Complexity describes - in simple words - how hard (complex) it is to reach a specific goal; and under which conditions. In cryptography, this mostly ends up in using the complexity theory to analyze things. One of the main goals of complexity theory is to prove lower bounds on the resources (e.g. ...

learn more… | top users | synonyms

1
vote
1answer
23 views

Time complexity of looking up in a rainbow table

It is mentioned in the famous paper Making a Faster Cryptanalytic Time-Memory Trade-Off (pdf) by Philippe Oechslin that: The total number of calculations we have to make is thus $\frac{t(t−1)}{2}...
0
votes
1answer
35 views

Can a low density subset sum problem be intractable?

Hardness of a subset sum problem depends on it's density. Is it possible for a subset sum problem to be intractable even if it's density is less than 0.9408?
0
votes
1answer
157 views

Performance of Fully homomorphic encryption VS Paillier encryption in Practice

Consider two schemes both have computation complexity linear to the input size (i.e. number of inputs). One scheme is based on Paillier encryption and the other one is based on fully homomorphic ...
5
votes
0answers
46 views

Quantum complexity of LWE

As per my understanding LWE is quantum secure because there is no known quantum algorithm to solve LWE in polynomial time. Due to the reductions given by Regev et al. If there is any algorithm that ...
3
votes
0answers
37 views

Computing cost for a trillionaire to compute GNFS in RFC 3766

RFC 3766, Section 4.1 discusses picking $n$ to achieve some target cost for employing the GNFS, i.e., $T$ is known and $N$ is unknown in the below equation: $$T = \kappa \cdot \exp{\left(c \cdot (\ln{...
3
votes
0answers
64 views

Majority encryption algorithm?

Assume that I want to leave an encrypted message to a group of $n$ people in a way that they can only decrypt it if they work together in the following sense: For some fixed $k < n$ every sub-...
3
votes
0answers
70 views

P-Complete hashes, hashing to a larger set

Historically hashes have been from a large set (say 256 characters) to a smaller set (256 bits). Also, hash functions that are P-complete have no known parallel algorithm; they must be computed ...
2
votes
0answers
37 views

DSSP reduction to DSSI

In “Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies" by DeFeo, Jao and Plut, a reduction from the Decisional Supersingular Product (DSSP) problem to Decisional ...
1
vote
0answers
166 views

Complexity of verifying OTP secret

What is the minimum number of unique pairs of digests and inputs to a one-time pass needed to verify that a secret is equal to a ...
1
vote
0answers
129 views

How to develop a public key cryptosystem based on a hard problem?

Recently, I found a function that is performed on a sequence to return another sequence. All known algorithms for finding the input, given the output are of exponential complexity. I want to propose ...
0
votes
0answers
45 views

Best/average/worst-case complexity for cryptography

I understand that the complexity of a problem can be measured by it's best-case, average-case, or worst-case complexity. Am I correct in thinking that, for cryptographic purposes, each of these is of ...
0
votes
0answers
123 views

Complexity using RSA

You encrypt a message using the RSA encryption system as $t^e \pmod n$ , where $t, e < n$ and $t$ is the numerical equivalent of the message. The message is written in a $27$-letter alphabet and is ...