From 5a6992455ed6a38e3af84bff43ed2336332202cc Mon Sep 17 00:00:00 2001 From: Michael Zhu Date: Mon, 15 Apr 2024 20:17:52 -0400 Subject: [PATCH 1/8] Reorganize 'how' and 'background' sections, jolt.md --- Cargo.toml | 6 +- book/src/SUMMARY.md | 9 +- book/src/background.md | 2 + book/src/{how => background}/gkr.md | 0 .../{how => background}/memory-checking.md | 0 book/src/how/bytecode.md | 1 + book/src/how/instruction_lookups.md | 50 +++++++++++ book/src/how/jolt.md | 79 +++++------------- book/src/how/lookups.md | 7 -- .../{constraints.md => r1cs_constraints.md} | 0 book/src/how/read_write_memory.md | 11 +++ book/src/how_it_works.md | 9 +- book/src/imgs/figure2.png | Bin 0 -> 188571 bytes 13 files changed, 98 insertions(+), 76 deletions(-) rename book/src/{how => background}/gkr.md (100%) rename book/src/{how => background}/memory-checking.md (100%) create mode 100644 book/src/how/bytecode.md create mode 100644 book/src/how/instruction_lookups.md delete mode 100644 book/src/how/lookups.md rename book/src/how/{constraints.md => r1cs_constraints.md} (100%) create mode 100644 book/src/how/read_write_memory.md create mode 100644 book/src/imgs/figure2.png diff --git a/Cargo.toml b/Cargo.toml index 3113bb0b4..dc682494a 100644 --- a/Cargo.toml +++ b/Cargo.toml @@ -80,6 +80,6 @@ inherits = "release" debug = false [patch.crates-io] -ark-ff = { git = "https://github.com/a16z/arkworks-algebra", branch = "optimize/field-from-u64" } -ark-ec = { git = "https://github.com/a16z/arkworks-algebra", branch = "optimize/field-from-u64" } -ark-serialize = { git = "https://github.com/a16z/arkworks-algebra", branch = "optimize/field-from-u64" } +ark-ff = { path = "../algebra/ff" } +ark-ec = { path = "../algebra/ec" } +ark-serialize = { path = "../algebra/serialize" } diff --git a/book/src/SUMMARY.md b/book/src/SUMMARY.md index 3260129af..946f278cf 100644 --- a/book/src/SUMMARY.md +++ b/book/src/SUMMARY.md @@ -11,15 +11,18 @@ - [Troubleshooting](./usage/troubleshooting.md) - [Contributors](./contributors.md) - [How it works](./how_it_works.md) - - [Lookups](./how/lookups.md) - - [Memory Checking](./how/memory-checking.md) - - [GKR](./how/gkr.md) - [Jolt](./how/jolt.md) + - [Instruction lookups](./how/instruction_lookups.md) + - [Read-write memory](./how/read_write_memory.md) + - [Bytecode](./how/bytecode.md) + - [R1CS constraints](./how/r1cs_constraints.md) - [Background](./background.md) - [Sumcheck](./background/sumcheck.md) - [Multilinear Extensions](./background/multilinear-extensions.md) - [Eq Extension](./background/eq-polynomial.md) - [Batched Polynomial Openings](./background/batched-openings.md) + - [Memory Checking](./background/memory-checking.md) + - [GKR](./background/gkr.md) - [Dev](./dev/README.md) - [Install](./dev/install.md) - [Tools](./dev/tools.md) diff --git a/book/src/background.md b/book/src/background.md index 269f4c360..928044346 100644 --- a/book/src/background.md +++ b/book/src/background.md @@ -1,5 +1,7 @@ # Background If you're interested in learning the nitty gritty details of SNARKs including questions like 'why', 'is it sound', you should read [Proofs and Args ZK](https://people.cs.georgetown.edu/jthaler/ProofsArgsAndZK.pdf) by Thaler. If you're simply interested in 'how', this section is for you. - [Sumcheck](./background/sumcheck.md) +- [GKR](./background/gkr.md) - [Multilinear Extensions](./background/multilinear-extensions.md) - [EQ Polynomial](./background/eq-polynomial.md) +- [Memory Checking](./background/memory-checking.md) \ No newline at end of file diff --git a/book/src/how/gkr.md b/book/src/background/gkr.md similarity index 100% rename from book/src/how/gkr.md rename to book/src/background/gkr.md diff --git a/book/src/how/memory-checking.md b/book/src/background/memory-checking.md similarity index 100% rename from book/src/how/memory-checking.md rename to book/src/background/memory-checking.md diff --git a/book/src/how/bytecode.md b/book/src/how/bytecode.md new file mode 100644 index 000000000..30404ce4c --- /dev/null +++ b/book/src/how/bytecode.md @@ -0,0 +1 @@ +TODO \ No newline at end of file diff --git a/book/src/how/instruction_lookups.md b/book/src/how/instruction_lookups.md new file mode 100644 index 000000000..120af68df --- /dev/null +++ b/book/src/how/instruction_lookups.md @@ -0,0 +1,50 @@ + +## Details on using Lasso to handle instruction execution + +Lasso requires that each primitive instruction satisfies a decomposability property. +The property needed is that the input(s) to the instruction can be broken into "chunks" (say, with each chunk +consisting of 16 bits), such that one can obtain the answer to the original instruction by +evaluating a simple function or functions on each chunk and then "collating" the results together. +For example, the bitwise-OR of two 32-bit inputs x and y can be computed by breaking each input up into 8-bit chunks, XORing +each 8-bit chunk of x with the associated chunk of y, and concatenating the results together. + +In Lasso, we call the task of evaluating a simple function on each chunk "subtable lookups" (the relevant lookup table +being the table storing all $2^{16}$ evaluations of the simple function). And the "collating" of +the results of the subtable lookups into the result of the original lookup (instruction execution on the un-chunked inputs) +is handled via an invocation of the sum-check protocol. We call this the "primary sumcheck" instance in Lasso. + +The "primary sumcheck" collation looks as follows for a trace of length $m$ and a VM with $f$ unique instructions. + +$\sum_{x \in `\{0,1\}`^{log(m)}} [\widetilde{eq}(r,x) \cdot \sum_{f \in `\{0,1\}`^{log(F)}} {\widetilde{flags_f}(x) \cdot g_f(\text{terms}_f(x))]}$ + +$\widetilde{flags_f}(x) = 1$ if the $f$-th instruction is used during the $x$-th step of the trace when. $x \in `\{0,1\}`^{log(m)}$ + +$g_f(...)$ is the collation function used by the $f$-th instruction. + +$terms_f(x) = [E_1(x), ... E_\alpha(x)]$ where $\alpha$ is the number of independent memories used by an instruction. For simple instructions like the EQ instruction, $\alpha = C$, $terms_f(x) = [E_1(x), ... E_C(x)]$. More complicated instructions such LT might have $terms_f(x) = [E_{eq}(x), E_{lt1}(x), E_{lt2}(x)]$. The exact layout is dependent on the number of subtables required by the decomposition of the instruction. The mappings can be found in the `JoltInstruction::subtable` method implementations. + +### Mental Model +For a given $r = x \in `\{0,1\}`^{log(m)}$ (think integer index of the instruction within the trace), $\widetilde{\text{eq}} = 0$ for all but one term of the outer sum. Similarly all $\widetilde{\text{flags}_f}(x) = 0$ for all but one term of the inner sum. Leaving just the collation function of a single instruction, evaluating to the collated lookup output of the single instruction. In reality $r$ is a random point $r \in \mathbb{F}^{log(m)}$ selected by the verifier over the course of the protocol. The evaluation point provides a distance amplified encoding of the entire trace of instructions. + + +To illustrate more concretely imagine a two-instruction VM for LT and EQ instructions with $C=1$. + +$$ +\sum_{x \in \{0, 1\}^{\log_2(m)}}{\widetilde{\text{eq}}(r,x) \cdot \left[ \widetilde{\text{flags}}_{\texttt{LT}}(x) \cdot g_{\texttt{LT}}(E_{\texttt{LT}}(x)) + \widetilde{\text{flags}}_{\texttt{EQ}}(x) \cdot g_{\texttt{EQ}}(E_{\texttt{EQ}}(x)) \right]} +$$ + + +## Subtable Flags +`TODO` +- We then use memory checking to determine that each of the memories $E_i$ is well formed +- At a given step of the CPU only a single instruction will be used, that means that only that instruction's subtables will be used. For the rest of the memories we insert a no_op with (a, v) = 0. In order to make the GKR trees cheaper to compute and sumcheck we'll add a single additional layer to the GKR tree. During this layer we'll "toggle" each of the GKR leaves to "1" in the case that it is an unused step of the CPU. This will make the binary tree of multiplication gates cheaper. We'll toggle based on a new flags polynomial called $subtable-flags_f$ which is the sum of all of the $instruction-flags_f$ used in the instruction collation above. +- The function to compute each of the leaves becomes $leaf[i] = \text{subtable-flags}[i] \cdot \text{fingerprint}[i] + (1 - \text{subtable-flags}[i])$ + + +# Lookups +Lasso is a lookup argument (equivalent to a SNARK for reads into a read-only memory). Lookup arguments allow the prover to convince the verifier that a (committed) set of values $Q$ is a subset of a lookup table $T$. Lasso is a special lookup argument with highly desirable asymptotic costs largely correlated to the number of queries $Q$ rather than the length of of the table $T$. + +A conversational background on lookups can be found [here](https://a16zcrypto.com/posts/article/building-on-lasso-and-jolt/). In short: Lookups are great for zkVMs as they allow constant cost / developer complexity for the prover algorithm per VM instruction. + +## Lasso +A detailed engineering overview of Lasso can be found [here](https://www.youtube.com/watch?v=iDcXj9Vx3zY). diff --git a/book/src/how/jolt.md b/book/src/how/jolt.md index 51ef95774..c5d6200ce 100644 --- a/book/src/how/jolt.md +++ b/book/src/how/jolt.md @@ -1,79 +1,40 @@ # Jolt -*Note: This section is still under construction. Expect more details in the future.* -`TODO` -- 3 phases of memory checking + primary sumcheck + r1cs -- subtable flags -> instruction flags -- R1CS checks -- -================== -## Jolt's three components +This section gives an overview of the core components of Jolt. -A VM does two things: - -a. Repeatedly execute the fetch-decode-execute logic of its instruction set architecture. - -b. Perform reads and writes to Random Access Memory (RAM). - -Accordingly, Jolt has three components: - -1. To handle the "execute" part of each fetch-decode-execute loop, it invokes the Lasso lookup argument. -2. To handle reads/writes to RAM (and to registers) it uses a memory-checking argument from Spice, which is closely related to Lasso itself. They are both based on "offline memory checking" techniques, the main difference being that Lasso supports read-only memory while [Spice](https://eprint.iacr.org/2018/907.pdf) supports read-write memory, making it slightly more expensive. -3. To handle the "fetch-decode" part of each fetch-decode-execute loop, and to capture some extra constraints not directly handled by Lasso itself, there is a minimal R1CS instance ( about 60 constraints per cycle of the RISC-V VM). - -To prove satisfaction of the R1CS in (3), Jolt uses [Spartan](https://eprint.iacr.org/2019/550), optimized for the highly-structured nature of the constraint system (e.g., the R1CS constraint matrices are block-diagonal with blocks of size only about 60 x 80). +## Jolt's four components +A VM does two things: -## Details on using Lasso to handle instruction execution - -Lasso requires that each primitive instruction satisfies a decomposability property. -The property needed is that the input(s) to the instruction can be broken into "chunks" (say, with each chunk -consisting of 16 bits), such that one can obtain the answer to the original instruction by -evaluating a simple function or functions on each chunk and then "collating" the results together. -For example, the bitwise-OR of two 32-bit inputs x and y can be computed by breaking each input up into 8-bit chunks, XORing -each 8-bit chunk of x with the associated chunk of y, and concatenating the results together. - -In Lasso, we call the task of evaluating a simple function on each chunk "subtable lookups" (the relevant lookup table -being the table storing all $2^{16}$ evaluations of the simple function). And the "collating" of -the results of the subtable lookups into the result of the original lookup (instruction execution on the un-chunked inputs) -is handled via an invocation of the sum-check protocol. We call this the "primary sumcheck" instance in Lasso. - -The "primary sumcheck" collation looks as follows for a trace of length $m$ and a VM with $f$ unique instructions. - -$\sum_{x \in `\{0,1\}`^{log(m)}} [\widetilde{eq}(r,x) \cdot \sum_{f \in `\{0,1\}`^{log(F)}} {\widetilde{flags_f}(x) \cdot g_f(\text{terms}_f(x))]}$ - -$\widetilde{flags_f}(x) = 1$ if the $f$-th instruction is used during the $x$-th step of the trace when. $x \in `\{0,1\}`^{log(m)}$ +- Repeatedly execute the fetch-decode-execute logic of its instruction set architecture. +- Perform reads and writes to Random Access Memory (RAM). -$g_f(...)$ is the collation function used by the $f$-th instruction. +The Jolt paper depicts these two tasks mapped to three components in the final Jolt proof: -$terms_f(x) = [E_1(x), ... E_\alpha(x)]$ where $\alpha$ is the number of independent memories used by an instruction. For simple instructions like the EQ instruction, $\alpha = C$, $terms_f(x) = [E_1(x), ... E_C(x)]$. More complicated instructions such LT might have $terms_f(x) = [E_{eq}(x), E_{lt1}(x), E_{lt2}(x)]$. The exact layout is dependent on the number of subtables required by the decomposition of the instruction. The mappings can be found in the `JoltInstruction::subtable` method implementations. +![Jolt Alpha](../imgs/figure2.png) -### Mental Model -For a given $r = x \in `\{0,1\}`^{log(m)}$ (think integer index of the instruction within the trace), $\widetilde{eq} = 0$ for all but one term of the outer sum. Similarly all $\widetilde{flags_f}(x) = 0$ for all but one term of the inner sum. Leaving just the collation function of a single instruction, evaluating to the collated lookup output of the single instruction. In reality $r$ is a random point $r \in \mathbb{F}^{log(m)}$ selected by the verifier over the course of the protocol. The evaluation point provides a distance amplified encoding of the entire trace of instructions. +The Jolt codebase is similarly organized, but instead separates read-write memory (comprising registers and RAM) from program code (aka bytecode, which is read-only), for a total of four components: +### Read-write memory -To illustrate more concretely imagine a two-instruction VM for LT and EQ instructions with $C=1$. +To handle reads/writes to RAM (and registers) Jolt uses a memory checking argument from Spice, which is closely related to Lasso itself. They are both based on "offline memory checking" techniques, the main difference being that Lasso supports read-only memory while [Spice](https://eprint.iacr.org/2018/907.pdf) supports read-write memory, making it slightly more expensive. This is implemented in [`read_write_memory.rs`](../../../jolt-core/src/jolt/vm/read_write_memory.rs). -$$ -\sum_{x \in \`\{0,1\\}`^{\log_2(m)}}{\widetilde{eq}(r,x) \cdot [ \widetilde{flags}_{LT}(x) \cdot g_{LT}(E_{LT}(x)) + \widetilde{flags}_{EQ}(x) \cdot g_{EQ}(E_{EQ}(x))]} -$$ +*For more details: [Read-write memory](./read_write_memory.md)* +### R1CS constraints -## Subtable Flags -`TODO` -- We then use memory checking to determine that each of the memories $E_i$ is well formed -- At a given step of the CPU only a single instruction will be used, that means that only that instruction's subtables will be used. For the rest of the memories we insert a no_op with (a, v) = 0. In order to make the GKR trees cheaper to compute and sumcheck we'll add a single additional layer to the GKR tree. During this layer we'll "toggle" each of the GKR leaves to "1" in the case that it is an unused step of the CPU. This will make the binary tree of multiplication gates cheaper. We'll toggle based on a new flags polynomial called $subtable-flags_f$ which is the sum of all of the $instruction-flags_f$ used in the instruction collation above. -- The function to compute each of the leaves becomes $leaf[i] = \text{subtable-flags}[i] \cdot \text{fingerprint}[i] + (1 - \text{subtable-flags}[i])$ +To handle the "fetch" part of the fetch-decode-execute loop, there is a minimal R1CS instance (about 60 constraints per cycle of the RISC-V VM). These constraints handle program counter (PC) updates and serves as the "glue" enforcing consistency between polynomials used in the components below. Jolt uses [Spartan](https://eprint.iacr.org/2019/550), optimized for the highly-structured nature of the constraint system (e.g., the R1CS constraint matrices are block-diagonal with blocks of size only about 60 x 80). This is implemented in [jolt-core/src/r1cs](../../../jolt-core/src/r1cs/). +*For more details: [R1CS constraints](./r1cs_constraints.md)* -## Read Write Memory (VM RAM) +### Instruction lookups -In contrast to our standard procedures for offline memory checking, the registers and RAM within this context are considered *writable* memory. This distinction introduces additional verification requirements: +To handle the "execute" part of the fetch-decode-execute loop, Jolt invokes the Lasso lookup argument. The lookup argument maps every instruction (including its operands) to its output. This is implemented in [instruction_lookups.rs](../../../jolt-core/src/jolt/vm/instruction_lookups.rs). -- The multiset equality typically expressed as $I \cdot W = R \cdot F$ is not adequate for ensuring the accuracy of read values. It is essential to also verify that each read operation retrieves a value that was written in a previous step. +*For more details: [Instruction lookups](./instruction_lookups.md)* -- To formalize this, we assert that the timestamp of each read operation, denoted as $\text{read\_timestamp}$, must not exceed the global timestamp at that particular step. The global timestamp is a monotonically increasing sequence starting from 0 and ending at $\text{TRACE\_LENGTH}$. +### Bytecode -- The verification of $\text{read\_timestamp} \leq \text{global\_timestamp}$ is equivalent to confirming that $\text{read\_timestamp}$ falls within the range $[0, \text{TRACE\_LENGTH}]$ and that the difference $(\text{global\_timestamp} - \text{read\_timestamp})$ is also within the same range. +To handle the "decode" part of the fetch-decode-execute loop, Jolt uses another instance of (read-only) offline memory-checking, similar to Lasso. The bytecode of the guest program is "decoded" in preprocessing, and the prover subsequently invokes offline memory-checking on the sequence of reads from this decoded bytecode corresponding to the execution trace being proven. This is implemented in [bytecode.rs](../../../jolt-core/src/jolt/vm/bytecode.rs). -- The process of ensuring that both $\text{read\_timestamp}$ and $(\text{global\_timestamp} - \text{read\_timestamp})$ lie within the specified range is known as range-checking. This is the procedure implemented in `timestamp_range_check.rs`. +*For more details: [Bytecode](./bytecode.md)* diff --git a/book/src/how/lookups.md b/book/src/how/lookups.md deleted file mode 100644 index b18661bcb..000000000 --- a/book/src/how/lookups.md +++ /dev/null @@ -1,7 +0,0 @@ -# Lookups -Lasso is a lookup argument (equivalent to a SNARK for reads into a read-only memory). Lookup arguments allow the prover to convince the verifier that a (committed) set of values $Q$ is a subset of a lookup table $T$. Lasso is a special lookup argument with highly desirable asymptotic costs largely correlated to the number of queries $Q$ rather than the length of of the table $T$. - -A conversational background on lookups can be found [here](https://a16zcrypto.com/posts/article/building-on-lasso-and-jolt/). In short: Lookups are great for zkVMs as they allow constant cost / developer complexity for the prover algorithm per VM instruction. - -## Lasso -A detailed engineering overview of Lasso can be found [here](https://www.youtube.com/watch?v=iDcXj9Vx3zY). diff --git a/book/src/how/constraints.md b/book/src/how/r1cs_constraints.md similarity index 100% rename from book/src/how/constraints.md rename to book/src/how/r1cs_constraints.md diff --git a/book/src/how/read_write_memory.md b/book/src/how/read_write_memory.md new file mode 100644 index 000000000..a19b59469 --- /dev/null +++ b/book/src/how/read_write_memory.md @@ -0,0 +1,11 @@ +## Read Write Memory (VM RAM) + +In contrast to our standard procedures for offline memory checking, the registers and RAM within this context are considered *writable* memory. This distinction introduces additional verification requirements: + +- The multiset equality typically expressed as $I \cdot W = R \cdot F$ is not adequate for ensuring the accuracy of read values. It is essential to also verify that each read operation retrieves a value that was written in a previous step. + +- To formalize this, we assert that the timestamp of each read operation, denoted as $\text{read\_timestamp}$, must not exceed the global timestamp at that particular step. The global timestamp is a monotonically increasing sequence starting from 0 and ending at $\text{TRACE\_LENGTH}$. + +- The verification of $\text{read\_timestamp} \leq \text{global\_timestamp}$ is equivalent to confirming that $\text{read\_timestamp}$ falls within the range $[0, \text{TRACE\_LENGTH}]$ and that the difference $(\text{global\_timestamp} - \text{read\_timestamp})$ is also within the same range. + +- The process of ensuring that both $\text{read\_timestamp}$ and $(\text{global\_timestamp} - \text{read\_timestamp})$ lie within the specified range is known as range-checking. This is the procedure implemented in `timestamp_range_check.rs`. diff --git a/book/src/how_it_works.md b/book/src/how_it_works.md index 4fd231cff..40eeebf3c 100644 --- a/book/src/how_it_works.md +++ b/book/src/how_it_works.md @@ -1,5 +1,6 @@ # How it works -1. [Lookups](./how/lookups.md) -2. [Memory Checking](./how/memory-checking.md) -3. [GKR](./how/gkr.md) -4. [Jolt](./jolt.md) +- [Jolt](./jolt.md) + - [Instruction lookups](./how/instruction_lookups.md) + - [Read-write memory](./how/read_write_memory.md) + - [R1CS constraints](./how/r1cs_constraints.md) + - [Bytecode](./how/bytecode.md) diff --git a/book/src/imgs/figure2.png b/book/src/imgs/figure2.png new file mode 100644 index 0000000000000000000000000000000000000000..3995950e8aa19c0e65326de92cdad0cb936e9046 GIT binary patch literal 188571 zcmeEuWmuJ4*Dj@isIWjvx=~^g(kUPaNP{#;Np~(O=@d{&QBaf+l$KodqEkRR7u^k# z>rD2y_tyQMZ@+)fpW_7=k54}{#<<5l?lB`&mE~?+yL}A}4ef^fLm726v?~f|Xc#9r zSHYf{emh4rH1sFd($cE(($ci5E{;#F?JUsHSYNuwNhmfwA!tdrVSG8)>Td{8p(4_}_QBv_Fn5Wo)MyjfL=6Zn2+p1uMnBkqABTtI95 z?v%5r1oh_Bk>GoV9PY=r(Bj!!d%Bbq+45{({lr4|T@DF1Q7S0(5`LFK;$!PwQI6wO zLq6wNgSeU>ymXN33(8m%2A~~ zO+hqD@T&PU2k?-2JTW6;zUE{ltb9`%a&8|Ja*KMCZmD+!EcYS%e)(zu%)4 z^prr4`Dkjs^C2M~H2Gr-9r>q9N@#b%HVztkm^B&}*g^-tx4|zO8s@7|G;Hvf5d6x# z$N1~$6@~Yhe{Ex&T%LGeLt0)Q{M9gXv9NG(wQ_U|TlXOcw;HzA)N#{MdL(S-XwPY4 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zIAbIL3oL}BAb4xU11vMCsF+^Jf&cdERLq^0YzJUX_ZpVO0C}nB$kDdE(tEUHX*gJ< z!Hx!{^RQY`U1s`cC*l4j)7s(jX=iS`=1%2zwfntHDl!jD8OKSE*go+;Vd>+nx?w~W z0I85jYp^(>{(CEAyk!9jg>(RsOcbg!#M3!h(9?}}Mcy`?1rBKnMgy_|B2nOn?R0zp zwhSG~zs!}{S?~xlpB5F+-5UOqJ^}kCKiz?h#4^6!d18O$Z}AamGK2tNH_R^= zZzT*tlKQmBec@L1_iKJ;qeo{ue6kbW{r4`~|J9Z|M9*Kz+y&~O{jHgS*WzQtVaB7% zfapm67M+0SJt=`5L&*4k=l|mxKT%*WP-Ng$!NLNY4vE|Z)c<~s-Y4MG z^U{6DarnQZkJX-Hu z>is{i5g~sovYWl(KS}=A;RY;vfM&dU(?-hp_iI?_fKN{npZ Date: Mon, 15 Apr 2024 20:42:25 -0400 Subject: [PATCH 2/8] Edits --- book/src/how/r1cs_constraints.md | 37 ++++++++++++++++---------------- 1 file changed, 18 insertions(+), 19 deletions(-) diff --git a/book/src/how/r1cs_constraints.md b/book/src/how/r1cs_constraints.md index f19986fb5..cf379378a 100644 --- a/book/src/how/r1cs_constraints.md +++ b/book/src/how/r1cs_constraints.md @@ -1,37 +1,36 @@ -# Constraint System +# R1CS constraints -The constraint system is used to enforce certain rules of the RISC-V fetch-decode-execute loop +Jolt usees R1CS constraints to enforce certain rules of the RISC-V fetch-decode-execute loop and to ensure -consistency between the proofs for the different modules of Jolt (memory-checking -and instruction lookups). +consistency between the proofs for the different modules of Jolt ([instruction lookups](./instruction_lookups.md), [read-write memory](./read_write_memory.md), and [bytecode](./bytecode.md)). ## Uniformity Jolt's R1CS is uniform, which means that the constraint matrices for an entire program are just repeated copies of the constraint matrices for a single CPU step. -Each step is conceptually simply and involves around 60 constraints and 80 variables. +Each step is conceptually simple and involves around 60 constraints and 80 variables. ## Input Variables and constraints The inputs required for the constraint system for a single CPU step are: -#### Pertaining to program code -* Input and output program counters (PCs): this is the only state passed between CPU steps. -* Program code read address: the address in the program code read at this step. -* A 5-tuple representation of the instruction: (`opcode_flags_packed`, `rs1`, `rs2`, `rd`, `imm`). +#### Pertaining to bytecode +* Program counters (PCs): this is the only state passed between CPU steps. +* Bytecode read address: the address in the program code read at this step. +* The preprocessed ("5-tuple") representation of the instruction: (`bitflags`, `rs1`, `rs2`, `rd`, `imm`). -#### Pertaining to memory -* The (starting) memory address read by the instruction: if the instruction is not a load/store, this is 0. +#### Pertaining to read-write memory +* The (starting) RAM address read by the instruction: if the instruction is not a load/store, this is 0. * The bytes written to or read from memory. #### Pertaining to instruction lookups * The chunks of the instruction's operands `x` and `y`. -* The chunks of the lookup query. +* The chunks of the lookup query. These are typically some combination of the operand chunks (e.g. the i-th chunk of the lookup query is often the concatenation of `x_i` and `y_i`). * The lookup output. -### Circuit and Instruction subtable flags: -* There are nine circuit flags used to guide the constraints and are dependent only on the opcode of the instruction. These are thus stored as part of the program code in Jolt. +### Circuit and instruction flags: +* There are nine circuit flags used to guide the constraints and are dependent only on the opcode of the instruction. These are thus stored as part of the preprocessed bytecode in Jolt. 1. `operand_x_flag`: 0 if the first operand is the value in `rs1` or the `PC`. 2. `operand_y_flag`: 0 if the second operand is the value in `rs2` or the `imm`. 3. `is_load_instr` @@ -41,11 +40,11 @@ The inputs required for the constraint system for a single CPU step are: 7. `if_update_rd_with_lookup_output`: 1 if the lookup output is to be stored in `rd` at the end of the step. 8. `sign_imm_flag`: used in load/store and branch instructions where the instruction is added as constraints. 9. `is_concat`: indicates whether the instruction performs a concat-type lookup. -* Subtable flags: these are the unary bits used to indicate which lookup subtable is queried by this instruction. There are as many per step as the number of unique subtables in Jolt, which is 19. +* Instruction flags: these are the unary bits used to indicate instruction is executed at a given step. There are as many per step as the number of unique instruction lookup tables in Jolt, which is 19. #### Constraint system -The constraints for a CPU step are detailed in the `get_jolt_matrices()` function in the `r1cs/constraints` module. +The constraints for a CPU step are detailed in the `get_jolt_matrices()` function in [`constraints.rs`](../../../jolt-core/src/r1cs/constraints.rs). ### Reusing commitments @@ -64,9 +63,9 @@ Spartan is adapted to take pre-committed witness variables. The uniformity of the constraint system allows us to heavily optimize both the prover and verifier. The main changes involved in making this happen are: -- Spartan is modified to only take in the constraint matrices a single step, and the total number of steps. Using this, the prover and verifier can efficient calculate the multilinear extensions of the full R1CS matrices. -- The commitment format of the witness values is change to reflect uniformity. All versions of a variable corresponding to each time step is committed together. This affects nearly all variable committed to in Jolt. +- Spartan is modified to only take in the constraint matrices a single step, and the total number of steps. Using this, the prover and verifier can efficiently calculate the multilinear extensions of the full R1CS matrices. +- The commitment format of the witness values is changed to reflect uniformity. All versions of a variable corresponding to each time step is committed together. This affects nearly all variables committed to in Jolt. - The inputs and witnesses are provided to the constraint system as segments. - Additional constraints are used to enforce consistency of the state transferred between CPU steps. -These changes and their impact on the code are visible in the `r1cs/spartan` module. +These changes and their impact on the code are visible in [`spartan.rs`](../../../jolt-core/src/r1cs/spartan.rs). From 90bafd2b901ba7450378494d5a8268fc4a7e20b6 Mon Sep 17 00:00:00 2001 From: Michael Zhu Date: Tue, 16 Apr 2024 15:44:48 -0400 Subject: [PATCH 3/8] Edit instruction lookups section --- book/src/how/instruction_lookups.md | 35 ++++++++++++++++------------- 1 file changed, 19 insertions(+), 16 deletions(-) diff --git a/book/src/how/instruction_lookups.md b/book/src/how/instruction_lookups.md index 120af68df..5ddf4ccd9 100644 --- a/book/src/how/instruction_lookups.md +++ b/book/src/how/instruction_lookups.md @@ -1,30 +1,42 @@ +# Instruction lookups -## Details on using Lasso to handle instruction execution +In Jolt, the "execute" part of the "fetch-decode-execute" loop is handled using a lookup argument (Lasso). +At a high level, the lookup queries are the instruction operands, and the lookup outputs are the instruction outputs. + +## Lasso + +Lasso is a lookup argument (equivalent to a SNARK for reads into a read-only memory). Lookup arguments allow the prover to convince the verifier that a (committed) set of values $Q$ is a subset of a lookup table $T$. Lasso is a special lookup argument with highly desirable asymptotic costs largely correlated to the number of queries $Q$ rather than the length of of the table $T$. + +A conversational background on lookups can be found [here](https://a16zcrypto.com/posts/article/building-on-lasso-and-jolt/). In short: lookups are great for zkVMs as they allow constant cost / developer complexity for the prover algorithm per VM instruction. + +A detailed engineering overview of Lasso (as a standalone lookup argument) can be found [here](https://www.youtube.com/watch?v=iDcXj9Vx3zY). + +## Using Lasso to handle instruction execution Lasso requires that each primitive instruction satisfies a decomposability property. The property needed is that the input(s) to the instruction can be broken into "chunks" (say, with each chunk consisting of 16 bits), such that one can obtain the answer to the original instruction by -evaluating a simple function or functions on each chunk and then "collating" the results together. +evaluating a simple function on each chunk and then "collating" the results together. For example, the bitwise-OR of two 32-bit inputs x and y can be computed by breaking each input up into 8-bit chunks, XORing each 8-bit chunk of x with the associated chunk of y, and concatenating the results together. -In Lasso, we call the task of evaluating a simple function on each chunk "subtable lookups" (the relevant lookup table +In Lasso, we call the task of evaluating a simple function on each chunk a "subtable lookup" (the relevant lookup table being the table storing all $2^{16}$ evaluations of the simple function). And the "collating" of the results of the subtable lookups into the result of the original lookup (instruction execution on the un-chunked inputs) is handled via an invocation of the sum-check protocol. We call this the "primary sumcheck" instance in Lasso. The "primary sumcheck" collation looks as follows for a trace of length $m$ and a VM with $f$ unique instructions. -$\sum_{x \in `\{0,1\}`^{log(m)}} [\widetilde{eq}(r,x) \cdot \sum_{f \in `\{0,1\}`^{log(F)}} {\widetilde{flags_f}(x) \cdot g_f(\text{terms}_f(x))]}$ +$\sum_{x \in \{0,1\}^{\log_2(m)}} \left[\widetilde{\text{eq}}(r,x) \cdot \sum_{f \in \{0,1\}^{\log_2(F)}} \widetilde{\text{flags}_f}(x) \cdot g_f(\text{terms}_f(x))\right]$ -$\widetilde{flags_f}(x) = 1$ if the $f$-th instruction is used during the $x$-th step of the trace when. $x \in `\{0,1\}`^{log(m)}$ +$\widetilde{\text{flags}_f}(x)$ is an indicator function for the $f$-th instruction: $\widetilde{\text{flags}_f}(x) = 1$ if instruction $f$ is used during the $x$-th step of the trace, when $x \in \{0,1\}^{\log_2(m)}$. $g_f(...)$ is the collation function used by the $f$-th instruction. -$terms_f(x) = [E_1(x), ... E_\alpha(x)]$ where $\alpha$ is the number of independent memories used by an instruction. For simple instructions like the EQ instruction, $\alpha = C$, $terms_f(x) = [E_1(x), ... E_C(x)]$. More complicated instructions such LT might have $terms_f(x) = [E_{eq}(x), E_{lt1}(x), E_{lt2}(x)]$. The exact layout is dependent on the number of subtables required by the decomposition of the instruction. The mappings can be found in the `JoltInstruction::subtable` method implementations. +$\text{terms}_f(x) = [E_1(x), ... E_\alpha(x)]$ where $\alpha$ is the number of independent memories used by an instruction. For simple instructions like the EQ instruction, $\alpha = C$, $\text{terms}_f(x) = [E_1(x), ... E_C(x)]$. More complicated instructions such LT might have $\text{terms}_f(x) = [E_{\texttt{EQ}}(x), E_{\texttt{LT1}}(x), E_{\texttt{LT2}}(x)]$. The exact layout is dependent on the number of subtables required by the decomposition of the instruction. The mappings can be found in the `JoltInstruction::subtable` method implementations. ### Mental Model -For a given $r = x \in `\{0,1\}`^{log(m)}$ (think integer index of the instruction within the trace), $\widetilde{\text{eq}} = 0$ for all but one term of the outer sum. Similarly all $\widetilde{\text{flags}_f}(x) = 0$ for all but one term of the inner sum. Leaving just the collation function of a single instruction, evaluating to the collated lookup output of the single instruction. In reality $r$ is a random point $r \in \mathbb{F}^{log(m)}$ selected by the verifier over the course of the protocol. The evaluation point provides a distance amplified encoding of the entire trace of instructions. +For a given $r = x \in \{0,1\}^{log(m)}$ (think integer index of the instruction within the trace), $\widetilde{\text{eq}} = 0$ for all but one term of the outer sum. Similarly all $\widetilde{\text{flags}_f}(x) = 0$ for all but one term of the inner sum. Leaving just the collation function of a single instruction, evaluating to the collated lookup output of the single instruction. In reality $r$ is a random point $r \in \mathbb{F}^{log(m)}$ selected by the verifier over the course of the protocol. The evaluation point provides a distance amplified encoding of the entire trace of instructions. To illustrate more concretely imagine a two-instruction VM for LT and EQ instructions with $C=1$. @@ -39,12 +51,3 @@ $$ - We then use memory checking to determine that each of the memories $E_i$ is well formed - At a given step of the CPU only a single instruction will be used, that means that only that instruction's subtables will be used. For the rest of the memories we insert a no_op with (a, v) = 0. In order to make the GKR trees cheaper to compute and sumcheck we'll add a single additional layer to the GKR tree. During this layer we'll "toggle" each of the GKR leaves to "1" in the case that it is an unused step of the CPU. This will make the binary tree of multiplication gates cheaper. We'll toggle based on a new flags polynomial called $subtable-flags_f$ which is the sum of all of the $instruction-flags_f$ used in the instruction collation above. - The function to compute each of the leaves becomes $leaf[i] = \text{subtable-flags}[i] \cdot \text{fingerprint}[i] + (1 - \text{subtable-flags}[i])$ - - -# Lookups -Lasso is a lookup argument (equivalent to a SNARK for reads into a read-only memory). Lookup arguments allow the prover to convince the verifier that a (committed) set of values $Q$ is a subset of a lookup table $T$. Lasso is a special lookup argument with highly desirable asymptotic costs largely correlated to the number of queries $Q$ rather than the length of of the table $T$. - -A conversational background on lookups can be found [here](https://a16zcrypto.com/posts/article/building-on-lasso-and-jolt/). In short: Lookups are great for zkVMs as they allow constant cost / developer complexity for the prover algorithm per VM instruction. - -## Lasso -A detailed engineering overview of Lasso can be found [here](https://www.youtube.com/watch?v=iDcXj9Vx3zY). From a4e3bf330cf82f388496a6d05a4a93b1cd0f80da Mon Sep 17 00:00:00 2001 From: Michael Zhu Date: Tue, 16 Apr 2024 20:54:45 -0400 Subject: [PATCH 4/8] Flesh out read-write memory section --- book/src/how/read_write_memory.md | 55 +++++++++++++++++++--- book/src/imgs/final_memory_state.png | Bin 0 -> 163511 bytes book/src/imgs/initial_memory_state.png | Bin 0 -> 76951 bytes book/src/imgs/memory_layout.png | Bin 0 -> 198632 bytes book/src/imgs/program_output_sumcheck.png | Bin 0 -> 149375 bytes 5 files changed, 49 insertions(+), 6 deletions(-) create mode 100644 book/src/imgs/final_memory_state.png create mode 100644 book/src/imgs/initial_memory_state.png create mode 100644 book/src/imgs/memory_layout.png create mode 100644 book/src/imgs/program_output_sumcheck.png diff --git a/book/src/how/read_write_memory.md b/book/src/how/read_write_memory.md index a19b59469..707aeff4e 100644 --- a/book/src/how/read_write_memory.md +++ b/book/src/how/read_write_memory.md @@ -1,11 +1,54 @@ -## Read Write Memory (VM RAM) +# Read-write memory (registers and RAM) -In contrast to our standard procedures for offline memory checking, the registers and RAM within this context are considered *writable* memory. This distinction introduces additional verification requirements: +Jolt proves the validity of registers and RAM using offline memory checking. -- The multiset equality typically expressed as $I \cdot W = R \cdot F$ is not adequate for ensuring the accuracy of read values. It is essential to also verify that each read operation retrieves a value that was written in a previous step. +## Memory layout -- To formalize this, we assert that the timestamp of each read operation, denoted as $\text{read\_timestamp}$, must not exceed the global timestamp at that particular step. The global timestamp is a monotonically increasing sequence starting from 0 and ending at $\text{TRACE\_LENGTH}$. +For the purpose of offline memory checking, Jolt treats registers, program inputs/outputs, and RAM as occupying one unified address space. +This remapped address space is laid out as follows: -- The verification of $\text{read\_timestamp} \leq \text{global\_timestamp}$ is equivalent to confirming that $\text{read\_timestamp}$ falls within the range $[0, \text{TRACE\_LENGTH}]$ and that the difference $(\text{global\_timestamp} - \text{read\_timestamp})$ is also within the same range. +![Memory layout](../imgs/memory_layout.png) -- The process of ensuring that both $\text{read\_timestamp}$ and $(\text{global\_timestamp} - \text{read\_timestamp})$ lie within the specified range is known as range-checking. This is the procedure implemented in `timestamp_range_check.rs`. +The zero-padding depicted above is sized so that RAM starts at a power-of-two offset (this is explained [below](#handling-program-io)). +As noted in the diagram, the size of the witness scales with the highest memory addressed over the course of the program's execution. +In addition to the zero-padding between the "Program I/O" and "RAM" sections, the end of the witness is zero-padded to a power of two. + +## Handling program I/O + +### Inputs + +Program inputs and outputs (and the panic bit, which indicates whether the proram panicked) live in the same memory address space as RAM. +Program inputs populate the designated input space upon initialization: +![init memory](../imgs/initial_memory_state.png) + +The verifier can efficiently compute the MLE of this initial memory state on its own (i.e. in time proportional to the IO size, not the total memory size). + +### Ouputs and panic + +On the other hand, the verifier cannot compute the MLE of the final memory state on its own –– though the program I/O is known to the verifier, the final memory state contains values written to registers/RAM over the course of program execution, which are *not* known to the verifier. + +The verifier is, however, able to compute the MLE of the program I/O values (padded on both sides with zeros) –– this is denoted `v_io` below. +If the prover is honest, then the final memory state (`v_final` below) should agree with `v_io` at the indices corresponding to program I/O. + +![final memory](../imgs/final_memory_state.png) + +To enforce this, we invoke the sumcheck protocol to perform a "zero-check" on the difference between `v_final` and `v_io`: + +![final memory](../imgs/program_output_sumcheck.png) + +This also motivates the zero-padding between the "Program I/O" and "RAM" sections of the witness. The zero-padding ensures that both `input_start` and `ram_witness_offset` are powers of two, which makes it easier for the verifier to compute the MLEs of `v_init` and `v_io`. + +## Timestamp range check + +In contrast to our usage of offline memory checking in other modules, registers and RAM are *writable* memory. +This distinction introduces additional requirements. + +The multiset equality check, typically expressed as $I \cdot W = R \cdot F$, is not adequate for ensuring the accuracy of read values. +It is essential to also verify that each read operation retrieves a value that was written in a *previous* step (not a future step). + +To formalize this, we assert that the timestamp of each read operation, denoted as $\text{read\_timestamp}$, must not exceed the global timestamp at that particular step. +The global timestamp starts at 0 and is incremented once per step. + +The verification of $\text{read\_timestamp} \leq \text{global\_timestamp}$ is equivalent to confirming that $\text{read\_timestamp}$ falls within the range $[0, \text{TRACE\_LENGTH})$ and that the difference $(\text{global\_timestamp} - \text{read\_timestamp})$ is also within the same range. + +The process of ensuring that both $\text{read\_timestamp}$ and $(\text{global\_timestamp} - \text{read\_timestamp})$ lie within the specified range is known as range-checking. 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The standard form allows combinations of both using a wiring predicate $\tilde{V}_i$, and two additional MLEs $\tilde{add}_i$ and $\tilde{mult}_i$. +GKR is a SNARK protocol for binary trees of multiplication / addition gates. The standard form allows combinations of both using a wiring predicate $\widetilde{V}_i$, and two additional MLEs $\widetilde{\text{add}}_i$ and $\widetilde{\text{mult}}_i$. -$\widetilde{V}_i(j)$ evaluates to the value of he circuit at the $i$-th layer in the $j$-th gate. For example $\tilde{V}_1(0)$ corresponds to the output gate. +$\widetilde{V}_i(j)$ evaluates to the value of he circuit at the $i$-th layer in the $j$-th gate. For example $\widetilde{V}_1(0)$ corresponds to the output gate. -$\widetilde{add}_i(j)$ evaluates to 1 if the $j$-th gate of the $i$-th layer is an addition gate. +$\widetilde{\text{add}}_i(j)$ evaluates to 1 if the $j$-th gate of the $i$-th layer is an addition gate. -$\widetilde{mult}_i(j)$ evaluates to 1 if the $j$-th gate of the $i$-th layer is a multiplication gate. +$\widetilde{\text{mult}}_i(j)$ evaluates to 1 if the $j$-th gate of the $i$-th layer is a multiplication gate. The sumcheck protocol is applied to the following: $$ -\tilde{V}_i(z) = \sum_{(p,\omega_1,\omega_2) \in \{0,1\}^{s_i+2s_{i+1}}} f_{i,z}(p,\omega_1,\omega_2), +\widetilde{V}_i(z) = \sum_{(p,\omega_1,\omega_2) \in \{0,1\}^{s_i+2s_{i+1}}} f_{i,z}(p,\omega_1,\omega_2), $$ where $$ -f_i(z, p, \omega_1, \omega_2) = \beta_{s_i}(z, p) \cdot \tilde{add}_i(p, \omega_1, \omega_2)(\tilde{V}_{i+1}(\omega_1) + \tilde{V}_{i+1}(\omega_2)) + \tilde{mult}_i(p, \omega_1, \omega_2)\tilde{V}_{i+1}(\omega_1) \cdot \tilde{V}_{i+1}(\omega_2) +f_i(z, p, \omega_1, \omega_2) = \beta_{s_i}(z, p) \cdot \widetilde{\text{add}}_i(p, \omega_1, \omega_2)(\widetilde{V}_{i+1}(\omega_1) + \widetilde{V}_{i+1}(\omega_2)) + \widetilde{\text{mult}}_i(p, \omega_1, \omega_2)\widetilde{V}_{i+1}(\omega_1) \cdot \widetilde{V}_{i+1}(\omega_2) $$ $$ \beta_{s_i}(z, p) = \prod_{j=1}^{s_i} ((1-z_j)(1-p_j) + z_j p_j). @@ -24,12 +24,12 @@ $$ Lasso and Jolt implement the [Thaler13](https://eprint.iacr.org/2013/351.pdf) version of GKR which is optimized for the far simpler case of a binary tree of multiplication gates. This simplifies each sumcheck to: $$ -\tilde{V}_i(z) = \sum_{p \in \{0,1\}^{s_i}} g^{(i)}_z(p), +\widetilde{V}_i(z) = \sum_{p \in \{0,1\}^{s_i}} g^{(i)}_z(p), $$ where $$ -g^{(i)}_z(p) = \beta_{s_i}(z, p) \cdot \tilde{V}_{i+1}(p,0) \cdot \tilde{V}_{i+1}(p,1) +g^{(i)}_z(p) = \beta_{s_i}(z, p) \cdot \widetilde{V}_{i+1}(p,0) \cdot \widetilde{V}_{i+1}(p,1) $$ GKR is utilized in [memory-checking](./memory-checking.html) for the multi-set permutation check. diff --git a/book/src/background/multilinear-extensions.md b/book/src/background/multilinear-extensions.md index 8e76ad138..6e2092ad8 100644 --- a/book/src/background/multilinear-extensions.md +++ b/book/src/background/multilinear-extensions.md @@ -29,4 +29,4 @@ for i in 0..half { ``` ### Multi Variable Binding -Another common algorithm is to take the MLE $\tilde{f}(x_1, ... x_v)$ and compute its evaluation at a single $v$-variate point outside the boolean hypercube $x \in \mathbb{F}^v$. This algorithm can be performed in $O(n log(n))$ time by preforming the single variable binding algorithm $log(n)$ times. \ No newline at end of file +Another common algorithm is to take the MLE $\tilde{f}(x_1, ... x_v)$ and compute its evaluation at a single $v$-variate point outside the boolean hypercube $x \in \mathbb{F}^v$. This algorithm can be performed in $O(n \log(n))$ time by preforming the single variable binding algorithm $\log(n)$ times. \ No newline at end of file diff --git a/book/src/background/sumcheck.md b/book/src/background/sumcheck.md index 342ef9c7d..c765697ca 100644 --- a/book/src/background/sumcheck.md +++ b/book/src/background/sumcheck.md @@ -6,7 +6,7 @@ Suppose we are given a $v$-variate polynomial $g$ defined over a finite field $\ $$ H := \sum_{b_1 \in \{0,1\}} \sum_{b_2 \in \{0,1\}} \cdots \sum_{b_v \in \{0,1\}} g(b_1, \ldots, b_v). $$ In order to execute the protocol, the verifier needs to be able to evaluate $g(r_1, \ldots, r_v)$ for a randomly chosen vector $(r_1, \ldots, r_v) \in \mathbb{F}^v$. Hence, from the verifier's perspective, the sum-check protocol _reduces_ the task -of summing $g$'s evaluations over $2^v$ inputs (namely, all inputs in $\{0, 1}^{v}$) to the task of evaluating $g$ +of summing $g$'s evaluations over $2^v$ inputs (namely, all inputs in $\{0, 1\}^{v}$) to the task of evaluating $g$ at a _single_ input in $(r_1, \ldots, r_v) \in \mathbb{F}^v$. The protocol proceeds in $v$ rounds as follows. In the first round, the prover sends a polynomial $g_1(X_1)$, and claims that From 9b02b37d2e588dda58481e2fb08fb8b8509656b7 Mon Sep 17 00:00:00 2001 From: Michael Zhu Date: Wed, 17 Apr 2024 15:53:49 -0400 Subject: [PATCH 7/8] revert Cargo.toml --- Cargo.toml | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/Cargo.toml b/Cargo.toml index dc682494a..3113bb0b4 100644 --- a/Cargo.toml +++ b/Cargo.toml @@ -80,6 +80,6 @@ inherits = "release" debug = false [patch.crates-io] -ark-ff = { path = "../algebra/ff" } -ark-ec = { path = "../algebra/ec" } -ark-serialize = { path = "../algebra/serialize" } +ark-ff = { git = "https://github.com/a16z/arkworks-algebra", branch = "optimize/field-from-u64" } +ark-ec = { git = "https://github.com/a16z/arkworks-algebra", branch = "optimize/field-from-u64" } +ark-serialize = { git = "https://github.com/a16z/arkworks-algebra", branch = "optimize/field-from-u64" } From f205ccb6076297f47be3bd5a30ccebfbd7d3af61 Mon Sep 17 00:00:00 2001 From: Michael Zhu Date: Wed, 17 Apr 2024 15:59:52 -0400 Subject: [PATCH 8/8] Add fetch-decode-execute diagram --- book/src/how/jolt.md | 2 ++ book/src/imgs/fetch_decode_execute.png | Bin 0 -> 91367 bytes 2 files changed, 2 insertions(+) create mode 100644 book/src/imgs/fetch_decode_execute.png diff --git a/book/src/how/jolt.md b/book/src/how/jolt.md index c5d6200ce..735676c45 100644 --- a/book/src/how/jolt.md +++ b/book/src/how/jolt.md @@ -15,6 +15,8 @@ The Jolt paper depicts these two tasks mapped to three components in the final J The Jolt codebase is similarly organized, but instead separates read-write memory (comprising registers and RAM) from program code (aka bytecode, which is read-only), for a total of four components: +![fetch-decode-execute](../imgs/fetch_decode_execute.png) + ### Read-write memory To handle reads/writes to RAM (and registers) Jolt uses a memory checking argument from Spice, which is closely related to Lasso itself. They are both based on "offline memory checking" techniques, the main difference being that Lasso supports read-only memory while [Spice](https://eprint.iacr.org/2018/907.pdf) supports read-write memory, making it slightly more expensive. 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13:55:05 -0400 Subject: [PATCH 5/8] Bytecode section --- book/src/how/bytecode.md | 46 +++++++++++++++++++++++++++++- book/src/how/read_write_memory.md | 4 +-- book/src/imgs/bitflags.png | Bin 0 -> 42322 bytes book/src/imgs/bytecode_trace.png | Bin 0 -> 108902 bytes 4 files changed, 47 insertions(+), 3 deletions(-) create mode 100644 book/src/imgs/bitflags.png create mode 100644 book/src/imgs/bytecode_trace.png diff --git a/book/src/how/bytecode.md b/book/src/how/bytecode.md index 30404ce4c..02ffb0b41 100644 --- a/book/src/how/bytecode.md +++ b/book/src/how/bytecode.md @@ -1 +1,45 @@ -TODO \ No newline at end of file +# Bytecode + +Jolt proves the validity of registers and RAM using offline memory checking. + +## Decoding an ELF file + +The tracer iterates over the `.text` sections of the program ELF file and decode RISC-V instructions. Each instruction gets mapped to a `BytecodeRow` struct: + +```rust +pub struct BytecodeRow { + /// Memory address as read from the ELF. + address: usize, + /// Packed instruction/circuit flags, used for r1cs + bitflags: u64, + /// Index of the destination register for this instruction (0 if register is unused). + rd: u64, + /// Index of the first source register for this instruction (0 if register is unused). + rs1: u64, + /// Index of the second source register for this instruction (0 if register is unused). + rs2: u64, + /// "Immediate" value for this instruction (0 if unused). + imm: u64, +} +``` + +The registers (`rd`, `rs1`, `rs2`) and `imm` are described in the [RISC-V spec](https://riscv.org/wp-content/uploads/2017/05/riscv-spec-v2.2.pdf). +The `bitflags` field is described in greater detail [below](#bitflags). + +The preprocessed bytecode serves as the (read-only) "memory" over which we perform offline memory checking. + +![bytecode_trace](../imgs/bytecode_trace.png) + +We currently assume the program bytecode is sufficiently short and known by the verifier, so the prover doesn't need to provide a commitment to it –– the verifier can compute the MLE of the bytecode on its own. +This guarantees that the bytecode trace is consistent with the agreed-upon program. + +Instead of $(a, v, t)$ tuples, each step in the bytecode trace is mapped to a tuple $(a, v_\texttt{bitflags}, v_\texttt{rd}, v_\texttt{rs1}, v_\texttt{rs2}, v_\texttt{imm}, t)$. +Otherwise, the offline memory checking proceeds as described in [Offline Memory Checking](../background/memory-checking.md). + + +## Bitflags + +The `bitflags` of a given instruction is the concatenation of its [circuit flags](./r1cs_constraints.md#circuit-and-instruction-flags) and [instruction flags](./instruction_lookups.md). +This concatenation is enforced by R1CS constraints. + +![bitflags](../imgs/bitflags.png) \ No newline at end of file diff --git a/book/src/how/read_write_memory.md b/book/src/how/read_write_memory.md index 707aeff4e..10f6f5abd 100644 --- a/book/src/how/read_write_memory.md +++ b/book/src/how/read_write_memory.md @@ -1,6 +1,7 @@ # Read-write memory (registers and RAM) Jolt proves the validity of registers and RAM using offline memory checking. +In contrast to our usage of offline memory checking in other modules, registers and RAM are *writable* memory. ## Memory layout @@ -40,8 +41,7 @@ This also motivates the zero-padding between the "Program I/O" and "RAM" section ## Timestamp range check -In contrast to our usage of offline memory checking in other modules, registers and RAM are *writable* memory. -This distinction introduces additional requirements. +Registers and RAM are *writable* memory, which introduces additional requirements compared to offline memory checking in a read-only context. The multiset equality check, typically expressed as $I \cdot W = R \cdot F$, is not adequate for ensuring the accuracy of read values. 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