of public keys that are affine elliptic-curve points chosen from a specific cyclic subgroup with prime order n

5.6.2.3.3ECC Full Public-Key Validation Routine

The recipient performs a successful full public-key validation of the received public key (see Sections 5.6.2.3.1for FFCdomain parameters andSection5.6.2.3.3for ECCdomain parameters).

Assurance of public-key validity –assurance that the public key of the other party (i.e., the claimed owner of the public key) has the (unique) correct representation for a non-identity element of the correct cryptographic subgroup, as determined by the

outside the subgroup

5.6.2.3.2ECC Full Public-Key Validation Routine

The recipient performs a successful full public-key validation of the received public key (see Sections 5.6.2.3.1 and 5.6.2.3.2).

Assurance of public-key validity – assurance that the public key of the other party (i.e., the claimed owner of the public key) has the (unique) correct representation for a non-identity element of the correct cryptographic subgroup, as determined by the domain parameters (see Sections 5.6.2.2.1 and 5.6.2.2.2). This assurance is required for both static and ephemeral public keys.

Misusing public keys as secrets: It might be tempting to use a pattern with a pre-message public key and assume that a successful handshake implies the other party's knowledge of the public key. Unfortunately, this is not the case, since setting public keys to invalid values might cause predictable DH output. For example, a Noise_NK_25519 initiator might send an invalid ephemeral public key to cause a known DH output of all zeros, despite not knowing the responder's static public key. If the parties want to authenticate with a shared secret, it should be used as a PSK.

Channel binding: Depending on the DH functions, it might be possible for a malicious party to engage in multiple sessions that derive the same shared secret key by setting public keys to invalid values that cause predictable DH output (as in the previous bullet). It might also be possible to set public keys to equivalent values that cause the same DH output for different inputs. This is why a higher-level protocol should use the handshake hash (h) for a unique channel binding, instead of ck, as explained in Section 11.2.

The public_key either encodes some value which is a generator in a large prime-order group (which value may have multiple equivalent encodings), or is an invalid value. Implementations must handle invalid public keys either by returning some output which is purely a function of the public key and does not depend on the private key, or by signaling an error to the caller. The DH function may define more specific rules for handling invalid values.

This check strikes a delicate balance: It checks Y sufficiently to prevent forgery of a (Y, Y^x) pair without knowledge of X, but the rejected values for X are unlikely to be hit by an attacker flipping ciphertext bits in the least-significant portion of X. Stricter checking could easily *WEAKEN* security, e.g. the NIST-mandated subgroup check would provide an oracle on whether a tampered X was square or nonsquare.

The client is relying on the server's unauthenticated DH public key Y to somehow authenticate the server's knowledge of X. Obviously, this is making an assumption about a DH that could be bad, thus is an unsafe protocol. This is Tor's (older) TAP circuit handshake (using regular DH, not ECDH). The original deployment was easily attacked by a fake server sending a public key Y = 0, 1, or -1, thus allowing the fake server to calculate Y^x without seeing X [TAP].

Thus it's an incomplete fix, and the correct solution is binding the transcript.

It's well-understood nowadays that channel binding must cover the session transcript.

A safe DH protocol is easy to instantiate with a wide range of DH algorithms, and in many cases non-DH key agreements (e.g. post-quantum algorithms, and encryption like RSA).

X25519 is very close to this ideal, with the exception that public keys have easily-computed equivalent values. (Preventing equivalent values would require a different and more costly check. Instead, protocols should "bind" the exact public keys by MAC'ing them or hashing them into the session key.)

Curve25519 key generation uses scalar multiplication with a private key "clamped" so that it will always produce a valid public key, regardless of RNG behavior.

* Valid points have equivalent "invalid" representations, due to the cofactor, masking of the high bit, and (in a few cases) unreduced coordinates.

With all the talk of "validation", the reader of JP's essay is likely to think this check is equivalent to "full validation" (e.g. [SP80056A]), where only valid public keys are accepted (i.e. public keys which uniquely encode a generator of the correct subgroup).

(1) The proposed check has the goal of blacklisting a few input values. It's nowhere near full validation, does not match existing standards for ECDH input validation, and is not even applied to the input.

If Alice generates all-zero prekeys and identity key, and pushes them to the Signal’s servers, then all the peers who initiate a new session with Alice will encrypt their first message with the same key, derived from all-zero shared secrets—essentially, the first message will be in the clear for an eavesdropper.

arguing that a zero check “adds complexity (const-time code, error-handling, and implementation variance), and is not needed in good protocols.”

Figure 7: One-phase experiment

We then considerthe same question for key-encapsulation mechanisms (KEMs)and show that in this case the fournotionsareall equivalent.

SHAKE256(96,μ‖SHAKE256(32,pk))

Asimilarstatementholdsforadditionallyhashingtheciphertextintothenalkey.Severalproto colsneedtoensurethatthekeydep endsonthecompleteviewofexchangedproto colmessages.Thisisthecase,forexample,fortheauthenticated-key-exchangeproto colsdescrib edintheKyberpap er[22,Sec.5].Hashingthefullproto colview(publickeyandciphertext)intothenalkeyalreadyaspartoftheKEMmakesitunnecessary(althoughofcoursestillsafe)totakecareofthesehashesonthehigherproto collayer

InanearlierversionofKyberweinstantiatedH,G,andPRFallwithSHAKE-256.WedecidedtochangethistodierentfunctionsfromtheFIPS-202familytoavoidanydomain-separationdiscussion.

KDF( ̄K‖H(c))

G(m‖H(pk))

weinstantiateKDFwithSHAKE-256

Asanadditionalup dateforround2,wealsopresentavariantofKyberthatinsteadofrelyingonKeccakforallsymmetricprimitives,reliesonAESandSHA-2.

These domain separators have bit patterns (0x5F=01011111,0x96=10010110) that were chosen to make it hard to use individual or consecutive bit flipping attacks to turn oneinto the other

Cryptology ePrint Archive, Report2001/108, 2001.<http://eprint.iacr.org>

SetK=KDF(Z‖PEH,KeyLen)

8.1.1 Prefix-freeness propertyAdditionally, a key encapsulation mechanism must satisfy the following property. The set of allpossible ciphertext outputs of the encryption algorithm should be a subset of acandidateset ofoctet strings (that may depend on the public key), such that the candidate set is prefix free andelements of the candidate set are easy to recognize (given either the public key or the privatekey).

DEM.Encrypt(K, L, M)

or instance, schemes that follow the CCA KEM/DEM framework are better suitable forstreaming applications where the receiver does not need to buffer the entire ciphertex

Theorem 3.1[Tag-KEM/DEM Composition Theorem] If the Tag-KEM is CCA secure and theDEM is one-time secure then the Hybrid PKE scheme in Section3is CCA secure. In particular,²pke<2²tkem+²dem.

Notethat, in the above syntactic definition,τis not included inψand explicitly given toTKEM.Dec