[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83569-en":3,"doc-seo-83569-105":30,"detail-sidebar-cat-0-en-105":92},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},83569,34359740700684,"Finn","https://ap-avatar.wpscdn.com/avatar/1f400023980c374ae676?_k=1777273430885731487",8,"Research & Report","All-out Attack: Optimal Block Withholding Under Pay-Per-Share Scheme","Analyzes Block Withholding (BWH) attacks in Nakamoto-style blockchains under Pay-Per-Share (PPS) and Full-PPS (FPPS) mining reward mechanisms. While BWH has been studied for block-dependent schemes, this work shows PPS/FPPS are not incentive compatible. The optimal attacker strategy is All-out Attack (AoA): devote all hashpower to the victim pool, submit only partial Proof-of-Work shares, and withhold every valid block. It also finds that Fork After Withholding variants add no further profit.","All-out Attack: Optimal Block Withholding Under  \nPay-Per-Share Scheme  \nMustafa Doger Sennur Ulukus  \nDepartment of Electrical and Computer Engineering  \nUniversity of Maryland, College Park, MD 20742  \n[doger@umd.edu](doger@umd.edu) [ulukus@umd.edu](ulukus@umd.edu)  \narXiv :2607 .0 1209v2 [ cs .CR] 3 Jul 2026  \nAbstract—Classical Block Withholding (BWH) attacks have been extensively studied in block-dependent reward schemes, where pool members are compensated upon a block discovery within the pool. However, most contemporary mining pools operate under share-based schemes, wherein participants are paid immediately upon submission of valid shares. In this paper, we analyze BWH under Pay-Per-Share (PPS) and Full-PPS (FPPS) schemes for Nakamoto-style blockchains and prove that these mechanisms are not incentive compatible – contrary to claims in prior literature. Under PPS/FPPS, the optimal strategy for a BWH attacker is the All-out Attack (AoA): the adversary allocates its entire hashpower toward the victim pool, submitting only partial Proof-of-Work shares (pPoW) while withholding all valid blocks, i.e., full Proof-of-Work (fPoW).  \nPrior to the first difficulty adjustment, the adversary incurs negligible loss from withheld fPoWs. After the adjustment reduces block difficulty, the adversary either generates more pPoWs per unit time or, if pPoW difficulty is held fixed, earns a higher reward per share, in both cases achieving a relative gain of 1α over pre-adjustment rates, where α is the adversarial hashpower fraction. Honest miners benefit at the same rate as the adversary per unit hashpower, while the victim pool operator bears all losses, paying out-of-pocket for pPoW submissions without receiving fPoW compensation in return. Finally, advanced BWH variants such as Fork After Withholding (FAW) yield no additional profit under PPS/FPPS.  \nI. INTRODUCTION  \nNakamoto consensus enables distributed participants in a network to reach agreement in a permissionless and trustless manner. By solving cryptographic puzzles – a process known as mining – participants, referred to as miners, become eligible to append a new block containing the embedded solution, termed Proof-of-Work (PoW), to the chronological chain, collectively called a blockchain. Nakamoto incentivizes mining by rewarding miners for successfully extending the blockchain and broadcasting newly mined blocks to other participants [1] .  \nAs the time required for a miner to discover a new block is inversely proportional to its computational power and exhibits high variance, miners often collaborate by forming mining pools. Pools provide participants with a more stable revenue stream by distributing block rewards among members proportional to their contributions. Historically, pools utilized blockdependent reward mechanisms such as Proportional (PROP) or Pay-Per-Last-N-Share (PPLNS), under which block rewards are distributed among members upon the successful mining of a block. In these schemes, pool participants collectively bear the variance associated with block discovery times. In  \ncontrast, most modern pools adopt share-based reward mechanisms such as Pay-Per-Share (PPS) and Full-PPS (FPPS), under which members receive immediate compensation for each share submitted. Consequently, the risk of mining time variance is entirely borne by the pool operator [2] .  \nEyal and Sirer [3] demonstrated that Nakamoto consensus is vulnerable to incentive-based attacks: a miner can temporarily withhold the blocks it mines according to a selfish mining strategy and subsequently releases them to replace those mined by other participants. Such an attack can increase the fraction of the blocks mined by the attacker and after the blockchain adjusts the difficulty, the attacker begins to accrue profits [4] . Similarly, a member can attack its pool by withholding the valid pool blocks (full PoW, fPoW) it mines, known as Block Withholding (BWH) attack [2] . In 2014, Eligius mining pool announced that i","cbCaiuf5XGeKic5f","https://ap.wps.com/l/cbCaiuf5XGeKic5f","pdf",268536,7,1,6,"English","en",105,"# Abstract\n# Introduction\n## Related Works and Our Contributions","[{\"question\":\"What makes BWH behave differently under PPS/FPPS compared with block-dependent payout schemes?\",\"answer\":\"In PPS/FPPS, miners get paid immediately per submitted valid share, so the pool operator absorbs the mining-time variance. This changes the game structure and breaks the assumptions used for block-dependent analyses, leading to different incentives.\"},{\"question\":\"What is the optimal BWH attacker strategy under PPS/FPPS?\",\"answer\":\"The optimal strategy is All-out Attack (AoA): allocate all hashpower to the victim pool while withholding every valid block (full PoW) and regularly submitting only partial PoW shares (pPoW).\"},{\"question\":\"Do advanced BWH variants like Fork After Withholding (FAW) increase profits under PPS/FPPS?\",\"answer\":\"No. The paper states that FAW yields no additional profit under PPS/FPPS, so the main advantage does not improve beyond AoA in that setting.\"}]",1784188904,15,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":87,"head_meta":89,"extra_data":91,"updated_unix":28},"all-out-attack-optimal-block-withholding-under-pay-per-share-scheme","",{"@graph":36,"@context":86},[37,54,69],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/all-out-attack-optimal-block-withholding-under-pay-per-share-scheme/83569/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":24,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-07-26","2026-07-16",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"What makes BWH behave differently under PPS/FPPS compared with block-dependent payout schemes?","Question",{"text":76,"@type":77},"In PPS/FPPS, miners get paid immediately per submitted valid share, so the pool operator absorbs the mining-time variance. This changes the game structure and breaks the assumptions used for block-dependent analyses, leading to different incentives.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"What is the optimal BWH attacker strategy under PPS/FPPS?",{"text":81,"@type":77},"The optimal strategy is All-out Attack (AoA): allocate all hashpower to the victim pool while withholding every valid block (full PoW) and regularly submitting only partial PoW shares (pPoW).",{"name":83,"@type":74,"acceptedAnswer":84},"Do advanced BWH variants like Fork After Withholding (FAW) increase profits under PPS/FPPS?",{"text":85,"@type":77},"No. The paper states that FAW yields no additional profit under PPS/FPPS, so the main advantage does not improve beyond AoA in that setting.","https://schema.org",{"og:url":52,"og:type":88,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":90,"canonical":52},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":93},[94,98,102,106,111,115,119,122,127,130,134],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":95,"show_sort_weight":96,"slug":97},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":103,"show_sort_weight":104,"slug":105},"Exam",70,"exam",{"id":107,"doc_module":4,"doc_module_name":46,"category_name":108,"show_sort_weight":109,"slug":110},5,"Comic",60,"comic",{"id":22,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},"Technology",50,"technology",{"id":20,"doc_module":4,"doc_module_name":46,"category_name":116,"show_sort_weight":117,"slug":118},"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":107,"slug":137},19,"General","general"]