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Norma

HackerNoon editorial team has launched to celebrate their achievements and share their struggles. We need more women in technology, and by sharing stories, we can encourage many girls to follow their dreams. ! this interview series with women in tech Share your story today Tell us about yourself! Thank you for having me! As a leading Product Manager at InDrive, a global ride-hailing service, I’m passionate about making transportation more accessible and efficient. With experience in the tech industry, surpassing more than five years, I’ve spearheaded product launches across 17 countries, impacting the lives of millions of users. Recently, I was honored to serve as a jury member for a 2023 Globee Women in Business Awards and the AI for Humanity Hackathon organized by Burning Heroes. As of 2024, I lead a talented team developing international ride-hailing services at InDrive, collaborating with colleagues from over 15 countries to ensure a seamless experience for riders and drivers worldwide. In particular, I specialize in optimizing driver-sender matches, creating solutions for users to make better deals within our platform, and using the latest cutting-edge technology, such as machine learning and economic principles. Such an approach enhances customer experience and platform efficiency – a win-win for everyone. Why did you choose this field in the first place? I’ve always been fascinated by technology’s potential to solve real-world problems and, most importantly, improve people’s lives. Plus, the fast-paced nature of tech keeps things exciting for me, with new challenges and opportunities to learn emerging technologies. In other words, the field offers a constant learning curve. Besides that, I'm particularly drawn to the collaborative culture where knowledge is shared openly within the tech community. This allows me to create solutions practically for every industry — medicine, AI, real estate — that can impact millions of people worldwide, which truly motivates me. What tech are you most excited/passionate about right now and why? While large language models (LLM) are the most anticipated development, several other technological advancements capture my interest. Here are a few areas I find particularly promising: New technologies, such as advanced biosensors and generic testing, tremendous possibilities for detecting severe diseases like cancer and autoimmune disorders at earlier stages. Additionally, the growing role of big data and its practical interpretation from medical scans (MRI and CT) can lead to better diagnoses, personalized treatment plans, and improved preventative care. In fact, several innovative startups are working in this direction, and I'm eager to see their progress. Healthcare advancements: offer Fully automating back-office processes through AI would benefit tech companies, manufacturers, and other industries. While it may seem ordinary, solving this narrow problem could have a massive impact on industry and enterprises’ efficiency and productivity. AI-powered enterprise automation: Platforms allowing users to create websites without coding are changing how people access technology creation. Recently, an AI tool code and communicated as a software engineer! Just imagine building mobile apps, data dashboards, or even simple workflow tools—all without writing a single line of code. These no-code tools and numerous pilot engineering tools are slowly transforming the landscape, empowering people, and reducing production costs in the digital world. Development through no-code tools: wrote Beyond my interest in the field, the increasing complexity of transportation technologies gives me goosebumps—from self-driving cars and trucks to AI optimization and next-generation predictive analytics. Future of transportation: What tech are you most worried about right now and why? One primary concern about generative AI is the potential misuse of personal data to train these models. Although data privacy regulations are strengthening globally, there’s a lingering suspicion that corporations can still misuse personal data to gain an unfair advantage in the market. This raises a crucial question: Are these regulations compelling, and can the non-tech person understand them? What are your hobbies and interests outside of tech? I enjoy various activities that challenge me mentally and physically in my spare time. Take, for instance, tennis. It is a great way to hone my focus and develop a winning mindset. Its practice also taught me the importance of teamwork and effective conflict resolution. At the same time, psychology is another area I’m passionate about. Currently, I’m delving into Jungian Analysis, which helps me communicate with platform users unbiasedly and glean deeper insights from our conversations. This knowledge and my understanding of cultural differences foster greater empathy — a crucial skill when working on a product used in over twenty countries. I find it helpful to take conversation pauses, ask thoughtful questions, and practice active listening to bridge cultural gaps. Let's talk about breaking the glass ceiling. What were the biggest challenges you faced as a woman in tech, and how did you deal with them? Undoubtedly, the glass ceiling in tech remains a persistent issue, and statistics paint a clear picture – men significantly outnumber women. For instance, women for 25.3% of Google’s new tech hiring in 2023, compared to 20.8% in 2018. At the same time, Microsoft’s workforce to 33.1% in 2023, up from 29.2% in 2018. Other companies, such as Facebook and Apple, showed similar trends. The numbers reveal a stark reality: only one in three women work in the , compared to management, consulting, legal, or finance. accounted rose tech sector Several factors contribute to this disparity. For example, societal expectations can differ for men and women, with women often taking on greater childcare and household responsibilities. Additionally, tech can feel like a male-dominated environment, lacking role models for female leadership and fostering unconscious bias against women leading times in a traditionally masculine style. To navigate these challenges, I choose teams with inclusive cultures and actively support other women in tech. Practically speaking, I am an active participant in communities like Women in Tech that offer invaluable support networks where we can share experiences, empower each other, and curb any misogyny. Though a topic of debate, positive discrimination holds potential in the current landscape. When equally qualified candidates exist, a diverse slate can highlight potential unconscious bias within homogenous environments. The most significant challenge is ascending the corporate ladder within a male-dominated hierarchy. While some advise leveraging charisma to stand out, a more sustainable approach lies in achieving goals through shared objectives and mutual respect. Focusing solely on gender differences can reinforce bias. In contrast, a business-oriented approach fosters collaboration and paves the way for advancement. Any questionable misogynistic story/situation you faced/handled and you want to share with the HackerNoon Fam? While I may not have personally faced misogyny, it's essential to acknowledge that these situations still exist. We've all likely witnessed or heard about them. That's why standing with those who challenge inequality and fight for a more inclusive space is crucial. What's your biggest achievement that you're really proud of? One of my most significant achievements was leading the launch of intercity delivery product, which is now the leader of the mobility market in its country. It resulted in 47.4 million monthly active users by 2023. I managed five teams with numerous stakeholders and oversaw all aspects of the project, from product research to market assessment to financial planning. The product went live in over 100 cities nationwide within several months. In your opinion, why do we see this huge gender gap in the tech industry, and how can we reduce it? As mentioned earlier, the significant gender gap in tech stems from societal expectations and the industry's current culture. To bridge this gap, we need a two-pronged approach. First, we need to cultivate a more inclusive culture within tech. Initiatives like mentorship programs and fostering diverse hiring practices can help. Second, we need to address societal expectations. Normalizing women in tech and providing them with the support they need to balance work and life can create a more equitable future for the industry. Who is your tech idol? Why? Tech is full of inspiring figures, and a few people who stand out for me are Julie Zhuo, Lenny Rachitski, and Paul Graham. Julie's journey from intern to VP of design at Facebook, especially as a minority woman, is a powerful testament to her talent and perseverance. Her recent article on navigating company politics completely changed my perspective on workplace conflicts and empowered me to be more constructive. Sharing valuable insights while in leadership demonstrates her commitment to giving back and helping countless professionals. Lenny Rachitski's insightful product management blog and interviews with industry leaders offer a goldmine of knowledge for anyone in the field. His ability to spark discussions relevant to global communities makes his work exceptionally valuable. I deeply appreciate his contributions - these insights from experienced professionals are invaluable in the market. Finally, Paul Graham's writing on is a constant source of motivation. I often revisit it for inspiration. great work Do you have any advice for aspiring girls who want to join the field? Make sure your passion for this field is the driving force behind your decision. It can be challenging without support, so I recommend building a strong community around you. Look for mentors, participate in online forums, or attend industry events to connect with others. Get real-world experience through volunteering or internships related to your field. The stronger your network and the more you learn, the more opportunities will come. However, it's essential to find something you enjoy. Remember, your career path is yours to define. Don't be afraid to explore and change course if needed. And, finally, believe in yourself – no one can tell you what's impossible.

Normalizing Women In Tech: Interview With Ksenia Mayorova, Leading Product Manager At InDrive

It seems that everything we have been doing for the last four years is talking about the elusive ‘new normal.’ First, it was the COVID-19 pandemic, then, it was our global shift to the remote mode, after that it was living in a world filled with economic and political uncertainty. And here we are, talking about it once again. What is the ‘new normal’ for 2024, and will we be able to overcome everything the year will throw at us? AI gains even more importance. In 2023, AI occupied the headlines in almost every media. And we thought the craze would die down in a few short months. As time goes on, we see AI becoming not only THE technology to watch but also feeling cozier and cozier in our minds and our work processes. Today, it is used to , , and even (the last one is appalling). Nevertheless, AI is seeping into our everyday lives more, and even the laggards (it’s a word now) of laggards can no longer ignore its impact on the world. decipher ancient scrolls enhance student creativity cheat people out of their money I think 2024 will become the year of not only further AI development but also AI regulation. The process in the US and EU, so more countries are likely to follow suit. has already started Low well-being rates According to the recent report by , “The percentage of Americans who evaluate their lives well enough to be considered "thriving" on Gallup’s Life Evaluation Index averaged a subdued 52.1% in 2023, higher than only the Great Recession era reading in 2008-2009 (50.2%) and the first year of the COVID-19 pandemic in 2020 (50.1%). [...] Between 2015 and 2019, and in 2021, more than 55% were thriving.” Gallup Economic, political, and ecological downturns have, sadly, become a part of our everyday lives. In fact, sometimes it seems our world is on fire, and there is nothing we can do about it. No wonder our mental health and well-being rates are so low. As bad as it may seem, there are things I find to be the most helpful when I am feeling down: Communication — even a simple work call can be therapeutic because it can help us switch our attention to something other than our personal state. Books — ever since childhood, I have considered books one of the best ways, if not to escape, than to enhance our reality. Reading is one of my favorite hobbies, and it helps me relax and almost forget about everything going on around me. Sports — whatever it may be, running, squash, yoga, or sports- has been a part of my personal and even work life. Scientific also supports this approach. It has been proven that sport improves mental health, decreases the rates of ‘psychological ill-being’, and improves interpersonal communication. Win-win. data Doing something for myself — whether it is traveling, studying, going to the gym, or watching a movie when I have the time, I have found dedicating at least 30 minutes a day to my personal needs fills me up with energy and brings me the inspiration I need to face any challenge that the world might throw at us. 2024 started off with low well-being rates, and we should do everything we can to bring the numbers up and meet 2025 on a high note. Teams will no longer tolerate toxic leaders “We know our worth” — this is the attitude professionals have been coming to for several years. In 2024, leaders who have been displaying a tendency to be may be in for an unpleasant surprise. Even despite all the , teams no longer want to put up with toxicity, micromanagement, arrogance, irritability, and bullying from their managers and leaders. Our world is filled with possibilities and, for that matter, vacancies for professionals in different fields and with different skill sets. toxic tech layoffs 2024 is the year for managers to stop perceiving their toxicity as something they should hold on to. It is also nothing to be proud of, so business leaders need to either adjust their attitude or watch their teams slip through their fingers. Burn- and rust-out rates are off the charts Toxic managers, the lack of stability, constant technological disruptions, and low mental health rates have led us to extremely high rates of and out. If 2024 numbers remain as high as they were in 2023 or, even worse, will keep on increasing, we will end up with the entire global workforce unable to perform, grow, develop their skills, and bring new and modern solutions to the table. burning rusting Leaders have to address the trend this year and make necessary adjustments to make sure their teams have all the conditions they need to perform well and keep their mental health in check. 2024 has brought new challenges for us to address. But if my years of working in the tech industry taught me anything, it is that we usually come to the right decision, overcome the challenges posed ahead of us, and come out even more capable. That is one of my goals for this year.

What is the 'New Normal' for 2024

Authors: (1) Chenhao Shi, Shanghai Jiao Tong University; (2) Ruibang Liu, Shanghai Jiao Tong University; (3) Guoqiang Li†, Shanghai Jiao Tong University. Table of Links Abstract & Introduction Preliminaries Normalization Algorithm Evaluation Conclusion & References IV. EVALUATION In this section, we introduced the self-designed benchmark used in this paper. We evaluated the effectiveness of the paradigm generation algorithm by analyzing the test results and the intermediate outputs. A. Benchmark Design To evaluate the proposed algorithm in this paper, we implemented the entire process of paradigm generation explained in the former section using Python to verify its results. Due to the lack of related research, this field has no comprehensive benchmark. Therefore, we summarized some rules for generating equivalent R1CS constraint groups based on the logic the mainstream Circom compiler used to create R1CS and designed a more comprehensive benchmark based on these rules. The benchmark includes the following main categories depending on the reflected situation: Replacement of variable order in R1CS. Transformation of constraint order in R1CS. Introduction of multiple new variables in a single linear constraint in R1CS. Introduction of new variables in multiple linear constraints in R1CS, with shared new variables. Merging and splitting of constraints in R1CS. The different categories in the benchmark correspond to the other reasons for generating equivalent R1CS. Each category contains 2-3 basic R1CS constraints. To comprehensively test the robustness and correctness of the algorithm, 5-6 equivalent R1CS constraint groups are generated for each R1CS based on the respective reasons. The equivalent constraint groups of each constraint group are paired and inputted into the algorithm to verify whether the algorithm can generate consistent and R1CS-compliant output results defined in definition II.5, when processing different equivalent constraint groups. The publicly available data set used in this study can be found at the following GitHub repository: https://github. com/Ash1sc/R1CS normalization benchmark. This repository contains the raw data that was utilized for testing purposes. It is important to note that the data set is licensed under the GNU General Public License version 3.0 (GPL-3.0). This license allows for the data set and scripts to be freely distributed, modified, and used, with the condition that any derived works are also licensed under the GPL-3.0 and that the original copyright and license information is retained. If you would like to learn more about the details of the GPL-3.0, please visit https://www.gnu.org/licenses/gpl-3.0.en.html. B. Result Evaluation Table I shows the result of the experiments. Observation shows that the generated paradigms meet the requirements of the R1CS paradigm mentioned above and have equal semantics as the original R1CS constraint groups. Through analysis of the intermediate outputs at each stage of the conversion process, it was found that for equivalent R1CS constraint groups generated by reordering constraints, the only difference in the resulting data flow graphs lies in the order in which nodes representing intermediate variables are created. This is due to different processing orders of each constraint during traversal, leading to other orders of introducing intermediate variables in each constraint. For equivalent R1CS constraint groups generated by variable replacement, the differences lie in the order in which RNodes representing initial variables in the R1CS are developed and in the order of addition in the summation chain structure caused by differences in variable order in linear constraints. However, these changes do not affect the selected tile set, and the same data flow graph is obtained after abstraction. In the final step of the algorithm, we proposed a novel variable ordering method to solve the sorting confusion issue when multiple variables are introduced to a linear constraint. Experimental results demonstrate that our algorithm is capable of correctly identifying these variables and produces a variable mapping sequence that conforms to the definition. After the abstraction of the data flow graph, the splitting and merging of linear constraints can lead to changes in the order of addition in the summation chain. However, this issue is resolved. When equivalent R1CS constraint groups are created through the merging and splitting of constraints, the only discrepancy in the resulting data flow graphs is with regards to the vertices representing intermediate variables. These vertices can either represent existing variables or intermediate variables introduced during the data flow graph’s creation. Nevertheless, the structure of the data flow graph remains unaffected. This paper is under CC BY 4.0 DEED license. available on arxiv

Insights from R1CS Normalization Benchmark Analysis

Authors: (1) Chenhao Shi, Shanghai Jiao Tong University; (2) Ruibang Liu, Shanghai Jiao Tong University; (3) Guoqiang Li†, Shanghai Jiao Tong University. Table of Links Abstract & Introduction Preliminaries Normalization Algorithm Evaluation Conclusion & References V. CONCLUSION In this paper, we propose an algorithm based on data flow analysis to construct a paradigm for R1CS. The correctness and equivalence of R1CS have long been challenging to study due to the diversity and flexibility of constraint construction methods. Our algorithm aims to eliminate the differences between equivalent R1CS constraint systems through a series of abstraction processes. We introduce ordering methods for internal variables and constraints in R1CS, which provide reference information for the final paradigm generation. Through experimental results, we demonstrate that our algorithm can identify equivalent R1CS resulting from constraint merging, intermediate variable selection, and variable and constraint reordering, and transform them into a unique paradigm. Therefore, R1CS plays an indispensable part in zk-SNARKS. Further work includes establishing rules for merging constraints and a more comprehensive benchmark. This requires us to conduct more in-depth research and exploration of the generation rules of R1CS to improve the algorithm. REFERENCES [1] S. Goldwasser, S. Micali, and C. Rackoff, “The knowledge complexity of interactive proof-systems,” in Providing Sound Foundations for Cryptography: On the Work of Shafi Goldwasser and Silvio Micali, 2019, pp. 203–225. [2] Zcash company, https://z.cash/, 2014. [3] E. B. Sasson, A. Chiesa, C. Garman, et al., “Zerocash: Decentralized anonymous payments from bitcoin,” in 2014 IEEE symposium on security and privacy, IEEE, 2014, pp. 459–474. [4] G. Drevon, J-r1cs – a json lines format for r1cs, 2019. [5] E. Albert, M. Belles-Mu ´ noz, M. Isabel, C. Rodrı ˜ eguez- ´ Nu´nez, and A. Rubio, “Distilling constraints in zero- ˜ knowledge protocols,” in Computer Aided Verification: 34th International Conference, CAV 2022, Haifa, Israel, August 7–10, 2022, Proceedings, Part I, Springer, 2022, pp. 430–443. [6] E. Ben-Sasson, A. Chiesa, M. Riabzev, N. Spooner, M. Virza, and N. P. Ward, “Aurora: Transparent succinct arguments for r1cs,” in Advances in Cryptology– EUROCRYPT 2019: 38th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Darmstadt, Germany, May 19–23, 2019, Proceedings, Part I 38, Springer, 2019, pp. 103–128. [7] J. Lee, S. Setty, J. Thaler, and R. Wahby, “Lineartime and post-quantum zero-knowledge snarks for r1cs,” Cryptology ePrint Archive, 2021. [8] A. Golovnev, J. Lee, S. Setty, J. Thaler, and R. S. Wahby, “Brakedown: Linear-time and post-quantum snarks for r1cs,” Cryptology ePrint Archive, 2021. [9] Y. Muzi, F. Muyue, B. Gu, et al., Semantic comparison method and device between a kind of source code and binary code, 2019. [10] G. Li, L. Zhongqi, Y. Dongsheng, and Y. Liu, Compiling method from intermediate language (il) program to c language program of instruction list, 2013. [11] Z. Yongsheng, C. Zhiyong, C. Rongtao, and W. Zhili, A kind of assembly language is to the code conversion method of higher level language and device, 2015. [12] E. Ben-Sasson, A. Chiesa, E. Tromer, and M. Virza, “Succinct {non-interactive} zero knowledge for a von neumann architecture,” in 23rd USENIX Security Symposium (USENIX Security 14), 2014, pp. 781–796. [13] V. Buterin, “Quadratic arithmetic programs: From zero to hero,” URl: https://medium. com/@ VitalikButerin/quadratic-arithmetic-programs-fromzero-to-hero-f6d558cea649, 2016. [14] H. Vollmer, Introduction to circuit complexity: a uniform approach. Springer Science & Business Media, 1999. [15] J. Groth, “On the size of pairing-based non-interactive arguments,” in Advances in Cryptology–EUROCRYPT 2016: 35th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Vienna, Austria, May 8-12, 2016, Proceedings, Part II 35, Springer, 2016, pp. 305–326. [16] J. B. Dennis, “First version of a data flow procedure language,” in Programming Symposium: Proceedings, Colloque sur la Programmation Paris, April 9–11, 1974, Springer, 2005, pp. 362–376. [17] P. C. Treleaven, D. R. Brownbridge, and R. P. Hopkins, “Data-driven and demand-driven computer architecture,” ACM Computing Surveys (CSUR), vol. 14, no. 1, pp. 93–143, 1982. [18] W. Xing and A. Ghorbani, “Weighted pagerank algorithm,” in Proceedings. Second Annual Conference on Communication Networks and Services Research, 2004., IEEE, 2004, pp. 305–314. [19] L. Page, S. Brin, R. Motwani, and T. Winograd, “The pagerank citation ranking: Bring order to the web,” Technical report, stanford University, Tech. Rep., 1998. This paper is under CC BY 4.0 DEED license. available on arxiv

Data-Flow-Based Normalization Generation Algorithm of R1CS: Conclusion & References

Authors: (1) Chenhao Shi, Shanghai Jiao Tong University; (2) Ruibang Liu, Shanghai Jiao Tong University; (3) Guoqiang Li†, Shanghai Jiao Tong University. Table of Links Abstract & Introduction Preliminaries Normalization Algorithm Evaluation Conclusion & References III. NORMALIZATION ALGORITHM In this section, we formally introduce various steps of the normalization generation algorithm and several data structures defined within the algorithm. A. Construction of RNode Graph Our study presents a novel data structure, RNode, that represents variable relationships within an R1CS arithmetic circuit. This structure, , facilitates efficient problem-solving by tracking interconnections among variables, which is formally defined as follows, RNode An RNode is a node of two types in the data flow graph constructed in this normalization algorithm. Definition III.1. RNode = ConstNode ∪ V arNode ConstNode = {ConstV alue, Operation, F ather, Child} V arNode = {Operation, F ather, Child} where ∀c is a ConstNode ∩ c.Operation = Null, c.child = ∅ ∀c is a ConstNode ∩ c.Operation ∈ {Add, Mul}, c.f ather = ∅ RNodes can be categorized into two types based on the variables they represent. The first category represents the original variables in the solution vector of the R1CS and the intermediate variables produced during the construction of the arithmetic circuit. The second category represents the constants in the data flow graph. Each RNode includes both an operator and a computed result, which store the calculation method between its two parent nodes and represent the calculated result of the subtree rooted in itself. The generation of the RNode Graph involves 3 main stages: Transform each constraint into an equation of a ∗ b = c, as required by the R1CS constraints. 2) Convert each constraint in the original R1CS constraint into an equation. 3) Organize the resulting equations containing common sub-expressions into a DAG-structured expression tree. The core logic of the RNode Graph generation algorithm is similar to the procedure we previously mentioned for constructing the RNode Graph. The RNode is a data structure used to store information about the variables in an R1CS during the construction of the RNode Graph. Unlike typical nodes in an expression tree, each RNode stores information about both the variable and operator involved in a given operation, allowing each operator’s output to be considered an intermediate variable and making it more closely aligned with the properties of an R1CS constraint set. In practice, the merging and splitting of constraints poses a challenge in determining the equivalence of R1CS constraint sets. However, our RNode graph generation algorithm has observed that this merging or splitting does not lead to substantial differences. When constraints are merged, one variable is subtracted from the original constraint set. For instance, the merging process can be exemplified by the following example. However, the subtracted variable will be added back into the RNode Graph as an intermediate node in the sum-product expression during the construction of the RNode Graph. The reverse is also true. Further abstraction of the RNode Graph is required to eliminate the difference observed in the graphs generated by equivalent R1CS due to the different variable ordering in the constraint set. The main difference is observed in the order of addition in constructing the expression of continuous addition. At this stage, we do not have sufficient information to determine the sequential execution order. During the algorithm execution flow, two variables are randomly selected and added together, resulting in a different structure in the graph. B. Tile Selection Here, we categorize tiles into three types and give the formal definition of tile. Definition III.2. Tile is a tree-like subgraph of the RNode Graph, representing a constraint in R1CS. Quadratic: Tiles with the form x ∗ y = z, where x, y, and z are variables. MulLinear: Tiles whose root is obtained by multiplying its two parents, with at least one of the parents being a constant. 3) AddLinear: Tiles whose root is obtained by adding its two parents. Tile is essentially a set of linear equations generated by applying certain constraints to variables in the R1CS. We can use tiles as building blocks to construct a normalized R1CS that is both correct and scalable. During tile selection, we divide the data flow graph from the previous step into 3 types. While AddLinear and MulLinear tiles are generated by linear constraints and are essentially linear tiles, their logical processing differs significantly. Hence, we discuss them as two separate types. We temporarily put aside the constraint merging step until we obtain more information about the tree in subsequent steps. If there is a need to generate merged formulas later, it can be achieved simply by applying a fixed algorithm to the unmerged formulas. The implementation of the tile selection algorithm is relatively simple. When the RNode graph is generated, we select a node with no successors and use it as the root to partition a subgraph from the RNode Graph as a tile. We then remove this tile from the RNode Graph and repeat this loop until the entire graph is partitioned. Detailed code will posted in github. The difference between data flow graphs generated by equivalent R1CS constraint systems lies in the order of node additions when processing linear tiles. However, the nodes added within a linear constraint, when considered as a set, are equivalent. This implies that the different addition order only affects the traversal order of the nodes. Therefore, if we consider the selected linear tiles as the products of the selected nodes and their respective coefficients, the chosen sets of linear tiles from equivalent R1CS constraint systems are the same. In other words, there is no distinction between the selected sets of tiles for equivalent R1CS constraint systems. Revised paragraph: The difference between data flow graphs generated by equivalent R1CS constraint systems lies in the order of node additions when processing linear tiles. However, the nodes added within a linear constraint, when considered as a set, are equivalent. This implies that the different addition order only affects the traversal order of the nodes. Therefore, the selected sets of linear tiles from equivalent R1CS constraint systems are the same if we consider the selected linear tiles as the products of the selected nodes and their respective coefficients. In other words, there is no distinction between the selected sets of tiles for equivalent R1CS constraint systems. C. Graph Abstraction We further abstract the data flow graph based on the selected tiles to eliminate the differences between various equivalent R1CS constraint systems. Specifically, we abstract linear tiles using a new node. By doing so, we mask the difference in addition order within linear tiles in the RNode Graph and transform the relationship between external nodes and specific nodes within the linear tile into a relationship between external nodes and the tile to which the particular node belongs. In this abstracted data flow graph, the types of edges are as follows: Non-linear tile abstract node to non-linear tile abstract node: The two vertices already existed in the original  RNode graph. This edge type remains consistent with the original RNode graph. 2) Non-linear tile abstract node to linear tile abstract node: This edge type exists only if there are non-abstract nodes in the linear tile represented by the abstract node. 3) Linear tile abstract node to linear tile abstract node: This edge type exists only if the two abstract nodes represent linear tiles that share common non-abstract nodes. D. Tile Weight Calculation In this step, we use the Weighted PageRank algorithm to calculate the scores of each vertex in the data flow graph. The previous steps eliminated the differences in the data flow graphs generated by equivalent R1CS through the abstraction of linear tiles. In the following step, constraints are generated on a tile-by-tile basis, and a criterion for tile order is proposed to sort the generated constraints. In the algorithm proposed in this paper, the Weighted PageRank algorithm is used to calculate the weights of each node in the abstracted data flow graph, which are then used as the basis for calculating the weights of the corresponding constraints for each tile. Compared to the traditional PageRank algorithm, this algorithm assigns weights to every edge in the graph and adjusts the iterative formula for node weights. In the Weighted PageRank algorithm, as mentioned in the former section, the formula for calculating node scores is defined as follows: In this algorithm, the primary purpose of using the Weighted PageRank algorithm is to reduce the symmetry of the abstracted data flow graph. The structure of the graph is significantly simplified in the previous step through the simplification of linear tiles. However, some structures in the graph still contain symmetric nodes. If general algorithms are used to calculate the weights of nodes, these symmetric nodes may be assigned the same weight, which can lead to problems in subsequent constraint generation and sorting. To address this issue, the Weighted PageRank algorithm is employed to calculate weights for different nodes. This helps increase the asymmetry of the graph and minimize the occurrence of nodes with the same score. In this algorithm, the iterative formula for scores in the Weighted PageRank algorithm is further adjusted. The node weights retained in the original data flow graph are set to 1, while for nodes abstracted from linear constraints, their weights are calculated through a series of steps. Finally, the variance of the normalized coefficients is utilized as the weight of the abstract node representing the linear constraint. In this algorithm, the iterative formula for the node score in the Weighted PageRank algorithm is given by: The scores for each node are calculated to determine the ranking of each constraint in the R1CS form. E. Constraint Generation In this step, we generate constraints in descending order of weight, with tiles as the unit, starting with quadratic constraints and followed by linear constraints. In this phase, a portion of the variable ordering was determined through the quadratic tile. In the tripartite matrix group of the R1CS paradigm, the three-row vectors corresponding to quadratic constraints each have only one non-zero coefficient. Still, in matrices A and B, the two-row vectors corresponding to the same constraint are equivalent in the constraint representation, consistent with the commutativity of multiplication. This results in two equivalent expressions for the same quadratic constraint. Figure 9 illustrates an example of equivalent terms for a quadratic constraint. In the abstract data flow graph, all vertices representing variables appearing in quadratic constraints are retained, making it possible to determine the choice of non-zero coefficients in the corresponding row vectors of matrices A and B in the tripartite matrix group of the R1CS paradigm based on the weights of each variable. The variables with higher weights are assigned to matrix A and given smaller indices in the variable mapping. The sorting rules for the ordering of variables that appear in quadratic constraints can be summarized as follows: Sort variables based on the highest weight value among all quadratic constraints in which they appear, such that variables with higher weight values have smaller indices in the variable mapping. 2) For variables that appear in the same constraint and have the same highest weight value sort them based on their scores in the Weighted PageRank algorithm for the nodes in the data flow graph corresponding to the variables. Variables with higher node scores will have smaller indices in the variable mapping and be assigned to the corresponding row vector in matrix A of the tripartite matrix group. F. Adjustment of Linear Constraints At this stage, the partition and ordering of constraints within a constraint group have been established, and the ordering of variables that appeared in quadratic constraints has also been determined. However, it is necessary to adjust the order of newly introduced variables in linear tiles in this step. As the example below demonstrates, introducing multiple new variables within a linear tile can result in disorderly sorting. This is because, in the previous actions, the specific structures of linear tile constraints were abstracted to eliminate differences in the RNode Graph. Therefore, we introduce a new method to order the newly introduced variables in linear tiles. For each new variable introduced in a linear tile, its weight is calculated as The new variables are sorted based on their weights. If the weights are the same, the coefficients of the variable in its linear tile are considered for comparison. The appearance of new variables in other linear tiles, to some extent, reflects their importance in the entire constraint group. Additionally, suppose certain new variables only appear in their constraints. In that case, their weights will be zero, and their ordering will only affect the constraints generated by their linear tile without changing the ordering of other constraints. Therefore, they can be sorted in descending order based on their coefficients alone. This paper is under CC BY 4.0 DEED license. available on arxiv

Streamlining R1CS Normalization: A Guide to the Normalization Algorithm

Authors: (1) Chenhao Shi, Shanghai Jiao Tong University; (2) Ruibang Liu, Shanghai Jiao Tong University; (3) Guoqiang Li†, Shanghai Jiao Tong University. Table of Links Abstract & Introduction Preliminaries Normalization Algorithm Evaluation Conclusion & References Abstract The communities of blockchains and distributed ledgers have been stirred up by the introduction of zeroknowledge proofs (ZKPs). Originally designed to solve privacy issues, ZKPs have now evolved into an effective remedy for scalability concerns and are applied in Zcash (internet money like Bitcoin). To enable ZKPs, Rank-1 Constraint Systems (R1CS) offer a verifier for bi-linear equations. To accurately and efficiently represent R1CS, several language tools like Circom, Noir, and Snarky have been proposed to automate the compilation of advanced programs into R1CS. However, due to the flexible nature of R1CS representation, there can be significant differences in the compiled R1CS forms generated from circuit language programs with the same underlying semantics. To address this issue, this paper uses a data-flow-based R1CS paradigm algorithm, which produces a standardized format for different R1CS instances with identical semantics. By using the normalized R1CS format circuits, the complexity of circuits’ verification can be reduced. In addition, this paper presents an R1CS normalization algorithm benchmark, and our experimental evaluation demonstrates the effectiveness and correctness of our methods. —Zero-knowledge proof; Rank-1 constraint systems; Data flow graph; ZKP programming; Normalization Index Terms I. INTRODUCTION (ZKPs) are increasingly recognized for their importance in modern cryptography [1], as one and more cryptographic communities seek to address some of the blockchain’s most significant challenges: privacy and scalability. It is also the essential technique in Zcash [2], [3]. From both user’s and developer’s perspectives, the heightened emphasis on information privacy and security has led to a greater appreciation for the privacy advantages offered by zero-knowledge proofs. As decentralized finance (DeFi) usage grows, zero-knowledge applications that provide scalability and privacy advantages will have more opportunities to increase industry-wide adoption. However, not all computational problems can be directly addressed using zero-knowledge proofs. Instead, we must transform the issue into the correct form of computation. The rank-1 constraint system (R1CS) describes the execution of statements written in high-level programming languages and is used by many ZKP applications, but there is no standard way of representing them [4]. Circom is a novel domain-specific language for transforming computational problems into R1CS format circuits.[5] In the specific process of a first-order zero-knowledge proof, we first convert the problem into a computational problem in Circom, then into R1CS format circuits. Zero-knowledge proofs Due to the flexible nature of R1CS representation and variation of program organizations and compiler optimization levels, there can be significant differences in the compiled R1CS forms generated from circuit language programs with the same underlying semantics, which leads to difficulties in further ZKP program analysis and verification. This paper proposes a data-flow-based algorithm for generating normalization of R1CS, enabling the conversion of different R1CS constraints into a normal form, facilitating the determination of equivalence and correctness. To achieve this, the algorithm starts by transforming an R1CS into a data flow graph structure resembling an expression tree. It then segments and abstracts the data flow graph, eliminating differences between equivalent R1CS constraints that may arise from the generation process. Finally, sorting rules are proposed to sort the constraints and variables within R1CS, ultimately resulting in a unique normal form for equivalent R1CS. Moreover, we classify and summarize the reasons and characteristics of the different equivalent R1CS generated, based on the constraint generation logic of mainstream compilers and the expressiveness of R1CS. In addition, based on the identified reasons for producing equivalent R1CS, we create a relatively complete benchmark. Our proposed algorithm, which can pass all test cases in the benchmark, demonstrates that equivalent R1CS can be converted into a unique and identical canonical form under various circumstances. This work contributes to R1CS optimization by providing a novel algorithm for generating canonical forms of equivalent R1CS constraints. Our algorithm can eliminate unnecessary redundancy and normalize representation, thus it can improve existing methods and facilitates the analysis of equivalence and correctness. Furthermore, the effectiveness and practicality of the proposed algorithm are demonstrated through our comprehensive benchmark. Eli et al. design, implement, and evaluate a zero-knowledge succinct non-interactive argument (SNARG) R1CS [6]. Historically, research investigating the factors associated with R1CS has focused on satisfiability. In paper[7], where the prover incurs finite field operations to prove the satisfiability of an n-sized R1CS instance [7]. Alexander et al. introduce Brakedown, the first built system that provides linear-time SNARKs for NP [8]. Related Work Considering Circom and R1CS format circuits as two languages before and after compilation, research on the generation of the R1CS paradigm is more akin to research on semantic consistency in the compilation. Currently, the patent applications and research papers propose ideas and solutions for generating compilation paradigms in other languages, mainly exploring data flow [9], syntax tree [10], or semantic mapping [11] aspects. These studies offer crucial insights into the fundamental information semantically identical programs entail in the compilation process. However, due to the inherent constraints embedded within the R1CS form, this paper ultimately elects to use data flow as a starting point for research. The paper is organized as follows: In the next section, a brief preliminary review of zero-knowledge proof and related tools. Section 3 provides the process of the proposed algorithm in this paper. The technical exposition in Section 4 explains in detail the logic of the critical steps and their formal description. Section 5 presents the specific categories of benchmarks and their corresponding experimental results. Lastly, Section 6 concludes the present study. Paper Organization This paper is under CC BY 4.0 DEED license. available on arxiv

Data-Flow-Based Normalization Generation Algorithm of R1CS

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