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# ZK Hash Function Cryptanalysis Bounties

## Terms

Task: find $X1,X2,Y1,Y2$ such that $\displaystyle Perm(X1,X2,0)=(Y1,Y2,0)$

where $Perm$ is the inner sponge permutation (bijective mapping) of the hash function the challenge list.

• Solutions should be sent to Dmitry Khovratovich before November 30th 2022.
• First come first win.
• Within 1 month after the submission the authors should provide a technical report with the attack description, which should be released to the public domain at latest December 1st 2022. The code should be also made public before this date.
• Total Bounty Budget: $200,000 USD. • Parameters are fixed on November 23rd 2021. ## Rescue Prime Design spec. • $p=18446744073709551557 \text{\textasciitilde} 2^{64}$ • $m=3$ • $alpha=3$ • Number of rounds: $N$ • Brute force attack complexity: $2^{64}$ We expect that a variant with $s$ bits of security to withstand attacks of complexity up to $2^{1.5s}$ time (function calls) and memory. Reference implementation and bounty instances. CategoryParametersSecurity Level (bits)Bounty Easy$\sout{N=4, m=3}$25$2,000
Easy$N=6, m=2$25$4,000 Medium$N=7, m=2$29$6,000
Hard$N=5, m=3$30$12,000 Hard$N=8, m=2$33$26,000

## Feistel-MIMC

Design spec.

• $p=18446744073709551557 \text{\textasciitilde} 2^{64}$
• $alpha=3$
• Task: find $X,Y$ such that $Feistel\text{\textendash}MiMC(X,0)=(Y,0)$
• Number of rounds: $r$
• Brute force attack complexity: $2^{64}$

We expect that a variant with $s$ bits of security to withstand attacks of complexity up to $2^{2s}$ time (function calls) and memory.

The initial parameters were broken and were replaced.

Reference implementation and bounty instances.

Easy$\sout{N=4, m=3}$25$2,000 Easy$N=6, m=2$25$4,000
Medium$N=7, m=2$29$6,000 Hard$N=5, m=3$30$12,000
Hard$N=8, m=2$33$26,000 ## Poseidon Design spec. • $p=18446744073709551557 \text{\textasciitilde} 2^{64}$ • $d=3$ • $t=3$ • Number of full rounds: $RF=8$ • Number of partial rounds $RP$ varies (see below) • Brute force attack complexity: $2^{64}$ We expect that a variant with $s$ bits of security to withstand attacks of complexity up to $2^{s+37}$ time (function calls) and memory. The initial parameters were broken and were replaced. Reference implementation and bounty instances. CategoryParametersSecurity Level (bits)Bounty Easy$\sout{RP=3}$8$2,000
Easy$\sout{RP=8}$16$4,000 Medium$\sout{RP=13}$24$6,000
Hard$RP=19$32$12,000 Hard$RP=24$40$26,000

## Reinforced Concrete

Design spec.

• Number of layers as in the original design
• Different prime field
• The best attack we have found for these variants is exhaustive search.
• Groebner basis challenges might be declared additionally.

We expect that a variant with $s$ bits of security to withstand attacks of complexity up to $2^{2s}$ time (function calls) and memory.

Decomposition and alpha/beta values.

Reference implementation and bounty instances.

Easy$p=281474976710597$24$4,000 Hard$p=72057594037926839$28$6,000
Hard$p=18446744073709551557$32\$12,000