Questions on the meaning, history, and usage of symbols and notation in cryptography. Please remember to mention where (book, paper, webpage, etc.) you encountered any notation you are asking about.
Questions tagged [notation]
107 questions
29
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What exactly is a negligible (and non-negligible) function?
The mathematical definition of neglible and non-neglible functions is fairly clear-cut, but why they are important and how they are used in cryptography?
Nico Bellic
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26
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4 answers
Why does key generation take an input $1^k$, and how do I represent it in practice?
In my lecture, the lecturer said:
Let $K$ be the key generation algorithm. Given a security parameter represented in unary, $1^k$, $K(1^k)$ will output a keypair $(pk; sk)$, known as the public key and the private (or secret) key, respectively.…
juaninf
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17
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How did || come to be used in crypto texts to represent concatenation?
In RFC5647, NIST SP 800-38D, etc., || is used to denote concatenation. How did that come to be?
In most programming languages || represents "or" and + denotes concatenation and the fact that crypto texts just kind of mixed it up seems to make for an…
neubert
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15
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What the X stands for in the front of Elliptic curve names like X25519
I have seen Curve25519 and X25519, Curve448 and X448. I've seen a small note in this answer
(Historical note: Originally, X25519 was called Curve25519, but now Curve25519 just means the elliptic curve and X25519 means the cryptosystem.)
Is it a…
kelalaka
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12
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Encoding vs. Compression vs. Encryption
In what ways does encryption differ from proprietary/secret compression schemes and codecs?
ProductionValues
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11
votes
1 answer
Why do crypto tools display key components in such an unusual format?
openssl x509 (v1.0.1f) displays public key moduli as arrays of hex-encoded bytes, 15 columns wide, starting with a leading 00::
Subject Public Key Info:
Public Key Algorithm: rsaEncryption
Public-Key: (1024 bit)
…
Dan Lenski
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11
votes
1 answer
How can I instantiate a generalized hash function?
I've come across a bunch of "strange" hash function notations, such as the following ones and now I don't know how to choose / instantiate them.
Can you please explain me what this notation means and how I can actually instantiate such a hash…
SEJPM
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10
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2 answers
Why is the polynomial of an LFSR called so?
As far as I understand, the "polynomial" of the LFSR tells us the positions of the register where taps are situated.
However, the natural way to look at the positions would be to think of them as $x_1, x_2, x_3,\cdots$. But we instead identify them…
Agnishom Chattopadhyay
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9
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What does "$<\!\!<\!\!<$" mean?
What does the symbol $<\!\!<\!\!<$ mean? It is normally followed by a number. An example:
It would be appreciated if you could explain it in fairly basic terms.
Nat
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9
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1 answer
What is the recommended format/notation for crypto design?
Is there a recommended format or formal notation for documenting the combination of symmetric and asymmetric encryption, key derivation and other algorithms (and their inputs and outputs) that I think meet the needs of the software I'm contributing…
Oli
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8
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1 answer
What does the $\|$ operation mean in cryptographic notation?
I am studying elliptic curves problems, which also includes study of related protocols such as ECIES. The problem is that I don't understand the notation $\|$. What does this operation mean?
Some stuff is mentioned on Wikipedia's Integration…
eXPi
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8
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2 answers
What does ⊕ mean in cryptography?
Can someone please help me with the question below?
Explain why 0 ⊕ x ≠ 1 ⊕ x, whatever the value of the bit x.
Hence, explain why flipping a bit in the plaintext produces a predictable
change in the ciphertext when using a stream cipher that XORs…
linux44
7
votes
1 answer
What does the expression $1^n$ mean as a function argument?
In a paper about predicate encryption or attribute based encryption, the setup function is mentioned with the $setup(1^n)$ or $setup(1^l)$. I want to know what is meant here.
Is it multiples of ones or representing something else?
Also, why is this…
s.venkatesan
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7
votes
1 answer
Why is the BSI not using powers of two?
In their Technical Guideline TR-02102-2 Cryptographic Mechanisms: Recommendations and Key Lengths the BSI is giving minimal key lengths for - e.g. the TLS handshake protocol. All of these are not integers that are a power of two. I always thought,…
Tom K.
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7
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2 answers
Probability conventions in cryptography
I am working on Victor Shoup's tutorial on game-based security proof and want to figure out some notions from the perspective of probability theory.
Consider the following PRF advantage defined on Page 11:
$$
\bigl|\,\Pr[s \leftarrow S: A^{F_s}() =…
X. G.
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