# Questions tagged [reduction]

Reduction is a technique for proving the security of a cryptosystem.

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### Proving an identification-scheme based on a digital signature is secure

I am trying to prove to myself that an identification scheme derived from a digital signature in a challenge/response manner is secure, based on the security of the digital signature scheme. I've ...
41 views

### worst case to average case reduction in non-cyclotomic Ring LWE

I understand that we need 2-to-power cyclotomic ring to show that the solving decision RLWE is as hard as solving search RLWE. Is there any chance to prove it without 'cyclotomic' property? For ...
93 views

### The rigorous proof in the commitment based on CRHF

I'm reading about the lecture of Yevgeniy Dodis. In his lecture 14, section 2.3.2, gives a commitment construction based on CRHF, but the proof of hiding is high-level. I want to know the rigorous ...
45 views

### Reduction from Distinguisher to Indishtinguishability

Content and Informal Problem Suppose a protocol $\pi$ doing an arbitrary task between two users A and B. I only know that $\pi$ relies on a IND-CPA symmetric encryption scheme $\mathcal{E} =$(KeyGen, ...
234 views

### Reducing exact SVP to exact SIVP

In "Efficient reductions among lattice problems" by Micciancio (2007) it is said, that SVP reduces to SIVP in their exact versions. I did not found anything about this fact, is a reduction ...
171 views

### How does the lengths of the Gram-Schmidt orthogonal basis of a lattice basis change after lll reduction?

Assuming there is a lattice basis $B=\{b_1,...,b_n\}$, we use $B^*=\{b_1^*,...,b_n^*\}$ to denote the Gram-Schmidt orthogonal basis, where $b_i^*=\pi_i(b_i)$ and $\pi_i(b_i)$ denotes the projection of ...
205 views

I have an idea but I don't know if it will work. For the appropriate $p$ it is easy to find $n$ linearly independent $x_i$. Then we compute the inner product between the $x_i$. I think the information ...
432 views

### What does 'a reduction is tight' mean rigorously?

As far as I know, when someone says 'a reduction is tight', it means that given that there is an adversary $A$ with advantage $\epsilon$ and running time $t$ and another adversary $B$ utilizing $A$ ...
186 views

### What does break with "usual" classical security reductions in quantum setting?

OK, so I know that this is somewhat really basic in "post-quantum discourse", but unfortunately I did not find any textbooks/entry level papers specific to the topic of reductions in the ...
1 vote
29 views

### Prove security against passive attacks by reduction

I have two private-key encryption ($Π$ and $Θ$) and their concatenation $Π\#Θ$. For example: $$Enc_{Π\#Θ}( \ ⟨k_Π, k_Θ⟩, \ ⟨m_Π, m_Θ⟩ \ ) = ⟨ \ Enc_Π(k_Π, m_Π),\ Enc_Θ(k_Θ, m_Θ) \ ⟩;$$ (Same for ...
1 vote
178 views

### Proving semantic security implies security from key-recovery attack

I am working on problem 2.11 from the book: A Graduate Course in Applied Cryptography by Dan Boneh and Victor Shoup. The problem reads as follows: Problem 2.11: Let $\mathcal{E} = (E, D)$ be a cipher ...
595 views

### Security reduction seems to wrongly show that a non-PRF is a PRF

This is a well-known exercise that has already even been posted here. I understand both arguments to prove and disprove that $F'$ and $\bar{F}$ are PRFs, as I explain below, however, it seems that the ...
98 views

### In reduction from search LWE to decsion LWE why sampling needs to repeat a polynomial number of times?

I've been reading through MIT's lecture notes on learning with errors here, and I'm trying to understand the reduction from Search LWE to Decision LWE, as described there in Section 2.7, "...
1 vote
94 views

### Private key encryption based on NP-complete problem

Over a decade ago, a question was asked on Stack Overflow, which basically asked if there were any encryption schemes that are reducible to an NP-complete problem, in the sense that breaking the ...
100 views

### How to reduce Diffie Hellman problem to ElGamal?

I'm trying to answer without success questions (ii - iv) Any hint will be appreciated :)
61 views

### Meta Reduction in Fiat Shamir Transformation

What is meant by meta reduction? What does it achieve and how is it different from the normal reduction technique?